Chap 01 22 Regular Physics

8 August 2007

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Chapters 01 to 22

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Homework Service Book — Physics -2-

00 Editing Examples00-01 Basic Templates00-02 User-Defined Macros00-03 Figure Files00-04 Basic Control Structures00-05 Advanced Control Structures00-06 Special Purpose Templates00-07 Basic Functions00-08 Special Functions00-09 Basic TEX Techniques00-10 Basic Tables00-11 Special Use Tables00-12 Using Macros in TEX00-13 Basic PSTricks Techniques00-14 Basic Graphs00-15 Using Figure Files in PSTricks00-16 Special Figures00-17 Using Macros in PSTricks00-18 Basic PPCHTeX Techniques00-19 PPCHTeX and PSTricks00-20 Basic Biology Templates00-21 Basic Chem Templates00-22 Basic PPCHTeX Structures00-23 Electron Dot Templates00-24 Complicated Chem Structures00-25 Basic CS Templates00-26 CS Structures00-27 Basic Math Templates00-28 Math Graphs00-29 Basic Physics Templates00-30 Physics Figures00-99 Associated problems in Chapter 0001 Physics and Measurement01-01 The SI System01-02 Standard Unit for Length, Mass, and

Time01-03 Derived Units01-04 The Building Blocks of Matter01-05 Density and Atomic Mass01-06 Dimensional Analysis01-07 Conversion of Units01-08 Order-of-Magnitude Calculations01-09 Significant Digits and Measurements01-10 Elementary Error Analysis01-11 Mathematical and Scientific Notation01-12 Coordinate Systems01-13 Mathematics Overview01-14 Scientific Method01-15 Scaling

01-16 Problem Solving Strategy01-17 Measurement Tools01-99 Associated problems in Chapter 0102 Motion in One Dimension02-01 Displacement02-02 Velocity and Speed02-03 Average Velocity for Motion along a

Straight Line02-04 Instantaneous Velocity and Speed02-05 Acceleration02-06 One-Dimensional Motion with Con-

stant Acceleration02-07 Freely Falling Objects02-08 One-Dimensional Motion: Calculus

Techniques02-09 Relative Velocities02-10 Frame of Reference02-99 Associated problems in Chapter 0203 Vectors03-01 Coordinate Systems and Frames of Ref-

erence03-02 Vector and Scalar Quantities03-03 Some Properties of Vectors03-04 Methods of Solving Triangles03-05 Graphical Addition of Vectors03-06 Components of a Vector03-07 Adding Vector Components03-08 Unit Vectors03-09 Vector Kinematics03-10 The Vector Dot (Scalar) Product03-11 The Vector Cross Product03-99 Associated problems in Chapter 0304 Motion in Two Dimensions04-01 Position and Displacement04-02 Average and Instantaneous Velocity04-03 Average and Instantaneous Accelera-

tion04-04 Two-Dimensional Motion with Con-

stant Acceleration04-05 Graphical Solutions04-06 Projectile Motion04-07 Uniform Circular Motion04-08 Tangential and Radial Acceleration04-09 Relative Velocity04-10 Relative Acceleration04-11 Relative Motion at High Speeds04-99 Associated problems in Chapter 0405 The Laws of Motion05-01 The Concept of Force


05-02 Newton’s First Law and InertialFrames

05-03 Inertial Mass05-04 Newton’s Second Law05-05 Weight05-06 Contact and Normal Forces05-07 Hooke’s Law05-08 Combining Forces05-09 Newton’s Third Law05-10 Free Body Diagrams in Problem Solv-

ing05-11 Static Applications of Newton’s Law05-12 Dynamic Applications of Newton’s

Law05-13 Friction05-14 Other Resistive Forces (Terminal Ve-

locity)05-15 The Fundamental Forces of Nature05-99 Associated problems in Chapter 0506 CircularMotion and Newton’s Laws06-01 Newton’s Second Law Applied to Uni-

form Circular Motion06-02 Banked and Unbanked Curves06-03 Nonuniform Circular Motion06-04 Circular Motion in Accelerated Frames06-05 Circular Motion in the Presence of Re-

sistive Forces06-06 Numerical Modeling (Euler’s Method)

in Particle Dynamics06-99 Associated problems in Chapter 0607 Work and Energy07-01 Forms of Energy07-02 Kinetic Energy07-03 Work07-04 Work: a General Constant Force07-05 Work: the Gravitational Force07-06 Work: a Spring Force07-07 Work: a General Varying Force07-08 Kinetic Energy and the Work-Energy

Theorem07-09 The Nonisolated System – Conserva-

tion of Energy07-10 Kinetic Friction07-11 Power07-12 Work and Energy in Three Dimensions07-13 Energy and the Automobile07-14 Kinetic Energy at High Speeds07-15 Simple and Compound Machines07-99 Associated problems in Chapter 07

08 Potential Energy and Conservationof Energy08-01 Potential Energy08-02 Spring Potential Energy08-03 Conservative and Nonconservative

Forces08-04 Conservative Forces and Potential En-

ergy08-05 Conservation of Mechanical Energy08-06 Changes in Mechanical Energy08-07 Relationship Between Conservative

Forces and Potential Energy08-08 Energy Diagrams and the Equilibrium

of a System08-09 Work Done on a System by an External

Force08-10 Conservation of Energy in General08-11 Mass-Energy Equivalence08-12 Quantization of Energy08-99 Associated problems in Chapter 0809 Linear Momentum and Collisions09-01 Linear Momentum09-02 Impulse and Momentum09-03 Conservation of Linear Momentum09-04 Elastic Collisions09-05 Inelastic Collisions09-06 One-Dimensional Collisions09-07 Two- and Three-Dimensional Colli-

sions09-08 The Center of Mass09-09 Finding the Center of Mass by Integra-

tion09-10 Motion of a System of Particles (Ex-

plosions)09-11 Energy of a System of Particles09-12 Energy and Momentum Conservation

in Collisions09-13 Center of Mass Reference Frame09-14 Rocket Propulsion09-99 Associated problems in Chapter 0910 Rotation of a Rigid Object About aFixed Axis10-01 Angular Position, Velocity and Accel-

eration10-02 Kinematic Equations for Uniformly

Accelerated Rotational Motion10-03 Vector Nature of Angular Quantities10-04 Relationships Between Angular and

Linear Quantities


10-05 Rotational Kinetic Energy10-06 Calculation of Moments of Inertia10-07 Torque10-08 Relationship Between Torque and An-

gular Acceleration10-09 Work, Power, and Energy in Rotational

Motion10-10 Problem Solving in Rotational Dynam-

ics10-99 Associated problems in Chapter 1011 Rolling Motion, Angular Momen-tum, and Torque11-01 Rotational Plus Translational Motion:

Rolling11-02 The Kinetic Energy of Rolling11-03 The Forces of Rolling11-04 The Yo-Yo11-05 The Torque Vector11-06 Angular Momentum of a Particle11-07 General Motion: Angular Momentum,

Torque of a System of Particles11-08 Rotation of a Rigid Body About a

Fixed Axis11-09 Rotational Imbalance11-10 Conservation of Angular Momentum11-11 Precession: Gyroscopes and Tops11-12 Rotating Frames of Reference: Inertial

Forces11-13 Coriolis Effect11-14 Quantization of Angular Momentum11-99 Associated problems in Chapter 1112 Static Equilibrium and Elasticity12-01 The Conditions for Equilibrium of a

Rigid Object12-02 Solving Statics Problems12-03 Stability and Balance: Center of Grav-

ity12-04 Levers and Pulleys12-05 Bridges and Scaffolding12-06 Arches and Domes12-07 Couples12-08 Other Objects in Static Equilibrium12-09 Static Equilibrium in an Accelerated

Frame12-10 Elasticity: Stress and Strain12-11 Fracturing12-99 Associated problems in Chapter 1213 Oscillatory Motion13-01 Simple Harmonic Motion

13-02 Mass Attached to a Spring13-03 Forces in Simple Harmonic Motion13-04 Energy in Simple Harmonic Motion13-05 The Simple Pendulum13-06 The Physical Pendulum and Torsion

Pendulum13-07 Simple Harmonic Motion Related to

Uniform Circular Motion13-08 Damped Oscillations13-09 Forced Oscillations: Resonance13-99 Associated problems in Chapter 1314 The Law of Gravity14-01 Newton’s Law of Gravity14-02 Gravitational Force Due to a System of

Particles14-03 Free Fall Acceleration and the Gravi-

tational Force14-04 Gravitation Inside the Earth14-05 Kepler’s Laws: Planetary and Satellite

Motion14-06 The Gravitational Field14-07 Gravitational Potential Energy14-08 Escape Velocity14-09 Energy: Planetary and Satellite Mo-

tion14-10 Gravitational Force: Extended Object

& Particle14-11 Gravitational Force: Particle & Spher-

ical Mass14-12 Principle of Equivalence14-99 Associated problems in Chapter 1415 Fluid Mechanics15-01 States of Matter15-02 Density and Specific Gravity15-03 Pressure15-04 Fluids at Rest: Variation of Pressure

with Depth15-05 Pressure Measurements (Atmospheric,

Gauge)15-06 Pascal’s Principle (Hydraulics)15-07 Buoyant Forces and Archimedes’ Prin-

ciple15-08 Fluid Dynamics15-09 Streamlines and the Equation of Con-

tinuity15-10 Bernoulli’s Equation15-11 Transport Phenomena15-12 Other Applications of Fluid Dynamics15-13 Energy from the Wind


15-14 Viscosity15-15 Surface Tension and Capillarity15-16 Pumps: the Heart15-99 Associated problems in Chapter 1516 Wave Motion16-01 Wave Characteristics and Propagation16-02 Transverse and Longitudinal Waves16-03 Speed of a Traveling Wave16-04 Energy Conservation16-05 One-Dimensional Traveling Waves16-06 Periodic Waves (Harmonic, Electro-

magnetic)16-07 Superposition and Interference of

Waves16-08 The Speed of Waves on Strings16-09 Reflection and Transmission of Waves16-10 Refraction of Waves16-11 Diffraction of Waves16-12 Sinusoidal Waves16-13 Energy Transmitted by Waves on

Strings16-14 The Linear Wave Equation16-15 Phasors16-99 Associated problems in Chapter 1617 Sound Waves17-01 Characteristics of Sound Waves17-02 Speed of Sound Waves17-03 Periodic Sound Waves17-04 Energy and Intensity of Sound Waves17-05 The Doppler Effect17-06 Quality of Sound (Noise)17-07 The Ear17-08 Sources of Musical Sound17-09 Digital Sound Recording17-10 Motion Picture Sound17-11 Sonar, Ultrasound, and Ultrasound

Imaging17-99 Associated problems in Chapter 1718 Superposition and Standing Waves18-01 Superposition of Sinusoidal Waves18-02 Interference of Sinusoidal Waves18-03 Standing Waves in General18-04 Standing Waves in a String Fixed at

Both Ends18-05 Forced Vibrations and Resonance18-06 Standing Waves in Air Columns18-07 Standing Waves in Rods, Plates, and

Membranes18-08 Complex Waves

18-09 Beats: Interference in Time18-10 Shock Waves and the Sonic Boom18-11 Harmonic Analysis and Synthesis18-12 Wave Packets and Dispersion18-99 Associated problems in Chapter 1819 Temperature19-01 Atomic Theory of Matter19-02 The Zeroth Law of Thermodynamics:

Thermal Equilibrium19-03 Celsius and Fahrenheit Temperature

Scales19-04 The Constant-Volume Gas Thermome-

ter and the Kelvin Scale19-05 Thermal Expansion of Solids and Liq-

uids19-06 Macroscopic Description of an Ideal

Gas19-07 Problem Solving: Ideal Gas Law19-99 Associated problems in Chapter 1920 Heat and the First Law of Thermo-dynamics20-01 Heat and Thermal Energy20-02 Internal Energy20-03 Heat Capacity and Specific Heat20-04 Heat Capacity of Gases20-05 Heat Capacity of Solids20-06 Latent Heat20-07 Phase Diagrams20-08 Calorimetry20-09 Work and Heat in Thermodynamic

Processes20-10 The First Law of Thermodynamics20-11 Work and the PV Diagram for a Gas20-12 Some Applications of the First Law of

Thermodynamics20-13 Heat and Energy Transfer20-14 Global Warming and Greenhouse

Gases20-99 Associated problems in Chapter 2021 The Kinetic Theory of Gases21-01 Molecular Model of an Ideal Gas21-02 Specific Heat of an Ideal Gas21-03 Adiabatic Processes for an Ideal Gas21-04 The Equipartition of Energy21-05 The Boltzmann Distribution Law21-06 Pressure, Temperature, and RMS

Speed21-07 Distribution of Molecular Speeds21-08 Translational Kinetic Energy


21-09 Mean Free Path21-10 Van der Waals’ Equation of State21-11 Vapor Pressure and Humidity21-12 Diffusion21-13 Failure of the Equipartition Theorem21-99 Associated problems in Chapter 2122 Heat Engines, Entropy, & Thermo-dynamics22-01 The Second Law of Thermodynamics22-02 Heat Engines22-03 Reversible and Irreversible Processes22-04 The Carnot Engine22-05 Gasoline and Deisel Engines22-06 Heat Pumps and Refrigerators22-07 Entropy22-08 Entropy Changes in Irreversible Pro-

cesses22-09 Entropy on a Microscopic Scale22-10 Human Metabolism22-11 Energy Availability: Heat Death22-12 Statistical Interpretation of Entropy

and the Second Law22-13 Third Law: Maximum Efficiencies22-99 Associated problems in Chapter 2223 Electric Fields23-01 Static Electricity: Electric Charge23-02 Quantized Charge23-03 Insulators and Conductors23-04 Induced Charge: the Electroscope23-05 Coulomb’s Law23-06 Conserved Charge23-07 The Electric Field23-08 Electric Field Due to a Point Charge23-09 Electric Field Due to an Electric Dipole23-10 Electric Field Due to a Line of Charge23-11 Electric Field Due to a Charged Sheet23-12 Electric Field Due to a Continuous

Charge Distribution23-13 Electric Field Lines23-14 Electric Fields and Conductors23-15 A Point Charge in a Electric Field23-16 A Dipole in a Electric Field23-17 Motion of Charged Particles in a Uni-

form Electric Field23-18 The Oscilloscope23-99 Associated problems in Chapter 2324 Gauss’s Law24-01 Electric Flux24-02 Gauss’s Law

24-03 Application: Charged Insulators24-04 Application: Charged Isolated Con-

ductors24-05 Application: Cylindrical Symmetry24-06 Application: Planar Symmetry24-07 Application: Spherical Symmetry24-08 Conductors in Electrostatic Equilib-

rium24-09 Experimental Proof of Gauss’ Law and

Coulomb’s Law24-99 Associated problems in Chapter 2425 Electric Potential25-01 Electric Potential Energy25-02 Potential Difference and Electric Po-

tential25-03 Equipotential Surfaces25-04 Calculating the Potential from the

Field25-05 Potential & Energy: Point Charges25-06 Potential & Energy: Systems of Point

Charges25-07 Potential & Energy: Electric Dipoles25-08 Potential & Energy: Continuous

Charge Distributions25-09 Potential & Energy: Charged Conduc-

tor25-10 Calculating the Field from the Poten-

tial25-11 Electrostatic Potential Energy: the

Electron Volt25-12 The Millikan Oil Drop Experiment25-13 Cathode Ray Tube: TV, Computer

Monitors, and Oscilloscopes25-14 The Van de Graaff Generator and

Other Applications25-99 Associated problems in Chapter 2526 Capacitance and Dielectrics26-01 Definition of Capacitance26-02 Calculation of Capacitance26-03 Combinations of Capacitors26-04 Energy Stored in a Charged Capacitor26-05 Capacitors with Dielectrics26-06 Dielectrics from a Molecular Level26-07 Dielectrics and Gauss’ Law26-08 Electric Dipole in an External Electric

Field26-09 Electrostatic Applications26-99 Associated problems in Chapter 2627 Current and Resistance


27-01 Electric Current27-02 Current Density and Drift Speed27-03 Resistance and Resistivity27-04 Ohm’s Law27-05 Microscopic View of Ohm’s Law27-06 Resistance and Temperature27-07 Semiconductors27-08 Superconductors27-09 Electrical Energy and Power27-10 Power in Household Circuits27-11 Electrical Hazards: Leakage Currents27-12 Electrical Energy in the Heart27-99 Associated problems in Chapter 2728 Direct Current Circuits28-01 Electromotive Force and Terminal

Voltage28-02 Work, Energy, and EMF28-03 Resistance: Series Circuits28-04 Resistance: Series/Parallel Combina-

tions28-05 Potential Difference Between Two

Points28-06 Complicated Circuits: Kirchoff’s Rules28-07 RC Circuits28-08 Electrical Instruments: Ammeter and

Voltmeter28-09 Household Wiring and Electrical

Safety28-10 Conduction of Electrical Signals by

Neurons28-11 Transducers and the Thermocouple28-99 Associated problems in Chapter 2829 Magnetic Fields29-01 Magnetic Fields and Forces29-02 Magnetism from Electric Currents29-03 Magnetic Force on a Current-Carrying

Conductor29-04 Torque on a Current Loop in a Uniform

Magnetic Field29-05 Motion of a Charged Particle in a Mag-

netic Field29-06 Applications of the Motion of Charged

Particles in a Magnetic Field29-07 Crossed Fields: Discovery of the Elec-

tron29-08 The Hall Effect29-09 Galvanometers, Motors, Loudspeakers29-10 Cyclotrons and Synchrotrons29-11 Mass Spectrometer

29-99 Associated problems in Chapter 2930 Sources of the Magnetic Field30-01 The Biot-Savart Law30-02 Magnetic Field Due to a Straight Wire30-03 Magnetic Force Between Two Parallel

Conductors30-04 Ampere’s Law30-05 The Magnetic Field of Current Loops30-06 The Magnetic Field Along the Axis of

a Solenoid30-07 A Current-Carrying Coil as a Magnetic

Dipole30-08 Magnetic Flux30-09 Gauss’s Law in Magnetism30-10 Displacement Current and the Gener-

alized Ampere’s Law30-11 Magnetism and Electrons: Spin30-12 Magnetism in Matter30-13 Diamagnetism30-14 Paramagnetism30-15 Ferromagnetism30-16 Magnetic Field of the Earth30-99 Associated problems in Chapter 3031 Faraday’s Law31-01 Faraday’s Law of Induction31-02 Motional EMF31-03 Lenz’s Law31-04 Induced EMF in a Moving Conductor31-05 Induced Electric Fields31-06 Electric Field from a Changing Mag-

netic Flux31-07 Generators and Motors31-08 Eddy Currents31-09 Maxwell’s Equations31-10 Sound Systems, Computer Memory,

the Seismograph31-99 Associated problems in Chapter 3132 Inductance32-01 Inductors and Inductance32-02 Self-Inductance, Self-Induced EMF32-03 RL Circuits32-04 Energy in a Magnetic Field32-05 Energy Density of a Magnetic Field32-06 Mutual Inductance32-07 Oscillations in an LC Circuit32-08 The RLC Circuit32-09 Critical Magnetic Fields32-10 Magnetic Properties of Superconduc-

tors


32-99 Associated problems in Chapter 3233 Alternating Current Circuits33-01 AC Sources33-02 Phasors33-03 Resistors in an AC Circuit33-04 Inductors in an AC Circuit33-05 Capacitors in an AC Circuit33-06 LC and RLC Circuits Without a Gen-

erator33-07 The RLC Series Circuit33-08 DampedOscillations in an RLCCircuit33-09 Power in an AC Circuit33-10 Resonance in a Series RLC Circuit33-11 Impedance Matching33-12 Filter Circuits33-13 The Transformer and Power Transmis-

sion33-14 Three-Phase AC33-99 Associated problems in Chapter 3334 Electromagnetic Waves34-01 Maxwell’s Equations and Hertz’s Dis-

coveries34-02 Plane Electromagnetic Waves34-03 Speed of Electromagnetic Waves34-04 Energy Carried by Electromagnetic

Waves: Poynting Vector34-05 Momentum and Radiation Pressure34-06 Radiation from an Infinite Current

Sheet34-07 The Production of Electromagnetic

Waves by an Antenna34-08 Properties of Electromagnetic Waves34-09 The Spectrum of Electromagnetic

Waves34-10 The Doppler Effect for Electromag-

netic Waves34-11 Radio and Television34-99 Associated problems in Chapter 3435 The Nature of Light and GeometricOptics35-01 The Nature of Light35-02 Wave-Particle Duality35-03 The Speed of Light35-04 Reflection35-05 Transmission and Refraction35-06 The Law of Refraction35-07 Dispersion and Prisms35-08 Huygens’ Principle35-09 Total Internal Reflection

35-10 Fermat’s Principle35-11 Mixing Pigments35-12 Luminous Intensity35-99 Associated problems in Chapter 3536 Geometric Optics36-01 Two Types of Image36-02 Images Formed by Flat Mirrors36-03 Images Formed by Concave Mirrors36-04 Images Formed by Convex Mirrors36-05 Spherical Mirrors: Ray Tracing36-06 Images Formed by Refracting Surfaces36-07 Atmospheric Refraction36-08 Images Formed by Thin Lenses36-09 Combinations of Lenses and Mirrors36-10 Thin Lenses: Ray Tracing36-11 Lensmaker’s Equation36-12 The Camera36-13 The Eye and Corrective Lenses36-14 The Simple Magnifier36-15 The Compound Microscope36-16 The Telescope36-17 Lens and Mirror Aberrations36-99 Associated problems in Chapter 3637 Interference of Light Waves37-01 Conditions for Interference37-02 Double Slit Interference: Young’s Ex-

periment37-03 Coherence37-04 Intensity Distribution of the Double-

Slit Interference Pattern37-05 Phasor Addition of Waves37-06 Change of Phase Due to Reflection37-07 Interference in Thin Films37-08 The Michelson Interferometer37-09 Using Interference to Read CDs and

DVDs37-99 Associated problems in Chapter 3738 Diffraction and Polarization38-01 Diffraction38-02 Huygens’ Principle and Diffraction38-03 Huygens’ Principle and the Law of Re-

fraction38-04 Single-Slit Diffraction38-05 Intensity in Single-Slit Diffraction38-06 Using Phasors to Add Harmonic Waves38-07 Fraunhofer and Fresnel Diffraction38-08 Resolution of Single-Slit and Circular

Apertures38-09 Resolution of Telescopes and Micro-


scopes: the λ Limit38-10 Resolution of the Human Eye and Use-

ful Magnification38-11 Diffraction by a Double Slit38-12 The Diffraction Grating38-13 Gratings: Dispersion and Resolving

Power38-14 X-Rays38-15 Diffraction of X-Rays by Crystals38-16 Polarization of Light Waves38-17 Polarization by Reflection38-18 The Spectrometer and Sprctroscopy38-99 Associated problems in Chapter 3839 Relativity39-01 Galilean Coordinate Transformations39-02 Lorenz Coordinate Transformations39-03 Postulates: Speed of Light39-04 The Michelson-Morley Experiment39-05 Consequences of Special Relativity39-06 The Lorentz Transformation for Dis-

placements39-07 The Lorentz Transformation for Time39-08 The Lorentz Transformation for Veloc-

ities39-09 Relativistic Momentum and Relativis-

tic Form of Newton’s Laws39-10 Relativistic Energy39-11 Mass as a Measure of Energy39-12 Photon Momentum39-13 Conservation of Relativistic Momen-

tum, Mass, and Energy39-14 Doppler Shift for Light39-15 Pair Production and Annihilation39-16 Matter and Antimatter39-17 General Relativity and Accelerating

Reference Frames39-99 Associated problems in Chapter 3940 The Quantum Theory of Light40-01 The Photon, the Quantum of Light40-02 Hertz’s Experiments: Light as an Elec-

tromagnetic Wave40-03 Blackbody Radiation and Planck’s Hy-

pothesis40-04 Light Quantization and the Photoelec-

tric Effect40-05 The Compton Effect40-06 Particle-Wave Complementarity, Dual-

ity: Double Slits40-07 Effect of Gravity on Light

40-08 The Wave Function40-09 Electron Microscopes40-99 Associated problems in Chapter 4041 The Particle Nature of Matter41-01 The Atomic Nature of Matter41-02 The Composition of Atoms41-03 Molecules41-04 The Bohr Atom41-05 QuantumModel of the Hydrogen Atom41-06 Franck-Herz Experiment41-99 Associated problems in Chapter 4142 Matter Waves42-01 de Broglie Waves42-02 The Time Independent Schrodinger

Equation42-03 The Davisson-Germer Experiment42-04 Fourier Integrals42-05 The Heisenberg Uncertainty Principle42-06 Wave Groups and Dispersion42-07 Wave-Particle Duality42-08 String Waves and Matter Waves42-99 Associated problems in Chapter 4243 QuantumMechanics in One Dimen-sion43-01 The Hydrogen Atom43-02 The Born Interpretation43-03 The Time-Dependent Schrodinger

Equation43-04 Wavefunction for a Free Particle43-05 Wavefunctions in the Presence of

Forces43-06 Particle in a Box43-07 Energies of a Trapped Electron43-08 Wave Functions of a Trapped Electron43-09 The Finite Square Well43-10 More Electron Traps43-11 Two- and Three-Dimensional Electron

Traps43-12 The Quantum Oscillator43-13 Expectation Values43-14 Observables and Operators43-99 Associated problems in Chapter 4344 Tunneling Phenomena44-01 The Square Barrier44-02 Barrier Penetration: Some Applica-

tions44-03 Decay Rates44-04 The Scanning Tunneling Microscope44-99 Associated problems in Chapter 44


45 Quantum Mechanics in Three Di-mensions45-01 Three-Dimensional Schrodinger Equa-

tion45-02 Particle in a Three-Dimensional Box45-03 Central Forces and Angular Momen-

tum45-04 Space Quantization45-05 Quantization of Angular Momentum

and Energy45-06 Atomic Hydrogen and Hydrogen-like

Ions45-99 Associated problems in Chapter 4546 Atomic Structure46-01 Some Properties of Atoms46-02 Atomic Spectra46-03 Orbital Magnetism and the Normal

Zeeman Effect46-04 Electron Spin46-05 The Spin-Orbit Interaction and Other

Magnetic Effects46-06 Angular Momenta and Magnetic

Dipole Moments46-07 The Stern-Gerlach Experiment46-08 Magnetic Resonance46-09 Electron Clouds46-10 Exchange Symmetry and the Exclusion

Principle46-11 Multiple Electrons in Rectangular

Traps46-12 Electron Interactions and Screening Ef-

fects46-13 The Periodic Table46-14 Isotopes46-15 X-Ray Spectra and Moseley’s Law46-16 Atomic Transitions46-17 Lasers and Holography46-18 How Lasers Work46-99 Associated problems in Chapter 4647 Statistical Physics47-01 The Maxwell-Boltzmann Distribution47-02 Quantum Statistics, Indistinguishabil-

ity, and the Pauli Exclusion Principle47-03 Applications of Bose-Einstein Statis-

tics47-04 An Application of Fermi-Dirac Statis-

tics: The Free-Electron Gas Theory ofMetals

47-99 Associated problems in Chapter 47

48 Molecular Structure48-01 Bonding Mechanisms48-02 Weak (van der Waals) Bonds48-03 Polyatomic Molecules48-04 Diatomic Molecules: Molecular Rota-

tion and Vibration48-05 Molecular Spectra48-06 Electron Sharing and the Covalent

Bond48-07 Bonding in Complex Molecules48-99 Associated problems in Chapter 4849 The Solid State49-01 Bonding in Solids49-02 Electrical Properties of Solids49-03 Energy Levels in a Crystalline Solid49-04 Insulators49-05 Metals49-06 Classical Free-Electron Model49-07 Quantum Theory of Metals49-08 Band Theory of Solids49-09 Semiconductor Devices49-10 Doped Semiconductors49-11 The p-n Junction49-12 The Junction Rectifier49-13 The Light-Emitting Diode (LED)49-14 Transistors and Integrated Circuits49-99 Associated problems in Chapter 4950 Superconductivity50-01 Magnetism in Matter50-02 A Brief History of Superconductivity50-03 Some Properties of Type I Supercon-

ductors50-04 Type II Superconductors50-05 Other Properties of Superconductors50-06 Electronic Specific Heat50-07 BCS Theory50-08 Energy Gap Measurements50-09 Josephson Tunneling50-10 High-Temperature Superconductivity50-11 Applications of Superconductivity50-99 Associated problems in Chapter 5051 Nuclear Structure51-01 Discovering the Nucleus51-02 Some Nuclear Properties51-03 Binding Energy and Nuclear Forces51-04 Nuclear Models51-05 Radioactivity51-06 Decay Processes51-07 Alpha Decay


51-08 Beta Decay51-09 Gamma Decay51-10 Half-Life and Rate of Decay51-11 Decay Series51-12 Radioactive Dating51-13 Measuring Radiation Dosage51-14 Natural Radioactivity51-99 Associated problems in Chapter 5152 Nuclear Physics Applications52-01 Nuclear Reactions52-02 Reaction Cross Section52-03 Interactions Involving Neutrons52-04 Nuclear Fission52-05 A Model for Nuclear Fission52-06 Nuclear Reactors52-07 A Natural Nuclear Reactor52-08 Nuclear Fusion52-09 Thermonuclear Fusion in the Sun and

Other Stars52-10 Controlled Thermonuclear Fusion52-11 Recent Fusion Energy Developments52-12 Interaction of Particles with Matter52-13 Radiation Damage in Matter52-14 Radiation Detectors52-15 Radiation Therapy52-16 Tracers52-17 Tomography Imaging: CAT Scans and

Emission Tomography52-18 NMR and MRI52-99 Associated problems in Chapter 5253 Particle Physics53-01 Elementary Particles53-02 The Fundamental Forces in Nature53-03 Particle Accelerators and Detectors53-04 Particle Exchange53-05 Particles and Antiparticles53-06 Mesons and the Beginning of Particle

Physics53-07 Classification of Particles53-08 Conservation Laws53-09 Particle Stability and Resonances53-10 Antiproton in a Bubble Chamber53-11 Leptons53-12 Hadrons53-13 Strange Particles and Strangeness53-14 Elementary Particle Production; Mea-

surement of Properties53-15 The Eightfold Way53-16 Quarks

53-17 Electroweak Theory and the StandardModel

53-18 Quasars53-19 Grand Unified Theory53-99 Associated problems in Chapter 5354 Astrophysics and Cosmology54-01 Stars and Galaxies54-02 The Birth and Death of Stars54-03 General Relativity: Gravity and the

Curvature of Space54-04 The Expanding Universe54-05 The Cosmic Connection54-06 Cosmic Background Radiation54-07 Dark Matter54-08 The Big Bang54-09 Early History of the Universe54-10 The Future of the Universe54-11 Problems and Perspectives54-99 Associated problems in Chapter 5455 Probability Distributions55-01 Uncertainites55-02 Parent and Sample Distributions55-03 Mean and Standard Deviation of Dis-

tributions55-04 Binomial Distribution55-05 Poisson Distribution55-06 Gaussian or Normal Error Distribution55-07 Lorentzian Distribution55-99 Associated problems in Chapter 5556 Error Analysis (see 01:11)56-01 Instrumental and Statistical Uncer-

tainties56-02 Propagation of Errors56-03 Specific Error Formulas56-04 Application of Error Equations56-99 Associated problems in Chapter 5657 Estimates of Mean and Errors57-01 Method of Least Squares57-02 Statistical Fluctuations57-03 χ2 Test of a Distribution57-99 Associated problems in Chapter 5758 Monte Carlo Techniques58-01 Introduction58-02 Random Numbers58-03 Random Numbers from Probability

Distributions58-04 Specific Distributions58-05 Efficiency58-99 Associated problems in Chapter 58


59 Least-Squares Fit to a Straight Line59-01 Dependent and Independent Variables59-02 Method of Least Squares59-03 Minimizing χ2

59-04 Error Estimation59-05 Some Limitations of the Least-Squares

Method59-06 Alternate Fitting Methods59-99 Associated problems in Chapter 5960 Least-Squares Fit to a Polynomial60-01 Determinate Solution60-02 Matrix Solution60-03 Independent Parameters60-04 Nonlinear Functions60-99 Associated problems in Chapter 6061 Least-Squares Fit to an ArbitraryFunction61-01 Nonlinear Fitting61-02 Searching Parameter Space61-03 Grid-Search Mechod61-04 Gradient-Search Method61-05 Expansion Methods61-06 The Marquardt Method61-07 Comments on the Fits61-99 Associated problems in Chapter 6162 Fitting Composite Curves62-01 Lorentzian Peak on Quadratic Back-

ground62-02 Area Determination62-03 Composite Plots62-99 Associated problems in Chapter 6263 DirectApplication of theMaximum-Likelihood Method63-01 Maximum-Likelihood Method63-02 Computer Example63-99 Associated problems in Chapter 6364 Testing the Fit64-01 χ2 Test of Goodness of Fit64-02 Linear-Correlation Coefficient64-03 F Test64-04 Confidence Intervals64-05 Monte Carlo Tests64-99 Associated problems in Chapter 64

Chapter 1, section 2, Standard Unit for Length, Mass, and Time 13

Kopp lect1 prob101:02, highSchool, multiple choice, < 1 min,fixed.

The standard of time is based on

1. the daily rotation of the earth.

2. the frequency of light emitted by 86Kr.

3. the yearly revolution of the earth aboutthe sun.

4. a precision pendulum clock.

5. None of these

Chapter 1, section 4, The Building Blocks of Matter 14

Concept 41 901:04, highSchool, multiple choice, < 1 min,fixed.

What is not an element?

1. hydrogen

2. carbon

3. oxygen

4. water

5. None of these

Conceptual 09 Q101:04, highSchool, multiple choice, < 1 min,fixed.

Part 1 of 2How many atoms are in a water molecule?

1. 1

2. 2

3. 3

4. 4

5. 5

Part 2 of 2How many elements are in a water molecule?

1. 1

2. 2

3. 3

4. 4

5. 5

Molecular Model01:04, highSchool, multiple choice, < 1 min,

fixed.

Part 1 of 3Are all molecules of a particular substance

alike?

1. Yes

2. No

Part 2 of 3Can molecules be broken into parts?

1. Yes

2. No

Part 3 of 3How big are molecules?

1. around 10−10 meters in scale



4. around 102 meters in scale

Chapter 1, section 5, Density and Atomic Mass 15

Conceptual 10 0201:05, highSchool, multiple choice, > 1 min,normal.

Part 1 of 2A perfectly spherical piece of metal is found

at the bottom of a wishing well. The mass ofthe object is 0.45 kg and the radius is 0.12 m.

What is its density?

Part 2 of 2What would be its weight if it had the samevolume and were make of pure gold? Thedensity of pure gold is 19300 kg/m3.

Conceptual 10 0301:05, highSchool, multiple choice, > 1 min,wording-variable.

Part 1 of 2Martin finds a piece of metal in a scrap yard

and weighs it. Its mass is found to be 4763 kgand its volume is 0.6 m3 as determined byimmersion in water.

The densities of common metals are

Metal Fe Al Hg Pb Au

g/cm3 7.9 2.7 13.6 11.3 19.3

What is the likely identity of this metal?

1. iron

2. aluminum

3. mercury

4. lead

5. gold

6. None of these

Part 2 of 2The density of copper is 8900 kg/m3.

What would be the volume of the scrapmetal if it had the same weight and weremade of copper?

Conceptual 10 0501:05, highSchool, numeric, < 1 min, normal.

What is the mass of water required to filla circular hot tub 3 m in diameter and 1.5 mdeep?


Martin says that knowing only the densityof a material is enough to identify uniquely amaterial of unknown origin.

Do you agree with him? Why?

1. Yes; different materials always have dif-ferent densities.

2. No; two materials can have the samedensity.

3. No; a particular material can have differ-ent densities.


Part 1 of 2In everyday use, the word “dense” is often

used interchangeably with the word “hard.”In physics, density and hardness have com-pletely different meanings.

Which object is the densest?

1. lead

2. diamond

3. iron

4. aluminum

Part 2 of 2Which object is the hardest?

1. lead


2. diamond

3. iron

4. aluminum


Consider a cube of soft, spongy material.

Which piece below has the larger density?

1. cutting out a piece of the cube that hasone-eighth the volume

2. compressing the cube until it has one-eighth the volume

3. Densities are the same.

4. Unable to determine


Consider two identical metal bottles A andB that can be used to hold compressed gases.A is filled with air at atmospheric pressure,and B is completely evacuated.

Which bottle is denser?

1. A

2. B

3. Densities are the same.



Diamond is a hard transparent materialmade of only carbon atoms. Graphite is ablack, soft material used to make pencil leadand is also made of only carbon atoms.

Do graphite and diamond have the samedensity? Why?

1. Yes; they are made of the same kind ofatom.

2. No; the atoms in diamond and graphiteare different.

3.No; the atoms are arranged differently.


In one scene in the movie The Godfather II,a solid gold phones is passed around a largetable for everyone to see. Suppose the volumeof gold in the phone was equal to the volumeof 10-centimeter cube of gold. The density ofgold is 19,300 kg/m3.

Could such a phone be casually passedaround a table from hand to hand? Whatis the weight of the phone?

1. Yes; it weighs about 4.5 lbs.

2. No; it weighs about 45 lbs.

3. Yes; it weighs about 9 lbs.

4. No; it weighs about 90 lbs.

Hewitt CP9 12 E0601:05, highSchool, multiple choice, < 1 min,fixed.


The uranium atom is the heaviest amongthe naturally occurring elements.

Why then, isn’t a solid bar of uranium thedensest metal?

1. A solid uranium bar contains a lot ofoxygen.

2. The uranium atoms lose most of theirneutrons when forming a solid bar.

3. Density is determined by the spacing be-tween the atoms as well as mass.

4. There are a lot of dangling bonds inside asolid bar of uranium.


Which has more volume – a kilogram ofgold or a kilogram of aluminum?

1. a kilogram of gold

2. a kilogram of aluminum

3. They have same volumes.

4. It cannot be determined.


What is correct?

1. The density of water is highest at 0 ◦C.

2. The density of water is highest at 1◦C.





Ratio of Planets01:05, highSchool, multiple choice, < 1 min,fixed.

Part 1 of 2Consider two planets, denoted 1 and 2,

which have uniform mass distributions. Themass density and the radius of planet 1 are ρ1

and R1, respectively, and those of planet 2 areρ2 and R2

Which of the following gives the ratio of

their massesM1

M2?

1.M1

M2=

(

ρ1

ρ2

)(

R1

R2

)3

2.M1

M2=

(

ρ1

ρ2

)(

R1

R2

)

3.M1

M2=

(

ρ1

ρ2

)(

R1

R2

)2

4.M1

M2=

(

ρ1

ρ2

)(

R2

R1

)3

5.M1

M2=

(

ρ1

ρ2

)(

R2

R1

)2

6.M1

M2=

(

ρ2

ρ1

)(

R1

R2

)3

7.M1

M2=

(

ρ2

ρ1

)(

R1

R2

)

8.M1

M2=

(

ρ2

ρ1

)(

R1

R2

)2

9.M1

M2=

(

ρ2

ρ1

)(

R2

R1

)3

10.M1

M2=

(

ρ2

ρ1

)(

R2

R1

)2

Part 2 of 2Which of the following gives the ratio of the

circular areas,A1

A2, defined by the two equa-

tors?

1.A1

A2=

(

R1

R2

)2

2.A1

A2=

(

R1

R2

)


3.A1

A2=

(

R1

R2

)3

4.A1

A2= π

(

R1

R2

)2

5.A1

A2= π

(

R1

R2

)3

6.A1

A2=

(

R2

R1

)2

7.A1

A2=

(

R2

R1

)

8.A1

A2=

(

R2

R1

)3

9.A1

A2= π

(

R2

R1

)2

10.A1

A2= π

(

R2

R1

)3

Scaling 0101:05, highSchool, multiple choice, < 1 min,wording-variable.

Part 1 of 3A solid aluminum cube has sides each of

length L . A second cube of the same materialhas sides three times the length of the firstcube, i.e., 3L .

Compared to the first cube, the density ofthe second cube is

1. the same as the first cube.

2. twenty-seven times as much as the firstcube.

3. eight times as much as the first cube.

4. sixty-four times as much as the firstcube.

5. nine times as much as the first cube.

6. four times as much as the first cube.

7. sixteen times as much as the first cube.

8. twenty-four times as much as the firstcube.

9. two times as much as the first cube.

10. None of these

Part 2 of 3Compared to the first cube, the weight of thesecond cube is










10. None of these

Part 3 of 3Compared to the first cube, the total surfacearea of the second cube is









8. ninty-six times as much as the first cube.


10. None of these

Chapter 1, section 6, Dimensional Analysis 20

Dimensional Analysis 030101:06, highSchool, multiple choice, < 1 min,normal.

This problem shows how dimensional anal-ysis helps us check and sometimes even find aformula.

A rope has a cross section A = 10 m2 anddensity ρ = 2000 kg/m3. The “linear” densityof the rope µ, defined to be the mass per unitlength, can be written in the form µ = ρxAy.

Based on dimensional analysis, determinethe powers x and y by choosing an expressionbelow.

1. µ = ρA

2. µ =ρ

A

3. µ = ρA2

4. µ =ρ

A2

5. µ =A

ρ

6. µ =1

ρA

7. µ =A2

ρ

8. µ =1

ρA2

9. µ =A

ρ2

10. µ =A2

ρ2

Dimensional Analysis 080101:06, highSchool, multiple choice, > 1 min,normal.

This problem shows how dimensional anal-ysis helps us check our work and sometimeseven help us find a formula.

A rope has a cross section A = 10 m2 anddensity ρ = 2000 kg/m3. The “linear” densityof the rope µ, is defined to be the mass perunit length, in the form µ = ρxAy .

Based on dimensional analysis, find thepowers x and y.

1. x = −2, y = 1

2. x = −1, y = 2

3. x = −1, y = −1

4. x = −2, y = −1

5. x = −2, y = 2

6. x = 1, y = 1

7. x = 1, y = 2

8. x = 1, y = −1

9. x = −1, y = 1

Dimensional Analysis 1301:06, highSchool, multiple choice, < 1 min,fixed.

Consider a piece of string which is placedalong the x-axis. Let ∆m be the mass of asegment of the string and ∆x the length ofthis segment. The linear mass density, µ, of apiece of string is defined as

µ =∆m

∆x.

Denote ρ to be its mass density defined as

ρ =mass

volume

and A its cross sectional area. Let us write

µ = ρxAy.

Using dimensional analysis, determine theequations which enable one to solve for x andy.

1. x = 1, 2y − 3x = −1

2. x = 1, 2y + 3x = −1

3. x = 1, 3x+ 2y = 1


4. x = 1, 2y − 3x = 1

5. x = 1, −2y − 3x = −1

6. x = −1, 2y − 3x = −1

7. x = −1, 2y + 3x = −1

8. x = −1, 3x+ 2y = 1

9. x = −1, 2y − 3x = 1

10. x = −1, −2y − 3x = −1

Dimension Of Constant01:06, highSchool, multiple choice, < 1 min,fixed.

The volume of an object is given as a func-

tion of time by V = A+B

t+C t4. Determine

the dimension of the constant C.

1. L2/T 4

2. L/T 4

3. L4/T 3

4. L/T

5. L3/T 4

Holt SF 01Rev 1401:06, highSchool, numeric, < 1 min, normal.

A metric ton is 1.000× 103 kg.How many 85 kg people can safely occupy

an elevator that can hold a maximum mass ofexactly 1 metric ton?

Laying Eggs 0101:06, highSchool, multiple choice, > 1 min,wording-variable.

Needing help, the secretary of theUnited States Department of Agricultureasked your teacher, “If a chicken-and-a-

half can lay an egg-and-a-half in a day-and-a-half, how many days will it taketwo chickens to lay thirty-two eggs?”

Please help your teacher select the correctanswer to the secretary’s question.

1. Two chickens will lay thirty-two eggs intwenty-four days.

2. Two chickens will lay thirty-two eggs intwelve days.

3. Two chickens will lay thirty-two eggs infifteen days.

4. Two chickens will lay thirty-two eggs intwenty-two days.

5. Two chickens will lay thirty-two eggs infourteen days.

6. Two chickens will lay thirty-two eggs intwenty-one days.

7. Two chickens will lay thirty-two eggs innine days.

8. Two chickens will lay thirty-two eggs ineighteen days.

9. Two chickens will lay thirty-two eggs insixteen days.

10. Two chickens will lay thirty-two eggs inten days.

SWCT Dimension01:06, highSchool, multiple choice, < 1 min,fixed.

Givenunits

position x L


time t T

velocity vL

T

acceleration aL

T 2

Find the exponent A in the equation

V =a2 tA

x

1. 1

2. 2

3. 3

4. 4

Volume Dimension 0201:06, highSchool, multiple choice, > 1 min,fixed.

Suppose the volume V of some object hap-pens to depend on time t according to theequation V (t) = At3 + B/t2, where A andB are some constants. Let L and T denotedimensions of length and time, respectively.

What is the dimension of the constant A?

1. L3/T3

2. L/T3

3. L2/T

4. L3 · T3

5. L/T

Volume Dimension 0401:06, highSchool, multiple choice, < 1 min,fixed.

The volume of an object as a function oftime is V (t) = At3, where A is some constant.Let L and T denote dimensions of length andtime, respectively.

Determine the dimension of the constantA?

1. L3/T3

2. L/T3

3. L2/T

4. L3 · T3

5. L/T

Chapter 1, section 7, Conversion of Units 23


Part 1 of 2The Statue of Liberty weighs nearly

205 tons.If a person can pull an average of

100 kg/person, how many people would ittake to move the Statue of Liberty?

Part 2 of 2The weight of the space shuttle is about4.5 million pounds.

How many people would it take to moveit?


A water holding tank measures 100 m long,45 m wide, and 10 m deep. Traces of mercuryhave been found in the tank, with a concen-tration of 60 mg/L.

What is the total mass of mercury in thetank?

Holt SF 01A 0101:07, highSchool, numeric, < 1 min, normal.

A human hair is approximately 50 µm indiameter.

Express this diameter in meters.

Holt SF 01A 01M01:07, highSchool, multiple choice, < 1 min,normal.

A human hair is approximately 50 µm indiameter.

Express this diameter in meters.

1. 5× 10−5 m

2. 5× 105 m

3. 5× 10−6 m

4. 5× 106 m

5. 5× 10−7 m

6. 5× 107 m

7. None of these


A typical radio wave has a period of 1 µs.Express this period in seconds.

Holt SF 01A 0301:07, highSchool, numeric, > 1 min, normal.

Part 1 of 3A hydrogen atom has a diameter of about

10 nm.a) Express this diameter in meters.

Part 2 of 3b) Express this diameter in millimeters.

Part 3 of 3c) Express this diameter in micrometers.

Holt SF 01A 0401:07, highSchool, multiple choice, < 1 min,normal.

Part 1 of 2The distance between the sun and the Earth

is about 1.5× 1011 m.a) Express this distance with an SI prefix.

1. 1.5× 10−1 Tm

2. 1.5× 10−1 Pm

3. 1.5× 10−1 Gm

4. 1.5× 10−1 Mm

5. 1.5× 10−1 mm

6. 1.5× 10−1 km

7. None of these


Part 2 of 2b) Express this distance in kilometers.

1. 1.5× 108 km

2. 1.5× 109 km

3. 1.5× 106 km

4. 1.5× 107 km

5. 1.5× 1010 km

6. 1.5× 1011 km

6. None of these

Holt SF 01A 040201:07, highSchool, multiple choice, < 1 min,normal.

The distance between the sun and the Earthis about 1.5 × 1011 m. Express this distancein kilometers.

1. 1.5× 108 km

2. 1.5× 109 km

3. 1.5× 106 km

4. 1.5× 107 km

5. 1.5× 1010 km

6. 1.5× 1011 km

7. None of these

Holt SF 01A 0501:07, highSchool, multiple choice, < 1 min,wording-variable.

The average mass of an automobile in theUnited States is about 1.440× 106 g.

Express this mass in kilograms.

1. 1.440× 103 kg

2. 1.440× 109 kg

3. 1.440× 1012 kg

4. 1.440× 10−3 kg

5. 1.440× 10−6 kg

6. 1.440× 10−9 kg

7. 1.440× 10−12 kg

8. 1.440× 100 kg

9. None of these

Holt SF 01Rev 1101:07, highSchool, numeric, > 1 min, normal.

Part 1 of 7a) Express 2 dm in millimeters.

Part 2 of 7b) Express 2 h 10 min in seconds.

Part 3 of 7c) Express 16 g in micrograms.

Part 4 of 7d) Express 0.75 km in centimeters.

Part 5 of 7e) Express 0.675 mg in grams.

Part 6 of 7f) Express 462 µm in centimeters.

Part 7 of 7g) Express 35 km/h in meters per second.


Part 1 of 5Use the SI prefixes to convert these hy-

pothetical units of measure into appropriatequantities.

a) Express 10 rations in dekarations.


Part 2 of 5b) Express 2000 mockingbirds in kilomock-ingbirds.

Part 3 of 5c) Express 10−6 phones in microphones.

Part 4 of 5d) Express 10−9 goats in nanogoats.

Part 5 of 5e) Express 1019 miners in examiners.


One cubic centimeter(

1.0 cm3)

of waterhas a mass of 0.001 kg at 25◦ C.

Find the mass of 1 m3 of water at 25◦ C.


A gram is

1. 10−6 kg

2. 10−3 kg

3. 1 kg

4. 103 kg

5. 106 kg

Volume Conversion 0201:07, highSchool, numeric, > 1 min, normal.

Part 1 of 2A volume of V = 1 liter is how many cubic

centimeters?

Part 2 of 2What would this same volume be in cubicmillimeters?

Chapter 1, section 8, Order-of-Magnitude Calculations 26

Figuring Physics 1201:08, highSchool, numeric, < 1 min, normal.

Suppose that you wish to find out howmuch gasoline is in an underground storagetank. You pour in one gallon of gasoline thatcontains some long half-life radioactive mate-rial that causes a Geiger constant to register50000 counts perminute above backgroundradiation. The next day you remove a gal-lon from the underground tank and measureits radioactivity to be 100 counts perminuteabove background.

How much gasoline is in the tank?

Holt SF 01Rev 4001:08, highSchool, numeric,> 1min, wording-variable.

You can obtain a rough estimate of thesize of a molecule with the following simpleexperiment: Let a droplet of oil spread outon a fairly large but smooth water surface.The resulting ”oil slick” that forms on thesurface of the water will be approximatelyone molecule thick.

Given an oil droplet with a mass of 9.00 ×10−7 kg and a density of 918 kg/m3 thatspreads out to form a circle with a radius of41.8 cm on the water surface, what is theapproximate diameter of an oil molecule?

Chapter 1, section 9, Significant Digits and Measurements 27

Holt SF 01Rev 1601:09, highSchool, multiple choice, < 1 min,wording-variable.

Part 1 of 5How many significant figures are in the fol-

lowing measurements?a) 300 000 000 m/s.

1. 1

2. 2

3. 3

4. 4

5. 5

6. 6

7. None of these

Part 2 of 5b) 25.030◦C.

1. 5

2. 1

3. 2

4. 3

5. 4

6. 6

7. None of these

Part 3 of 5c) 0.006 070◦C.

1. 4

2. 1

3. 2

4. 3

5. 5

6. 6

7. None of these

Part 4 of 5d) 1.004 J.

1. 4

2. 1

3. 2

4. 3

5. 5

6. 6

7. None of these

Part 5 of 5e) 1.3 05 20 MHz.

1. 6

2. 1

3. 2

4. 3

5. 4

6. 5

7. None of these


Part 1 of 3The value of the speed of light is now known


to be 2.997 924 58 × 108 m/s. Express thespeed of light

a) with three significant figures.

1. 3× 108 m/s

2. 3.00× 108 m/s

3. 3.0× 108 m/s

4. 2.998× 108 m/s

5. 2.9979× 108 m/s

6. 2.99792× 108 m/s

7. 2.997925× 108 m/s

8. 2.9979246× 108 m/s

9. None of these

Part 2 of 3b) with five significant figures.

1. 3× 108 m/s

2. 3.0× 108 m/s

3. 3.00× 108 m/s

4. 2.9979× 108 m/s

5. 2.998× 108 m/s

6. 2.99792× 108 m/s

7. 2.997925× 108 m/s

8. 2.9979246× 108 m/s

9. None of these

Part 3 of 3c) with seven significant figures.

1. 3× 108 m/s

2. 3.0× 108 m/s

3. 3.00× 108 m/s

4. 2.998× 108 m/s

5. 2.9979× 108 m/s

6. 2.997925× 108 m/s

7. 2.99792× 108 m/s

8. 2.9979246× 108 m/s

9. None of these

Holt SF 01Rev 1901:09, highSchool, multiple choice, < 1 min,normal.

Part 1 of 4How many significant figures are in the fol-

lowing measurements?a) 78.9± 0.2 m.

1. 3

2. 1

3. 2

4. 4

5. 5

6. 6

7. None of these

Part 2 of 4b) 3.788× 109 s.

1. 4

2. 1

3. 2

4. 3


5. 5

6. 6

7. None of these

Part 3 of 4c) 2.46× 106 kg.

1. 3

2. 1

3. 2

4. 4

5. 5

6. 6

7. None of these

Part 4 of 4d) 0.0032 mm.

1. 2

2. 1

3. 3

4. 4

5. 5

6. 6

7. None of these

Holt SF 01Rev 2001:09, highSchool, multiple choice, > 1 min,wording-variable.

Part 1 of 4Use significant figures to calculate the fol-

lowing:a) Find the sum of the measurements 756 g,

37.2 g, 0.83 g, and 2.5 g.

1.Whole number (797 g)

2. Hundredths (796.53 g)

3. Tenths (796.5 g)

4. Tens (800 g)

5. Three significant figures (797 g)

6. Two significant figures (800 g)

7. One significant figure (800 g)

8. None of these

Part 2 of 4

b) Find the quotient3.2 m

3.563 s.

1. Two significant figures (0.90 m/s)

2. One significant figure (0.9 m/s)

3. Three significant figures (0.898 m/s)

4. Four significant figures (0.8981 m/s)

5. Tenths (0.9 m/s)

6. Hundredths (0.90 m/s)

7. Thousandths (0.898 m/s)

8. None of these

Part 3 of 4c) Find the product of 5.67 mm and π.

1. Three significant figures (17.8 mm)

2. Two significant figures (18 mm)

3. Four significant figures (17.81 mm)

4. Five significant figures (17.813 mm)

5.Whole number (18 mm)


6. Tenths (17.8 mm)

7. Hundredths (17.81 mm)

8. Thousandths (17.813 mm)

9. None of these

Part 4 of 4d) Find the difference of 27.54 s and 3.8 s.

1. Tenths (23.7 s)

1. Tens (20 s)

1.Whole number (24 s)

1. Hundredths (23.74 s)

3. One significant figure (20 s)

3. Two significant figures (24 s)

3. Three significant figures (23.7 s)

3. Four significant figures (23.74 s)

4. None of these


A fisherman catches two sturgeons. Thesmaller of the two has a measured length of93.46 cm (two decimal places and four signif-icant figures), and the larger fish has a mea-sured length of 135.3 cm (one decimal placeand four significant figures).

What rule must be used on the sum to findthe total length of the two fish?

1. Tenths (228.8 cm)

2.Whole number (229 cm)

3. Hundredths (228.76 cm)

4. Hundreds (230 cm)

5. Two significant figures (230 cm)

6. Three significant figures (229 cm)

7. Four significant figures (228.8 cm)

8. Five significant figures (228.76 cm)

9. None of these


A farmer measures the distance around arectangular field. The length of each long sideof the rectangle is found to be 38.44 m, andthe length of each short side is found to be19.5 m.

What is the total distance around the field?

1. Tenths (115.9 m)

2.Whole number (116 m)

3. Hundredths (115.88 m)

4. Hundreds (120 m)

5. Two significant figures (120 m)

6. Three significant figures (116 m)

7. Four significant figures (115.9 m)

8. Five significant figures (115.88 m)

9. None of these

Chapter 1, section 11, Mathematical and Scientific Notation 31

Summation Notation01:11, highSchool, numeric, > 1 min, normal.

Compute the value of

14∑

i=1

xi ,

where xi = 3 i+ 2 .

Chapter 1, section 12, Coordinate Systems 32

Scaling of a Sphere01:12, highSchool, numeric, > 1 min, normal.

Part 1 of 2The radius of a small ball is around 3 cm.

The radius of a basketball is about 4 timeslarger.

What is the ratio of the surface areas of thesmall ball and a basketball?

Part 2 of 2What is the ratio of their volumes?

Chapter 1, section 13, Mathematics Overview 33

Conceptual 13 0501:13, highSchool, multiple choice, > 1 min,fixed.

Part 1 of 4You have a collection of eight numbered

balls; 1 through 4 are orange and 5 through 8are green.

How many different arrangements of theseballs in a line are possible?

1. 576

2. 40320

3. 16777216

4. 70

5. 24

Part 2 of 4What percentage of those arrangements havefour orange balls followed by four green balls?

1. 7%

2. 1.4%

3. 50%

4. 4.2%

5. 0.06%

Part 3 of 4For a collection of 12 balls (six orange andsix green), what percentage of the total ar-rangement have six orange balls followed bysix green balls?

1. 0.11%

2. 50%

3. 0.14%

4. 2.0%

5. 10−6

Part 4 of 4What happens to the probability of an or-dered configuration as the total number ofballs increases?

1. lower

2. higher

3. Does not change



Part 1 of 2How many different ways are there to ar-

range five coins in a row if one is heads-up andthe other four are tails-up?

1. 5

2. 120

3. 24

4. 10

Part 2 of 2What if two were heads-up and three weretails-up?

1. 5

2. 10

3. 20

4. 120

Holt SF 01Rev 3701:13, highSchool, numeric,< 1min, wording-variable.

Chapter 1, section 13, Mathematics Overview 34

Part 1 of 4Consider a circle of radius 3.5 cm.a) Calculate its circumference (C = 2πr).

Part 2 of 4b) Calculate its area

(

A = πr2)

.

Part 3 of 4Consider a circle of radius 4.65 cm.

c) Calculate its circumference (C = 2πr).

Part 4 of 4d) Calculate its area

(

A = πr2)

.

Straight Line Equation01:13, highSchool, multiple choice, > 1 min,wording-variable.

A graph of a straight line going through twopoints is shown below.

�

�

y

−5 −3 −1 0 1 2 3 4 5

x

−5−4−3−2−1012345

What is the equation y = f(x) of this line?

1. y = +5

4x− 1

2

2. y = +5

4x+

1

2

3. y = −5

4x− 1

2

4. y = −5

4x+

2

5

5. y = +4

5x− 1

2

6. y = +4

5x− 2

5

7. y = −4

5x− 1

2

8. y = −4

5x+

1

2

9. y = +5

4x+

2

5

10. y = +5

4x− 2

5

Temperature Conversion 0101:13, highSchool, multiple choice, < 1 min,fixed.

The formula to convert temperature in de-grees Celsius to temperature in Kelvin is

K = C + 273 .

For this formula C is the input andK is theoutput.

Rewrite the formula so that K is the inputand C is the output.

1. C = K − 273

2. C = K + 273

3. C =K

273

4. K = C + 273

5. None of these

Chapter 1, section 14, Scientific Method 35


Which of the following is not a scientifichypotheses?

1. Chlorophyll makes grass green.

2. The Earth rotates about its axis becauseliving things need light and darkness to alter-nate.

3. Tides are caused by the moon.

4. The Earth rotates around the Sun.

5. The wind is caused by the Sun.

Hewitt CP9 01 P0101:14, highSchool, multiple choice, < 1 min,fixed.

What is a fact?

1. A phenomenon about which competentobservers who have made a series of observa-tions are in agreement

2. A reasonable explanation of an observa-tion or experimental result that is not fullyaccepted until tested over and over again byexperiment

3. A general hypothesis or statement aboutthe relationship of natural quantities that hasnot been contradicted; also known as a prin-ciple

4. An orderly method for gaining, organiz-ing, and applying new knowledge

5. A synthesis of a large amount of infor-mation that encompasses well-tested and ver-ified hypotheses about certain aspects of thenature

Hewitt CP9 01 P02

01:14, highSchool, multiple choice, < 1 min,fixed.

What is a hypothesis?







What is a law?








What is the scientific method?







What is a theory?






Hewitt CP9 01 R0101:14, highSchool, multiple choice, < 1 min,fixed.

Which of the following activities involvesthe human expression of passion, talent, andintelligence?

1. painting and sculpture

2. literature

3. music

4. religion

5. science

6. All of these

Lunatick01:14, highSchool, multiple choice, > 1 min,fixed.

Sun

Figure: Artist conception of the Moon,Earth, and Sun’s plantary system. The


size and identification of the Earth andMoon does not conceptually matter.

If you were on the Moon, the Earth would

1. show no phases.

2. show phases that are the same as theMoon’s phase (i.e., when there is a full Moon,there is a full Earth and vice versa).

3. show phases opposite to the Moon’s phase(i.e., at the time when there is a new Moon,there is a old Earth and vice versa).

4. show phases that are the same as theMoon’s phase (since the Moon’s phase is dueto the Earth’s shadow on the Moon and vice

versa).

Chapter 1, section 15, Scaling 38


The surface area-to-volume ratio of a cuberesting on another surface is the ratio of thesurface area of the five exposed sides to thevolume. Suppose a small cube-shaped build-ing with a flat roof measures 10 meters on aside and has a surface area-to-volume ratio ofa. A similar building 5 meters on a side has asurface area-to-volume ratio of b.

What relationship would a and b have?

1. a = b

2. a > b

3. a < b



Large things tend to have less surface areacompared to their volume.

Based on this fact, who is more likely toget cold in the winter, a fully grown man or asmall child?

1. a fully grown man

2. a small child

3. Either



The average two-year-old boy is 36 inches(3 feet) tall and weighs 30 pounds. Supposethat when he is fully grown, he is 6 feet tall.

If the rules of scaling apply, how much will

he weigh when he is fully grown?

1. 240 pounds

2. 120 pounds

3. 160 pounds

4. 150 pounds

Hewitt CP 12 3701:15, highSchool, multiple choice, < 1 min,fixed.

Who has more need for drink in a dry desertclimate - a child or an adult?

1. A child

2. An adult

3. The same for each

4. More information is needed.


How does the thickness of paint sprayedon a surface change when the sprayer is heldtwice as far away?

1. remains the same

2. doubles

3. quadruples

4. drops to one quater of the original value

5. halves

6. more information is needed to answer thequestion

Hewitt CP9 12 2101:15, highSchool, multiple choice, < 1 min,fixed.

Chapter 1, section 15, Scaling 39

A candy maker making taffy apples decidesto use 100 kg of large apples rather than 100kg of small apples.

Will the candy maker need to make moreor less taffy to cover the appples?

1. More

2. Less

3. The same amount



A thick rope is stronger than a thin rope ofthe same material.

Is a long rope stronger than a short rope?

1. Yes

2. No

3. More information is needed about theirwidths.


Consider two bridges that are exact repli-cas of each other except that every dimen-sion in the larger is exactly twice that of theother; that is, twice as long, structural ele-ments twice as thick, etc.

Which bridge is more likely to collapse un-der its own weight?

1. The smaller one

2. The larger one

3. They have the same strength.


Scaling 01 v101:15, highSchool, multiple choice, < 1 min,wording-variable.

A solid aluminum cube has sides each oflength L . A second cube of the same materialhas sides three times the length of the firstcube, i.e., 3L .

Compared to the first cube, the total sur-face area of the second cube is








8. ninty-six times as much as the first cube.


10. None of these

Chapter 1, section 16, Problem Solving Strategy 40

Burning Forests 0201:16, highSchool, numeric, > 1 min, normal.

In May 1998, forest fires in southern Mexicoand Guatemala spread smoke all the way toAustin. Those fires consumed forest land at arate of 23100 acres/week.

An acre is 4047 m2.On the average, how many square meters

of forest are burned down every minute?

Divide by one01:16, highSchool, numeric, < 1 min, fixed.

Ismarelda has enoughmoney to purchase 23bottles of root beer for a party at her house.She is expecting 3 guests.

What is the largest number of bottles ofroot beer she needs to purchase if she wantseveryone (including herself) to have an equalnumber of root beers?

Hewitt CP9 01 P0701:16, highSchool, numeric, < 1 min, fixed.

Using a lens let the solar image fall upon acoin lying on cardboard. Position the card-board so that the image just covers the coin.This is a convenient way to measure the diam-eter of the image. Then measure the distancebetween the lens and the coin. Your ratio ofimage size to image distance should be about1

110.

Using the information that the Sun is150,000,000 kilometers distant, calculate thediameter of the Sun.


A billionaire offers to give you $5 billion ifyou will count out the amount in $1 bills ora lump sum of $5000. Assume that you cancount at an average rate of one bill per second,and be sure to allow for the fact that you needabout 10 hours a day for sleeping and eating.Which offer should you accept?

In order to answer this, how long will ittake you to count out the $5 billion?


Exactly 1 qt of ice cream is to be made inthe form of a cube.

What should be the length of one side inmeters for the container to have the appropri-ate volume?

(

4 qt = 3.786× 10−3 m3.)


Part 1 of 2An ancient unit of length called the cubit

was equal to approximately 50 centimeters,which is, or course, approximately 0.50 me-ters. It has been said that Noah’s ark was300 cubits long, 50 cubits wide, and 30 cubitshigh.

Estimate the volume of the ark using 1 palm= 0.08 m and 6 palms = 1 cubit.

Part 2 of 2Estimate the volume of a typical home(2000 ft2 in size and 10 ft tall).

Holt SF 01Rev 4201:16, highSchool, numeric, > 1 min, fixed.

If one micrometeorite (a sphere with a di-ameter of 1.0 × 10−6 m) struck each squaremeter of the moon each second, it would takemany years to cover the moon with microme-teorites to a depth of 1.0 m. Consider a cubicbox, 1.0 m on a side, on the moon.

How long would it take to completely fillthe box with micrometeorites?


Part 1 of 2Assuming biological substances are 90%

water and the density of water is 1000 kg/m3,estimate the masses of the following:

a) a spherical cell with a diameter of 1 µm

Chapter 1, section 16, Problem Solving Strategy 41(

volume =4

3πr3

)

.

Part 2 of 2b) a fly, which can be approximated by acylinder 4 mm long and 2 mm in diameter(

volume = πr2`)

.


Part 1 of 2The radius of the planet Saturn is 5.85 ×

107 m, and its mass is 5.68× 1026 kg.Find the average density of Saturn (its mass

divided by its volume) if the volume of a

sphere is given by4

3π r3.

Part 2 of 2Find the surface area of Saturn if the surfacearea of a sphere is given by 4π r2.

Snail Species01:16, highSchool, numeric, < 1 min, fixed.

A 19th century British naturalist with apenchant for archaic units of measurementdescribed a species of snail crawling at anaverage speed of one furlong per fortnight.Recently, a biology student re-measured thesnail’s average speed and reported it as onecentimeter per minute.

Which of the following is the most likelyexplanation of the student’s result?Note: A furlong is one eighth of 1 mile or220 yards; a yard is 3 feet or 0.9144 meter;a fortnight is a time interval of 14 days or14× 24 hours.

1. The student got a different species of snailcrawling at least ten times faster than the onedescribed by the naturalist.

2. The student’s snails are crawling at ex-actly the same snail’s pace they ever did,but he reported a slightly different value fortheir speed because he rounded it in differentunits.

3. Evolution in action: Even the snails aremore than twice as fast than they used tobe.

4. Pollution in action: The snails are sick ofsome environmental toxins and crawl at lessthan half their healthy speed.

5. The student got a different species of snailcrawling at least ten times slower than the onedescribed by the naturalist.

6. The student has smoked too much weedand lost all sense of time; his measurementsare off the mark by two orders of magnitudeor worse.

Steel I Beam 0101:16, highSchool, numeric, > 1 min, normal.

Part 1 of 2A structural I beam is made of iron. A view

of its cross-section and its dimensions is shownin the figure, where d = 3 cm, w = 20 cm,h = 25 cm and the length (not shown) of thebeam is ` = 1.5 m.

The density of iron is 7560 kg/m3 . Theatomic weight of iron is 55.85 g/mol and Avo-gadro number is NA = 6.02214× 1023 /mol.

20 cm

25 cm

3 cm

3 cm

What is the mass of a section 1.5 m long?

Part 2 of 2How many atoms are there in this section?

Temperature Change 0101:16, highSchool, numeric, > 1 min, fixed.

Chapter 1, section 16, Problem Solving Strategy 42

The following table shows the daily hightemperatures for a week in May.

Day Temp Day Temp

Sun. 76◦ Thurs. 75◦

Mon. 72◦ Fri. 74◦

Tues. 80◦ Sat. 78◦

Wed. 75◦

Find the net change in temperature (thesum of all of the temperature changes).

Chapter 2, section 1, Displacement 43

Mile Markers02:01, highSchool, numeric, > 1 min, normal.

Part 1 of 2While John is traveling along an interstate

highway, he notices a(n) 160 mi marker as hepasses through town. Later John passes a(n)115 mi marker.

a) What is the distance between town andJohn’s current location?

Part 2 of 2b) What is John’s current position?

Chapter 2, section 2, Velocity and Speed 44

Ant Race02:02, highSchool, numeric, > 1 min, normal.

Two ants race across a table 50 cm long.One travels at 4 cm/s and the other at 2 cm/s.

When the first one crosses the finish line,how far behind is the second one?

Concept 20 P0302:02, highSchool, numeric, < 1 min, normal.

An oceanic depth-sounding vessel surveysthe ocean bottom with ultrasonic waves thattravel 1530 m/s in seawater.

How deep is the water directly below thevessel if the time delay of the echo to theocean floor and back is 6 s?


A bat flying in a cave emits a sound andreceives its echo 0.1 s later.

How far away is the cave wall? (Assumethe speed of sound to be 340 m/s.)

Concept 20 P0502:02, highSchool, multiple choice, < 1 min,wording-variable.

You watch a distant lady driving nailsinto her front porch at a regular rate of 2strokes per second. You hear the sound of theblows exactly synchronized with the blowsyou see. And then you hear one more blowafter you see her stop hammering.

How far away is she? The speed of sound is340 m/s.

1. 270 m.

2. 680 m.

3. 1360 m.

4. 170 m.

5. 85 m.

Displacement Curve e102:02, highSchool, multiple choice, > 1 min,fixed.

Consider a moving object whose po-sition x is plotted as a function ofthe time t on the following figure:

x

1I 2 3

1

2

3

tOII III

Clearly, the object moved in different waysduring the time intervals denoted I, II and IIIon the figure.

During which interval(s) does the objecthave non-zero, positive acceleration?

1. During interval I only.

2. During interval II only.

3. During interval III only.

4. During each of the three intervals.

5. During none of the three intervals.

6. During intervals I and II only.

7. During intervals I and III only.

8. During intervals II and III only.

Flight time02:02, highSchool, multiple choice, < 1 min,fixed.

An airplane starts from A and goes to B ata constant speed. After reaching B it returnsto A at the same speed. There was no wind.Now, assume there was a wind from A to B ofconstant magnitude.

Assume: The wind speed is less than that


of the plane (i.e., in magnitude).When will the round trip take more time

when there is a wind or when there is nowind?

1. Time taken is more when there is nowind.

2.Time taken is more when there is constantwind.

3. Same in both cases because one way thewind helps you and the other way it troublesyou.

4. Insufficient data.

Glacier Movement 0202:02, highSchool, numeric, > 1 min, normal.

A glacier advances at 4.8× 10−6 cm/s.How far will it move in 7 years?

Hewitt CP9 03 E0102:02, highSchool, numeric, < 1 min, normal.

What is the impact speed when a car mov-ing at 100 km/h bumps into the rear of an-other car traveling in the same direction at98 km/h?

Hewitt CP9 03 P0102:02, highSchool, numeric, < 1 min, normal.

The ocean’s level is currently rising atabout 1 mm per year.

At this rate, in how many years will sealevel be 3 m higher than now?


Use the fact that the speed of light in avacuum is about 3.00× 108 m/s to determinehow many kilometers a pulse from a laserbeam travels in exactly one hour.

Holt SF 02A 01

02:02, highSchool, numeric,< 1min, wording-variable.

Heather and Matthew walk eastward witha speed of 0.98 m/s east.

If it takes them 34 min to walk to the store,how far have they walked?


Runner A is initially 6.0 km west of a flag-pole and is running with a constant velocityof 9.0 km/h due east. Runner B is initially 5.0km east of the flagpole and is running with aconstant velocity of 8.0 km/h due west.

How far are the runners from the flagpolewhen their paths cross?


Part 1 of 2Two cars travel westward along a straight

highway, one at a constant velocity of85 km/h, and the other at a constant velocityof 115 km/h.

a) Assuming that both cars start at thesame point, how much sooner does the fastercar arrive at a destination 16 km away?

Part 2 of 2b) How far must the cars travel for the fastercar to arrive 15 min before the slower car?


One swimmer in a relay race has a 0.50 slead and is swimming at a constant speed of4.00 m/s. The swimmer has 50.0 m to swimbefore reaching the end of the pool. A secondswimmer moves in the same direction as theleader.

What constant speed must the secondswimmer have in order to catch up to theleader at the end of the pool?



How long does it take an automobile trav-eling 60.0 km/h to become even with a carthat is traveling in another lane at 40.0 km/hif the cars’ front bumpers are initially 125 mapart?

Kinematics2 v202:02, highSchool, multiple choice, < 1 min,fixed.

The graph shows position as a function oftime for two trains running on parallel tracks.At time t = 0 (origin) the position of bothtrains is 0.

position

timetB

B

A

Which is true?

1. At time tB, both trains have the samevelocity

2. Both trains speed up all the time

3. Both trains have the same velocity atsome time before tB

4. Somewhere on the graph, both trains havethe same acceleration

Light From the Sun02:02, highSchool, numeric, > 1 min, fixed.

Light from the sun reaches Earth in 8.3 min.The velocity of light is 3× 108 m/s.

How far is the Earth from the sun?

Moving Glacier02:02, highSchool, numeric, > 1 min, normal.

A glacier moves with a speed of 48 nm/s.How many years would it take for the glacierto move 0.78 km?

Picking up the Slack 0202:02, highSchool, numeric, > 1 min, normal.

A 20-car train standing on the siding isstarted in motion by the train’s engine. Thereare 5 cm of slack between the engine and eachof the cars. The engine moves at a constantspeed of 40 cm/s.

How much time is required for the pulse totravel the length of the train?

Problems 08 0102:02, highSchool, multiple choice, < 1 min,fixed.

Consider a bicycle that has wheels with acircumference of 2m.

What is the linear speed of the bicycle whenthe wheels rotate at 1 revolution per second?

1. 0.5m/s.

2. 1m/s.

3. 2m/s.

4. 4m/s.

Velocity vs Time 0502:02, highSchool, multiple choice, > 1 min,wording-variable.

Part 1 of 3Consider the plot below describing motion

along a straight line with an initial position ofx0 = 10 m.


−2−10

1

2

3

4

5

1 2 3 4 5 6 7 8 9

�

�

�

�

�

time (s)

velocity

(m/s)

What is the position at 2 seconds?

Part 2 of 3What is the position at 6 seconds?


Velocity vs Time 1202:02, highSchool, numeric,> 1min, wording-variable.

Part 1 of 3The scale on the horizontal axis is 5 s per

division and on the vertical axis 3 m/s perdivision.

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9

v(t)

time (× 5 s)

velocity

(×3m/s)

What is the time represented by the secondtic mark on the horizontal axis?

Part 2 of 3What is the velocity represented by the thirdtic mark on the vertical axis?

Part 3 of 3What is the velocity when t = 10 s?

Chapter 2, section 3, Average Velocity for Motion along a Straight Line 48

Average Velocity02:03, highSchool, numeric, > 1 min, normal.

Part 1 of 2You drive a car 2 h at 40 km/h, then 2 h at

60 km/h.What is your average velocity?

Part 2 of 2What is your average velocity if you drive adistance of 100 km at a speed of 40 km/h, thenthe same distance at a speed of 60 km/h?

Car and Checkpoints 01 v102:03, highSchool, numeric, > 1 min, normal.

Consider a car which is traveling along astraight road with constant acceleration a.There are two checkpoints A and B which area distance 100 m apart. The time it takes forthe car to travel from A to B is 5 s.

A B

4 m/s2

100 m

Find the velocity vB for the case where theacceleration is 4 m/s2.

Comparison of Average Velocity02:03, highSchool, multiple choice, < 1 min,fixed.

The position-versus-time graph below de-scribes the motion of three different bodies(labelled 1, 2, 3).

123

xB

xA

tA

tB

x

t

A

B

Consider the average velocities of the threebodies. Which of the following statements iscorrect?

1. v̄1 = v̄2 = v̄3

2. v̄1 > v̄2 > v̄3

3. v̄1 < v̄2 < v̄3

4. v̄1 > v̄2 and v̄3 > v̄2

Hewitt CP9 03 P0702:03, highSchool, numeric,> 1min, wording-variable.

A reconnaissance plane flies 600 km awayfrom its base at 400 m/s, then flies back to itsbase at 600 m/s.

What is its average speed?

Holt SF 02A 0202:03, highSchool, numeric,< 1min, wording-variable.

If Joe rides south on his bicycle in a straightline for 15 min with an average speed of 12.5km/h, how far has he ridden?

Holt SF 02A 0302:03, highSchool, numeric,> 1min, wording-variable.

Part 1 of 2It takes you 9.5 min to walk with an average


velocity of 1.2 m/s to the north from the busstop to the museum entrance.

a) How far did you walk?

Part 2 of 2b) What is your direction?

1. North

2. East

3. South

4.West

Holt SF 02A 04 0502:03, highSchool, numeric,> 1min, wording-variable.

Part 1 of 2Simpson drives his car with an average ve-

locity of 48.0 km/h to the east.a) How long will it take him to drive 144

km on a straight highway?

Part 2 of 2b) How much time would Simpson save byincreasing his average velocity to 56.0 km/hto the east?


Part 1 of 2A bus travels 280 km south along a straight

path with an average velocity of 88 km/h tothe south. The bus stops for 24 min, then ittravels 210 km south with an average velocityof 75 km/h to the south.

a) How long does the total trip last?

Part 2 of 2b) What is the average velocity for the totaltrip?


A bus travels from El Paso, Texas, to anarea near Chihuahua, Mexico, in 5.2 h withan average velocity of 73 km/h to the south.

What is the bus’s displacement?


A school bus takes 0.530 h to reach theschool from your house.

If the average velocity of the bus is 19.0km/h to the east, what is the displacement?


Part 1 of 2Consider the position-time graph for a

squirrel running along a clothesline.

�

�

�

�

�

�

1 2 3 4 50

1

2

3

4

−1−2

time (s)

position(m

)

a) What is the squirrel’s displacement atthe time t = 4.0 s?

Part 2 of 2b) What is the squirrel’s average velocity dur-ing the time interval between 0.0 s and 4.0s?

Holt SF 02Rev 10A02:03, highSchool, numeric,> 1min, wording-variable.

Part 1 of 2Consider the position-time graph for a


squirrel running along a clothesline.

�

�

�

�

�

�

1 2 3 4 50

1

2

3

4

−1−2

time (s)

position(m

)

a) What is the squirrel’s displacement atthe time t = 3.5 s?

Part 2 of 2b) What is the squirrel’s average velocity dur-ing the time interval between 0.0 s and 3.5s?


The Olympic record for the marathon is 2h, 9 min, 21 s.

If the average speed of a runner achievingthis record is 5.436 m/s, what is the marathondistance?


Part 1 of 4Two cars are traveling on a desert road

between three consecutive poles, as shown inthe figure. After 5.0 s, they are side by sideat the next telephone pole. The distancebetween the poles is 70.0 m.

CarA

CarB

CarA

CarB

Note: Figure is not drawn to scale.a) Find the displacement of Car A after 5.0

s.

Part 2 of 4b) Find the displacement of Car B after 5.0 s.

Part 3 of 4c) Find the average velocity of Car A during5.0 s.

Part 4 of 4d) Find the average velocity of Car B during5.0 s.


Part 1 of 2Sally travels by car from one city to an-

other. She drives for 30.0 min at 80.0 km/h,12.0 min at 105 km/h, and 45.0 min at 40.0km/h, and she spends 15.0 min eating lunchand buying gas.

a) Find the total distance traveled.

Part 2 of 2b) Find the average speed for the trip.


Part 1 of 6The figure shows the position of a runner at

different times during a run.


�

�

�

�

0 10 20 30 400

1

2

3

4

5

time (min)

position(×

1000

m)

Note: Figure is drawn to scale.

a) For the time interval between t = 0 minand t = 10 min, what is the runner’s displace-ment?

Part 2 of 6b) For the same time interval, find the run-ner’s average velocity.

Part 3 of 6c) For the time interval between t = 10 minand t = 20 min, what is the runner’s displace-ment?

Part 4 of 6d) For the same time interval, find the run-ner’s average velocity.

Part 5 of 6e) What is the runner’s total displacement?

Part 6 of 6f) Find the average velocity for the entirerun.


The Earth’s radius is about 6380 km. Thespace shuttle is orbiting about 320.0 km aboveEarth’s surface.

If the average speed of the space shuttle is

27800 km/h, find the time required for it tocircle Earth.

Lou 2 802:03, highSchool, numeric, < 1 min, normal.

A polar bear starts at the North Pole. Ittravels 1 km South, then 1 km East, then1 km North to return to its starting point.This trip takes 1 h.

What was the bear’s average velocity?

SWCT Average Speed02:03, highSchool, multiple choice, < 1 min,fixed.

Chuck drove 35 mi from Austin to San Mar-cos in 40 min, stopped 30 min for a ham-burger, and then drove 45 mi to San Antonioin 50 min. What was Chuck’s average speed?

1. 30 mph

2. 40 mph

3. 43 mph

4. 50 mph

5. 53 mph

6. 56 mph

Wrong Way to San Antonio02:03, highSchool, numeric, < 1 min, normal.

Part 1 of 2A student wanted to drive from Austin to

San Antonio, 80 miles south of Austin onhighway I35. Unfortunately, he entered thehighway in the wrong direction and drove allthe way to Waco — 100 miles north of Austin— before he noticed his error. In Waco,he turned around, drove back to Austin andcontinued to San Antonio. The whole triptook 5.6 hours.

What was the student’s average speed dur-ing this trip?


Part 2 of 2What was the student’s average velocity dur-ing his trip? Take your positive direction tobe southbound on I35.

Chapter 2, section 4, Instantaneous Velocity and Speed 53

Average and Instantaneous V02:04, highSchool, numeric, > 1 min, normal.

Part 1 of 4The position versus time for a certain ob-

ject moving along the x-axis is shown. Theobject’s initial position is −2 m.

−12−10−8−6−4−20

2

4

6

8

10

12

0 1 2 3 4 5 6 7 8 9

�

�

� �

�

�

time (s)

position(m

)

Find the instantaneous velocity at 1 s.

Part 2 of 4Find the instantaneous velocity at 6 s.

Part 3 of 4Find the average velocity between 0 s and 4 s.

Part 4 of 4Find the average velocity over the whole timeshown.


You are stopped for speeding.Which of the following is your traffic fine

based on?

1. average speed

2. instantaneous speed

3. linear speed

4. circle speed

5. None of these


Part 1 of 3Consider the acceleration of gravity to be

10 m/s2 .What is the magnitude of the instantaneous

velocity (speed) of a freely falling object 10 safter it is released from a position of rest?

Part 2 of 3What is its average speed during this 10 sinterval?

Part 3 of 3How far will it fall during this time?

Chapter 2, section 5, Acceleration 54

Acceleration and Velocity02:05, highSchool, multiple choice, > 1 min,fixed.

Which of the following describe possiblescenarios?A) An object has zero instantaneous velocity

and non-zero acceleration.B) An object has negative acceleration and

is speeding up.C) An object has positive acceleration and

constant velocity.D) An object has positive velocity and zero

acceleration.E) An object has increasing positive posi-

tion and negative velocity.F) An object has decreasing positive posi-

tion and negative acceleration.

1. All are possible.

2. None are possible.

3. A, B, D, E, and F only.

4. A, B, C, D, and F only.

5. A, D, and F only.

6. D and F only.

7. A, D, E, and F only.

8. A, B, D, and F only.

9. B, C, and D only.

10. A, C, D, and F only.

Acceleration Curve CPS02:05, highSchool, multiple choice, < 1 min,fixed.

The diagram describes the acceleration vs tbehavior for a car moving in the x-direction.

� �

a

P Q

t0At the point Q, the car is moving

1. with an increasing speed

2. with a constant speed

3. with a decreasing speed

Acceleration vs Time 0202:05, highSchool, numeric, > 1 min, normal.

Part 1 of 2Consider the plot below describing the ac-

celeration of a particle along a straight linewith an initial position of −30 m and an ini-tial velocity of −14 m/s.

−10

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8 9

time (s)

acceleration

(m/s

2)

What is the velocity at 3 s?

Part 2 of 2What is the position at 3 s?

Acceleration vs Time 04


02:05, highSchool, numeric,> 1min, wording-variable.


celeration of a particle along a straight linewith an initial position of 0 m and an initialvelocity of 0 m/s.

−5−4−3−2−10

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9time (s)

acceleration

(m/s

2)


Part 2 of 4Calculate the magnitude of the position dis-placement after the car travels the first 5 s.

Part 3 of 4Calculate the position displacement after thecar travels from 9 s to 13 s, if the car does notexperience any acceleration during this timeperiod.

Part 4 of 4Calculate the magnitude of the car’s averagevelocity from 5 s to 9 s.

Acceleration vs Time 0502:05, highSchool, numeric, > 1 min, normal.


celeration of a particle along a straight linewith an initial position of 0 m and an initialvelocity of 0 m/s.

−3−2−10

1

2

3

4

0 1 2 3 4 5 6 7 8 9time (s)

acceleration

(m/s

2)


Part 2 of 4Calculate the position after the car traveledthe first 7 s.

Part 3 of 4Calculate the position displacement after thecar travels from 7 s to 9 s.


Antilock Brakes02:05, highSchool, multiple choice, > 1 min,fixed.

The following acceleration vs timeplots show data gathered from an au-tomobile fitted with an accelerometer.


0 2 4 6 8 10Time (seconds)

0

0 2 4 6 8 10Time (seconds)

0

A

A

In each case the driver accelerated to cruisingspeed and then slammed on the brakes. Inone case the car is equipped with an antilockbraking system (ABS), while in the other thecar is not. ABS tends to prevent skidding anddid just that in this experiment, allowing amore rapid deceleration.

Which data set, the upper or lower, morelikely came from the car equipped with ABS,and why?

1. Upper case, because of data in the first2.5 seconds.

2. Upper case, because of data between 2.5and 6.5 seconds.

3. Upper case, because of data between 6.5and 9 seconds.

4. Upper case, because of data between 9and 10 seconds.

5. Lower case, because of data in the first2.5 seconds.

6. Lower case, because of data between 2.5and 6.5 seconds.

7. Lower case, because of data between 6.5and 9 seconds.

8. Lower case, because of data between 9and 10 seconds.

Baseball Acceleration02:05, highSchool, numeric, > 1 min, normal.

A baseball goes from zero to 30 m/s in0.11 s.

What is its average acceleration?

Car at Speed Trap02:05, highSchool, multiple choice, < 1 min,fixed.

A car is moving at constant speed on thefreeway. The driver sees a patrol car at timet1 and rapidly slows down by around 10 milesper hour. After continuing at this speed for afew minutes, the driver at time t2 returns tothe earlier constant speed.

Let us plot the acceleration of the car as afunction of time; take the forward directionof motion as positive. Which of the followinggraphs correctly describes the car’s accelera-tion a(t)?

1.

t1

time

0

0a

t2

2.

t1

time

0

0a

t2

3.


t1

time

0

0a

t2

4.

t1

time

0

0a

t2

5.

t1

time

0

0a

t2

6.

t1

time

0

0a

t2

7.

t1

time

0

0a

t2

8.

t1

time

0

0a

t2


Part 1 of 2If a race car completes a 3 mi oval track in

58 s, what is its average speed?

Part 2 of 2Did the car accelerate?

1. Yes, the direction of the motionchanged.

2. No, the speed didn’t change.

3. Yes, the speed changed.


If your car goes from 0 mi/h to 60 mi/h in6 s, what is your average acceleration?

Conceptual 03 0302:05, highSchool, numeric, > 1 min, fixed.

The hare and the tortoise are at the startingline together. When the gun goes off, the haremoves off at a constant speed of 10 meters persecond. (Ignore the acceleration required toget the animal to this speed.) The tortoisestarts more slowly, but accelerates at a rateof 2 meters per second. Make a table showingthe positions of the two racers after 1 second,2 seconds, 3 seconds, and so forth.

How long will it be before the tortoisepasses the hare?

Describing Motion02:05, highSchool, multiple choice, > 1 min,


fixed.

Part 1 of 2A car initially at rest on a straight road

accelerates according to the acceleration vstime plot given below. Take forward to bethe positive direction.

t

a

t1 t2

t3 t4

Which of the following graphs schemati-cally describes the motion of the car?

1. The car goes forward and then goes back-ward, ending where it started.

2. The car beginning at rest, goes up to ahigh speed, stops moving, travels backward,and stops.

3. The car beginning at rest, acceleratesto a high speed, cruises for a short while,decelerates to a lower speed, then cruises.

4. The car beginning at rest, acceleratesto a low speed, comes to a stop, acceleratesbackwards and cruises moving in reverse.

5. The car goes backward and then goesforward.

6. The car goes forward and then goes back-ward, ending behind where it started.

Part 2 of 2Which of the following graphs describes thevelocity vs time of the car?

1.t

v

t1 t2 t3 t4

2. t

v

t1t2 t3 t4

3. t

v

t1

t2 t3t4

4. t

v

t1

t2 t3t4

5. t

v

t1 t2

t3 t4

6. t

v

t1 t2

t3t4

7. t

v

t1 t2

t3 t4

8. t

v

t1 t2

t3 t4

10. None of these graphs is correct.

Dimensional Analysis 070102:05, highSchool, multiple choice, > 1 min,fixed.

Consider the following set of equations,where s, s0, x and r have units of length,


t has units of time, v has units of velocity,g and a have units of acceleration, and k isdimensionless.

Which one is dimensionally incorrect?

1. t =v

a+x

v

2. a = g +k v

t+v2

s0

3. t = k

√

s

g+a

v

4. v2 = 2 a s+k s v

t

5. s = s0 + v t+v2

a


Light travels in a straight line at a constantspeed of 300,000 m/s.

What is the acceleration of light?

1. 300,000 m/s2

2. 300.0 m/s2

3. 30 m/s2

4. 0 m/s2

5. All are wrong.


Can an object reverse its direction of travelwhile maintaining a constant acceleration?

1. Yes; a ball tossed upward reverses itsdirection of travel at its highest point.

2. No; the direction of the speed is alwaysthe same as the direction of the acceleration.

3. Yes; a ball thrown toward a wall bouncesback from the wall.

4. No; if the acceleration is constant, thedirection of the speed remains unchanged.

5. All are wrong.


You drive north on a highway, then, with-out changing speed, you round a curve anddrive east.

What is the change of your velocity andyour acceleration?

1. The velocity does not change; the accel-eration changes.

2. The velocity changes; the accelerationdoes not change.

3. Both velocity and acceleration change.

4. Neither velocity nor accelerationchange.

5. It cannot be determined by the informa-tion given.


Harry says acceleration is how fast you go.Carol says acceleration is how fast you getfast. They look to you for confirmation.

Who is correct?

1. Harry is correct.

2. Carol is correct.

3. They are both correct in different as-pects.

4. Neither is correct.

5. It cannot be determined by the informa-


tion given.


Starting from rest, Car 1 accelerates to aspeed of 30 km/h, Car 2 accelerates to a speedof 35 km/h, Car 3 accelerates backwards to aspeed of 40 km/h, and Car 4 is still.

Which car underwent the greatest acceler-ation?

1. Car 1

2. Car 2

3. Car 3

4. Car 4



Which of the following is an example ofsomething that undergoes acceleration whilemoving at constant speed?

1. A car making a circle in a parking lot

2. A football flying in the air

3. A car moving straight backwards on theroad

4. A man standing in an elevator

5. None of these. An object that undergoesan acceleration has to change its speed


What is not an example wherein the accel-eration of a body is opposite in direction to

its velocity?

1. A football tossed up and rising

2. A car braking to a stop

3. An apple falling from a tree

4. A tennis ball being hit by a racket

5. A swimmer entering a water pool byjumping

Hewitt CP9 03 E1902:05, highSchool, multiple choice, < 1 min,normal.

Which is greater, an acceleration from25 km/h to 30 km/h or an acceleration from96 km/h to 100 km/h if both occur during thesame time?

1. from 25 km/h to 30 km/h

2. from 96 km/h to 100 km/h

3. They are equal.

4. More inforation needed to answer thequestion.


What is the acceleration of a vehicle thatchanges its velocity from 100 km/h to a deadstop in 10 s ?

Hockey Puck Acceleration02:05, highSchool, multiple choice, < 1 min,fixed.

Henry hits a hockey puck at time, t ≈ t0,which is stopped by a net starting at time,t ≈ t1.

Which of the following curves could de-scribe the acceleration of the hockey puck?


1.t

a

t0

t1

2.

ta t0t1

3.t

a

t0

t1

4.

ta t0t1

5.t

a

t0

t1

6.

ta t0t1

7. t

a

t0

t1

8. ta t0t1

10. None of these graphs are correct.

Holt SF 02B 0102:05, highSchool, numeric,< 1min, wording-variable.

When the shuttle bus comes to a suddenstop to avoid hitting a dog, it acceleratesuniformly at −4.1 m/s2 as it slows from 9.0m/s to 0 m/s.

Find the time interval of acceleration forthe bus.

Holt SF 02B 0202:05, highSchool, numeric,> 1min, wording-variable.

A car traveling at 7.0 m/s accelerates 2.5m/s2 to reach a speed of 12.0 m/s.

How long does it take for this accelerationto occur?


With an average acceleration of −0.50m/s2, how long will it take a cyclist to bring abicycle with an initial speed of 13.5 m/s to acomplete stop?


Turner’s treadmill starts with a velocity of−1.2 m/s and speeds up at regular intervalsduring a half-hour workout. After 25 min, thetreadmill has a velocity of −6.5 m/s.

What is the average acceleration of thetreadmill during this period?


Part 1 of 2Suppose a treadmill has an average acceler-

ation of 0.0047 m/s2.a) How much does its speed change after

5.0 min?


Part 2 of 2b) If the treadmill’s initial speed is 1.7 m/s,what will its final speed be?


A car traveling in a straight line has a ve-locity of +5.0 m/s. After an acceleration of0.75 m/s2, the car’s velocity is +8.0 m/s.

In what time interval did the accelerationoccur?



of an object along a straight path as shown inthe figure below.

−6−5−4−3−2−10

1

2

3

0 1 2 3 4 5 6 7 8 9

�

�

�

�

� �

� �

time (s)

velocity

(m/s)

Find the average acceleration during thetime interval 0 s to 3 s.

Part 2 of 6Find the average acceleration during the timeinterval 3 s to 6 s.

Part 3 of 6Find the average acceleration during the timeinterval 0 s to 9 s.

Part 4 of 6Find the instantaneous acceleration at 2 s.




Part 1 of 3A train travels between stations 1 and 2,

as shown in the figure. The engineer of thetrain is instructed to start from rest at station1 and accelerate uniformly between points Aand B, then coast with a uniform velocity be-tween points B and C, and finally accelerateuniformly between points C and D until thetrain stops at station 2. The distances AB,BC, and CD are all equal, and it takes 5.00min to travel between the two stations. As-sume that the uniform accelerations have thesame magnitude, even when they are oppositein direction.

Station A Station B

A B C D

a) How much of this 5.00 min period doesthe train spend between points A and B?

Part 2 of 3b) How much of this 5.00 min period does thetrain spend between points B and C?

Part 3 of 3c) How much of this 5.00 min period does thetrain spend between points C and D?


A tennis ball with a velocity of +10.0 to


the right is thrown perpendicularly at a wall.After striking the wall, the ball rebounds inthe opposite direction with a velocity of−8.00m/s to the left.

If the ball is in contact with the wall for0.012 s, what is the average acceleration ofthe ball while it is in contact with the wall?


Is it possible for a particle’s instantaneousvelocity and instantaneous acceleration to beof the opposite sign at a given instant in time?

1. yes

2. no

3. need more information to answer theproblem

Stroboscopic Analysis02:05, highSchool, multiple choice, > 1 min,fixed.

Part 1 of 2A particle’s position, captured by a strobe

camera, is shown below. The positions havebeen labeled times t0 through t8. The timeintervals are equally separated.

t0

t1

t2

t3

t4t5t6t8

t5t6

West East

North

South

Describe the instantaneous velocity vectorsfor successive instances.

1. Pointing Southward and decreasing inmagnitude.

2. Pointing Northward and constant in mag-nitude.

3. Pointing Northward and increasing inmagnitude.

4. Pointing Northward and decreasing inmagnitude.

5. Pointing Southward and constant in mag-nitude.

6. Pointing Southward and increasing inmagnitude.

7. Cannot be determined from the giveninformation.

Part 2 of 2Which of the following can describe the in-stantaneous acceleration vectors of the par-ticle at the successive intervals shown in thefigure.

1. Pointing Northward and constant in mag-nitude.

2. Pointing Northward and increasing inmagnitude.

3. Pointing Northward and decreasing inmagnitude.

4. Pointing Southward and constant in mag-nitude.

5. Pointing Southward and increasing inmagnitude.

6. Pointing Southward and decreasing inmagnitude.

7. Cannot be determined from the giveninformation.

SWCT Sign of A and V02:05, highSchool, multiple choice, < 1 min,fixed.


A car going north on Guadalupe ap-proaches a red light at 24th street. The driverapplies the brakes. Which of the following isthen true?

1. a < 0, v < 0

2. a < 0, v > 0

3. a = 0, v < 0

4. a = 0, v > 0

5. a > 0, v < 0

6. a > 0, v > 0

Velocity vs Time 0702:05, highSchool, numeric, > 1 min, normal.

Part 1 of 5The scale on the horizontal axis is 5 s per

division and on the vertical axis 4 m/s perdivision. The initial position is 50 m.

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9

v(t)

time × ( 5 s )

velocity×

(4m/s

)

What is the initial velocity?

Part 2 of 5What is the position when t = 0?

Part 3 of 5What is the position when t = 30 s?

Part 4 of 5What is the acceleration is represented by thegraph?

Part 5 of 5In which direction is the motion?

1. forward

2. backward

3. Unable to determine.

Velocity vs Time 1302:05, highSchool, numeric, < 1 min, normal.

Part 1 of 2The velocity v(t) of some particle is plotted

as a function of time on the graph below.The scale on the horizontal axis is 9 s per

grid square and on the vertical axis 2 m/s pergrid square.

Initially, at t = 0 the particle is at x0 =60 m.

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9

v(t)

time × (9 s)

velocity×

(2m/s)

What is the position x of the particle attime t = 36 s?

Part 2 of 2What is the particle’s acceleration?

Zero Change in Velocity02:05, highSchool, multiple choice, < 1 min,fixed.

Assume: Quantities are instantaneous un-less stated otherwise.

The change in velocity ∆v of an object iszero over a short time interval ∆t.

Which of the following must be true?


1. The object must be at rest.

2. The object must have constant accelera-tion over the interval.

3. The object must have constant velocityover the interval.

4. The object must have zero average accel-eration over the interval.

5. The object must have zero average veloc-ity over the interval.

6. The object must be changing position.

7. The object must begin and end at thesame position.

8. Nothing can be determined without addi-tional information.

Chapter 2, section 6, One-Dimensional Motion with Constant Acceleration 66

Concept 07 5202:06, highSchool, numeric, > 1 min, normal.

This question is typical on some driver’slicense exams: A car moving at 55 km/h skids14 m with locked brakes.

How far will the car skid with locked brakesat 137.5 km/h?

Holt SF 02C 0102:06, highSchool, numeric,> 1min, wording-variable.

A car accelerates uniformly from rest to aspeed of 23.7 km/h in 6.5 s.

Find the distance the car travels during thistime.


When Maggie applies the brakes of her car,the car slows uniformly from 15.0 m/s to 0m/s in 2.50 s.

How many meters before a stop sign mustshe apply her brakes in order to stop at thesign?


Hint: To answer this question, calculate thedistance the plane travels while it is comingto a rest.

A jet plane lands with a speed of 100 m/sand can accelerate uniformly at a maximumrate of −5.0 m/s2 as it comes to rest.

Can this plane land at an airport where therunway is 0.80 km long?

Holt SF 02C 0402:06, highSchool, numeric, > 1 min, normal.

A driver in a car traveling at a speed of78 km/h sees a cat 101 m away on the road.

How long will it take for the car to acceler-

ate uniformly to a stop in exactly 99 m?


A car enters the freeway with a speed of 6.4m/s and accelerates uniformly for 3.2 km in3.5 min.

How fast is the car moving after this time?

Holt SF 02D 0102:06, highSchool, numeric,> 1min, wording-variable.

Part 1 of 2A car with an initial speed of 23.7 km/h

accelerates at a uniform rate of 0.92 m/s2 for3.6 s.

a) Find the final speed of the car.

Part 2 of 2b) Find the displacement of the car after thattime.


Part 1 of 2An automobile with an initial speed of 4.30

m/s accelerates uniformly at the rate of 3.0m/s2.

a) Find the final speed of the car after 5.0s.

Part 2 of 2b) Find the displacement of the car after 5.0s.


Part 1 of 2A car starts from rest and travels for 5.0 s

with a uniform acceleration of −1.5 m/s2.a) What is the final velocity of the car?


Part 2 of 2b) How far does the car travel in this timeinterval?


Part 1 of 2A driver of a car traveling at 15.0 m/s ap-

plies the brakes, causing a uniform accelera-tion of −2.0 m/s2.

a) How long does it take the car to acceler-ate to a final speed of 10.0 m/s?

Part 2 of 2b) How far has the car moved during thebraking period?

Holt SF 02E 0102:06, highSchool, numeric,< 1min, wording-variable.

A baby sitter pushing a stroller starts fromrest and accelerates uniformly at a rate of0.500 m/s2.

What is the velocity of the stroller after ithas traveled 6.32 m?

Holt SF 02E 0202:06, highSchool, numeric,> 1min, wording-variable.

Part 1 of 3A car traveling initially at +7.0 m/s accel-

erates uniformly at the rate of +0.80 m/s2 fora distance of 245 m.

a) What is its velocity at the end of theacceleration?

Part 2 of 3b) What is its velocity after it accelerates for125 m?

Part 3 of 3c) What is its velocity after it accelerates for67 m?

Holt SF 02E 03


Part 1 of 2A car accelerates uniformly in a straight

line from rest at the rate of 2.3 m/s2.a) What is the speed of the car after it has

traveled 55 m?

Part 2 of 2b) How long does it take the car to travel 55m?


A certain car is capable of accelerating at auniform rate of 0.85 m/s2.

What is the magnitude of the car’s displace-ment as it accelerates uniformly from a speedof 83 km/h to one of 94 km/h?

Holt SF 02E 0502:06, highSchool, numeric, > 1 min, normal.

An aircraft has a lift off speed of 120 km/h.What minimum uniform acceleration does

this require if the aircraft is to be airborneafter a takeoff run of 240 m?


A motorboat accelerates uniformly from avelocity of 6.5 m/s to the west to a velocity of1.5 m/s to the west.

If its acceleration was 2.7 m/s2 to the east,how far did it travel during the acceleration?


A car traveling at +7.0 m/s accelerates atthe rate of 0.80 m/s2 for an interval of 2.0 s.

Find vf .



Part 1 of 2A snowmobile has an initial velocity of +3.0

m/s.a) If it accelerates at the rate of +0.50 m/s2

for 7.0 s, what is the final velocity?

Part 2 of 2b) If instead it accelerates at the rate of −0.60m/s2, how long will it take to reach a completestop?


Part 1 of 3A car moving westward along a straight,

level road increases its velocity uniformly from+16 m/s to +32 m/s in 10.0 s.

a) What was the car’s acceleration?

Part 2 of 3b) How far did it move while accelerating?

Part 3 of 3c) What was its average velocity?


A ball initially at rest rolls down a hill withan acceleration of 3.3 m/s2.

If it accelerates for 7.5 s, how far will itmove?


A bus slows down uniformly from 75.0km/h to 0 km/h in 21.0 s.

How far does it travel before stopping?


Part 1 of 2A car accelerates from rest at −3.00 m/s2.a) What is the velocity at the end of 5.0 s?

Part 2 of 2b) What is the displacement after 5.0 s?


A car accelerates uniformly from rest to aspeed of 65 km/h (18 m/s) in 12 s.

Find the distance the car travels during thistime.


Part 1 of 2A car starts from rest and travels for 5.0

s with a uniform acceleration of +1.5 m/s2.The driver then applies the brakes, causing auniform acceleration of −2.1 m/s2.

a) If the brakes are applied for 3.0 s, howfast is the car going at the end of the brakingperiod?

Part 2 of 2b) How far has it gone from its start?


A boy sledding down a hill accelerates at1.40 m/s2.

If he started from rest, in what distancewould he reach a speed of 7.00 m/s?



Part 1 of 2A plane lands with a velocity of +120 m/s

and accelerates at a maximum rate of −6.0m/s2.

a) From the instant the plane touches therunway, what is the minimum time neededbefore it can come to rest?

Part 2 of 2The plane is landing on a naval aircraft carrierthat is 0.80 km long.

b) What distance does the plane require toland?


Part 1 of 2A sailboat starts from rest and accelerates

at a rate of 0.21 m/s2 over a distance of 280 mm.

a) Find the magnitude of the boat’s finalvelocity.

Part 2 of 2b) How long does it take the boat to travelthis distance?


An elevator is moving upward 1.20 m/swhen it experiences an acceleration of 0.31m/s2 downward, over a distance of 0.75 m.

What will its final speed be?


Part 1 of 4Two students are on a balcony 19.6 m above

the street. One student throws a ball verti-cally downward at 14.7 m/s. At the sameinstant, the other student throws a ball verti-cally upward at the same speed. The second

ball just misses the balcony on the way down.a) What is the magnitude of the velocity of

the first ball as it strikes the ground?

Part 2 of 4b) What is the magnitude of the velocity ofthe second ball as it strikes the ground?

Part 3 of 4c) What is the difference in the time the ballsspend in the air?

Part 4 of 4d) How far apart are the balls 0.800 s afterthey are thrown?


A ranger in a national park is driving at56 km/h when a deer jumps onto the road65 m ahead of the vehicle. After a reactiontime of t s, the ranger applies the brakes toproduce an acceleration of −3.0 m/s2.

What is the maximum reaction time al-lowed if the ranger is to avoid hitting thedeer?


Part 1 of 2A speeder passes a parked police car at 30.0

m/s. Instantaneously, the police car startsfrom rest with a uniform acceleration of 2.44m/s2.

a) How much time pases before the speederis overtaken by the police car?

Part 2 of 2b) How far does the speeder get before beingovertaken by the police car?

Holt SF 02Rev 52 5302:06, highSchool, numeric,> 1min, wording-variable.


Part 1 of 5An ice sled powered by a rocket engine

starts from rest on a large frozen lake andaccelerates at 13.0 m/s2. At t1 the rocketengine is shut down and the sled moves withconstant velocity v for another t2 s. The totaldistance traveled by the sled is 5.30 × 103 mand the total time is 90.0 s.

a) Find t1.

Part 2 of 5b) Find t2.

Part 3 of 5c) Find v.

Part 4 of 5At the 5800 m mark, the sled begins to accel-erate at −7.0 m/s2.

d) What is the final position of the sledwhen it comes to rest?

Part 5 of 5e) How long does it take for the sled to cometo rest?


Part 1 of 4A professional race-car driver buys a car

that can accelerate at 5.9 m/s2. The racerdecides to race against another driver in asouped-up stock car. Both start from rest,but the stock-car driver leaves 1.0 s before thedriver of the sports car. The stock car moveswith a constant acceleration of +3.6 m/s2.

a) Find the time it takes the sports-cardriver to overtake the stock-car driver.

Part 2 of 4b) Find the distance the two drivers travelbefore they are side by side.

Part 3 of 4c) Find the velocity of the race car when thetwo drivers are side by side.

Part 4 of 4d) Find the velocity of the stock car when thetwo drivers are side by side.


Part 1 of 3Two cars are traveling along a straight line

in the same direction, the lead car at 25 m/sand the other car at 35 m/s. At the momentthe cars are 45 m apart, the lead driver ap-plies the brakes, causing the car to have anacceleration of −2.0 m/s2.

a) How long does it take for the lead car tostop?

Part 2 of 3Assume that the driver of the chasing carapplies the brakes at the same time as thedriver of the lead car.

b) What must the chasing car’s minimumnegative acceleration be to avoid hitting thelead car?

Part 3 of 3c) How long does it take the chasing car tostop?

Linear Bicycle02:06, highSchool, numeric, > 1 min, normal.

Given: A bicycle has a speed of 6 m/sat t1 = 3.4 s and a constant acceleration of3 m/s2 .Given: The bicycle is at the origin (on thepositive x-axis) when t0 = 1.6 s.

What position does the bicycle have withrespect to the origin at t2 = 6.9 s?



along a straight line with an initial position of


x0 = 10 m.

−4−3−2−10

1

2

3

4

5

6

7

8

9

1 2 3 4 5 6 7 8 9

�

�

�

�

�

time (s)

velocity

(m/s)

What is the velocity at 2 seconds?



Part 4 of 5What is the velocity at 8 seconds?




along a straight line with an initial position ofx0 = 10 m.

−2−10

1

2

3

4

5

1 2 3 4 5 6 7 8 9

�

�

�

�

�

time (s)

velocity

(m/s)

What is the velocity at 2 seconds?




Velocity vs Time 04 e102:06, highSchool, numeric,< 1min, wording-variable.

Consider the plot below describing motionalong a straight line with an initial position ofx0 = 10 m.

−2−10

1

2

3

4

5

1 2 3 4 5 6 7 8 9

�

�

�

�

�

time (s)

velocity

(m/s)

What is the position at 9 seconds?

Velocity vs Time 1502:06, highSchool, numeric,> 1min, wording-


variable.

Part 1 of 4Consider the plot below describing the ve-

locity of a particle along a straight line withan initial position of 0 m and an initial veloc-ity of 0 m/s.

−8−7−6−5−4−3−2−10

1

2

3

4

0 1 2 3 4 5 6 7 8 9

� �

� �

� �

time (s)

velocity

(m/s)

What is the acceleration at 6 s?

Part 2 of 4Calculate the distance traveled (magnitudeof the position displacement) after the cartravels the first 7 s.

Part 3 of 4Calculate the position displacement after thecar traveled from 7 s to 9 s.


Chapter 2, section 7, Freely Falling Objects 73

Acceleration of Falling Object02:07, highSchool, multiple choice, < 1 min,fixed.

If you drop an object, it accelerates down-ward at 9.8m/s2 (in the absence of air resis-tance). If instead you throw it downward, itsdownward acceleration after release is

1. less than 9.8m/s2

2. 9.8m/s2

3. more than 9.8m/s2

Ball Dropped From Rest 0202:07, highSchool, numeric, > 1 min, normal.

Part 1 of 3A ball is dropped from rest at point O.

After falling for some time, it passes by awindow of height 3 m and it does so duringtime 0.3 s.

The acceleration of gravity is 9.8 m/s2 .

O

A

B

3 m

� ��

�

�

�

�

�

�

�

�

�

x

y

The ball accelerates all the way down; letvA be its speed as it passes the window’s topA and vB its speed as it passes the window’sbottom B.

How much did the ball speed up as it passedthe window; i.e., calculate ∆vdown = vB−vA ?

Part 2 of 3Calculate the speed vA at which the ballpasses the window’s top.

Part 3 of 3Now consider a new situation:

The ball is thrown upward from the ground

with an initial velocity that takes exactly thesame time tBA = tAB = 0.3 s to pass by thewindow, with the ball moving up rather thandown.

Consider the ball’s slowdown during thistime:

Let v′B be the ball’s speed (do not confusethe speed with the velocity) as it passes thewindow’s bottom on the way up and let v′A beits speed as it passes the window’s top, also inits way up.

How does the ball’s slowdown

∆vup = v′B − v′Acompare to its speedup ∆vdown on the waydown?

1. ∆vup > ∆vdown.

2. ∆vup = ∆vdown.

3. ∆vup < ∆vdown.

4. ∆vup > ∆vdown if the mass of the ballis less than 0.1 kg and ∆vup < ∆vdown if themass of the ball is greater than 0.1 kg

5. ∆vup < ∆vdown if the mass of the ballis less than 0.1 kg and ∆vup > ∆vdown if themass of the ball is greater than 0.1 kg

Ball Dropped From Rest 0302:07, highSchool, numeric, > 1 min, normal.

Part 1 of 2A ball is dropped from rest at point O

(height unknown). After falling for sometime, it passes by a window of height 3 mand it does so during time tAB = 0.3 s.


O

A

B

3 m

� ��

�

�

�

�

�

�

�

�

�

x

y


The ball accelerates all the way down; letvA be its speed as it passes the window’s topA and vB its speed as it passes the window’sbottom B.

How much did the ball speed up as it passedthe window; i.e., calculate ∆vdown = vB−vA ?

Part 2 of 2Calculate the speed vA at which the ballpasses the window’s top.

Ball M 0102:07, highSchool, multiple choice, > 1 min,normal.

A ball is thrown upward. Its initial ver-tical speed v0, acceleration of gravity g, andmaximum height hmax are shown in the figurebelow.

Neglect: Air resistance. The accelerationof gravity is 9.8 m/s2 .

�

�

�

�

�

�

�

�

� � �

�

�

�

�

�

�

�

�

�

v 0

9.8m/s

2

hm

ax

What is its maximum height, hmax (interms of the initial speed v0)?

1. hmax =v20

2 g

2. hmax =3 v2

0

4 g

3. hmax =5 v2

0

8 g

4. hmax =

√5 v2

0

2√2 g

5. hmax =v20

4 g

6. hmax =v20√2 g

7. hmax =v20

g

8. hmax =

√3 v2

0

2 g

9. hmax =

√3 v2

0

2√2 g




�

�

�

�

�

�

�

�

� � �

�

�

�

�

�

�

�

�

�

v 0

9.8m/s

2

hm

ax

What is its initial vertical speed, v0 (interms of the maximum height hmax)?

1. v0 =√

2 g hmax

2. v0 =√

g hmax

3. v0 = 2√

g hmax

4. v0 =√2 g hmax


5. v0 =

√

1

2g hmax

6. v0 =1

2

√

g hmax

7. v0 =1√2g hmax

8. v0 =g√2hmax

9. v0 =√

2 g hmax



Given: g = 9.8 m/s2 .Neglect: Air resistance.

�

�

�

�

�

�

�

�

� � �

�

�

�

�

�

�

�

�

�

v 0

9.8m/s

2

hm

ax

Whatis its time interval, tup (in terms ofthe initial speed v0), between the release ofthe ball and the time it reaches its maximumheight?

1. tup =v0

g

2. tup =v0

2 g

3. tup =v0

4 g

4. tup =v0√2 g

5. tup =2 v0

g

6. tup =4 v0

g

7. tup =

√3 v0

g

8. tup =

√2 v0

g

9. tup =

√2 v0√3 g




�

�

�

�

�

�

�

�

� � �

�

�

�

�

�

�

�

�

�

v 0

9.8m/s

2

hm

ax

What is its time interval, tup (in terms ofthe maximum height hmax), between the re-lease of the ball and the time it reaches itsmaximum height?

1. tup =

√

2hmax

g

2. tup =

√

4hmax

g


3. tup = 2

√

hmax

g

4. tup =

√

hmax

2 g

5. tup =

√2 g

hmax

6. tup =

√4 g

hmax

7. tup =2√g

hmax

8. tup =

√g

2hmax

9. tup =hmax

g

10. tup =g

hmax


Part 1 of 2A ball is thrown upward. Its initial ver-

tical speed v0, acceleration of gravity g, andmaximum height hmax are shown in the figurebelow.


�

�

�

�

�

�

�

�

� � �

�

�

�

�

�

�

�

�

�

v 0

9.8m/s

2

hm

ax

What is its maximum height, hmax (interms of the initial speed v0)?

1. hmax =v20

2 g

2. hmax =3 v2

0

4 g

3. hmax =5 v2

0

8 g

4. hmax =

√5 v2

0

2√2 g

5. hmax =v20

4 g

6. hmax =v20√2 g

7. hmax =v20

g

8. hmax =

√3 v2

0

2 g

9. hmax =

√3 v2

0

2√2 g

Part 2 of 2Find the speed v

Aof the ball (in terms of

the initial speed v0) as the ball passes a pointA, which is at one quarter of the maximum

heighthmax

4.

1. vA=

√3 v0

2

2. vA=

3 v0

8

3. vA=

3 v0

4

4. vA=

5 v0

8

5. vA=

√5 v0

2√2

6. vA=v0

2

7. vA=

v0√2

8. vA=v0

4

9. vA=

√3 v0

2√2

Ball M 06


02:07, highSchool, multiple choice, > 1 min,normal.

Part 1 of 2A ball is thrown upward. After reaching

a maximum height, it continues falling backtowards Earth. On the way down, the ballis caught at the same height at which it wasthrown upward.


Its initial vertical speed v0, accelerationof gravity g, and maximum height hmax areshown in the figure below.

�

�

�

�

�

�

�

�

��

�

�

�

�

�

�

�

�

�

v 0

9.8m/s

2

hm

ax

If the time (up and down) the ball remainsin the air is t, calculate its speed vf when itcaught.

1. vf =1

2g t

2. vf = 2 g t

3. vf = g t

4. vf = 4 g t

5. vf =1

4g t

6. vf =√2 g t

7. vf =1√2g t

Part 2 of 2

If the time the ball remains in the air is t,calculate the maximum height hmax the ballattained while in the air.

1. hmax =1

8g t2

2. hmax = 8 g t2

3. hmax = 2 g t2

4. hmax = g t2

5. hmax = 4 g t2

6. hmax =1

2g t2

7. hmax =1

4g t2


A ball is thrown upward. After reachinga maximum height, it continues falling backtowards Earth. On the way down, the ballis caught at the same height at which it wasthrown upward.


Its initial vertical speed v0, accelerationof gravity g, and maximum height hmax areshown in the figure below.

�

�

�

�

�

�

�

�

��

�

�

�

�

�

�

�

�

�

v 0

9.8m/s

2

hm

ax

If the time (up and down) the ball remains


in the air is ttrip, calculate its speed vf whenit caught.

1. vf =1

2g ttrip

2. vf = 2 g ttrip

3. vf = g ttrip

4. vf = 4 g ttrip

5. vf =1

4g ttrip

6. vf =√2 g ttrip

7. vf =1√2g ttrip

8. vf =1

3g ttrip

9. vf =2

3g ttrip

10. vf =

√2

3g ttrip

Ball N 0102:07, highSchool, numeric, > 1 min, normal.

A ball is thrown upward. Its initial verti-cal speed is 12.1 m/s , acceleration of gravityis 9.8 m/s2 , and maximum height hmax areshown in the figure below.

Neglect: Air resistance.

�

�

�

�

�

�

�

�

� � �

�

�

�

�

�

�

�

�

�

12.1

m/s

9.8m/s

2

hm

ax

What is its maximum height, hmax ?


A ball is thrown upward. Its initial verticalspeed is v0, acceleration of gravity is 9.8 m/s2 ,and maximum height is 7.4 m , as shown inthe figure below.


�

�

�

�

�

�

�

�

� � �

�

�

�

�

�

�

�

�

�

v 0

9.8m/s

27.4m

What is its initial vertical speed, v0?


A ball is thrown upward. Its initial verti-cal speed is 12.1 m/s , acceleration of gravityis 9.8 m/s2 , and maximum height hmax areshown in the figure below.



�

�

�

�

�

�

�

�

� � �

�

�

�

�

�

�

�

�

�

12.1

m/s

9.8m/s

2

hm

ax

What is its time interval, tup, between therelease of the ball and the time it reaches itsmaximum height?


A ball is thrown upward. Its initial verticalspeed, acceleration of gravity is 9.8 m/s2 , andmaximum height is 7.4 m , as shown in thefigure below.


�

�

�

�

�

�

�

�

� � �

�

�

�

�

�

�

�

�

�

v 0

9.8m/s

27.4m

What is its time interval, tup (in terms ofthe maximum height), between the release ofthe ball and the time it reaches its maximumheight?

Ball N 06

02:07, highSchool, numeric, > 1 min, normal.

Part 1 of 2A ball is thrown upward. After reaching

a maximum height, it continues falling backtowards Earth. On the way down, the ballis caught at the same height at which it wasthrown upward.

Neglect: Air resistance.Its initial vertical speed v0, acceleration of

gravity is 9.8 m/s2 , and maximum heighthmax are shown in the figure below.

�

�

�

�

�

�

�

��

� ��

�

�

�

�

�

�

�

�

v 0

9.8m/s

2

hm

ax

If the time (up and down) the ball remainsin the air is 1.64 s, calculate its speed when itcaught.

Part 2 of 2However, if the time the ball remains in theair is 1.77 s, calculate the maximum heighthmax the ball attained while in the air.

Ball Thrown Up 0502:07, highSchool, multiple choice, > 1 min,fixed.

Michael stands motionless holding a base-ball in his hand. After a while he tosses itupwards, and it travels up for a while be-fore turning about and heading towards theground. Define upwards to be positive.

Which of the following diagrams can de-scribe the vertical acceleration of the ball,while it is in Michael’s hand and after he letsit go, assuming it has not yet hit the ground?


1.

a

t

2.

a

t

3.

a

t

4.

at

5.

at

6.

at

Ball Thrown Up 0602:07, highSchool, multiple choice, > 1 min,fixed.

A child throws a steel ball straight up. Con-sider the motion of the ball only after it hasleft the child’s hand but before it touches theground, and assume that forces exerted by theair are negligible.

For these conditions, the force(s) acting onthe ball is

1. a downward force of gravity along with asteadily decreasing upward force.

2. a steadily decreasing upward force fromthe moment it leaves the child’s hand untilit reaches its highest point; on the way downthere is a steadily increasing downward forceof gravity as the object gets closer to earth.

3. an almost constant downward force ofgravity along with an upward force thatsteadily decreases until the ball reaches itshighest point; on the way down there is onlyan almost constant force of gravity.

4. an almost constant downward force ofgravity only.

5. None of these - the ball falls back to theground because of its natural tendency to reston the surface of the earth.

Ball Thrown Up 1002:07, highSchool, numeric, > 1 min, normal.

A ball is thrown straight up and reaches amaximum height in 5 s.


t

hA

y

tB

hB

tA

�

�

�

�

�

�

�

�

�

��

�

�

�

�

�

�

�

�

�

�

v0

O

B

A

tA is the timeto reach itsmaximumheight hA

Figure is not drawn to scale.What was its initial speed?


A ball is thrown straight up and reaches amaximum height of 5 m .



t

hA

y

tB

hB

tA

�

�

�

�

�

�

�

�

�

��

�

�

�

�

�

�

�

�

�

�

v0

O

B

A


Figure is not drawn to scale.What was its initial speed?


A ball is thrown straight up and passespoint B (at a height of 40 m above its startingpoint O) in 5 s.


t

hAy

5 s

40m

tA

�

�

�

�

�

�

�

�

�

��

�

�

�

�

�

�

�

�

�

�

v0

O

B

A


Figure is not drawn to scale.What was its initial speed ‖~v0‖ ?

Bullet Fired Up02:07, highSchool, numeric, > 1 min, normal.

A bullet is fired straight up from a gun witha muzzle velocity of 125 m/s.

The acceleration of gravity is 9.8 m/s2 .Neglecting air resistance, what will be its

displacement after 1 s?

Diving Board02:07, highSchool, multiple choice, > 1 min,wording-variable.

Part 1 of 2A boy steps off a 12-foot high diving board

with no initial vertical velocity, obeying thelaw

h = −16 t2 + v0 t+ s ,

where v0 is the velocity, t is in seconds, and sis the initial height.

How long does it take him to hit the water?

Part 2 of 2He springs off the diving board with an initialvertical velocity of 15 m/s.

How long does it take him to hit the wa-ter?

Dropped Tennis Ball02:07, highSchool, numeric, > 1 min, normal.

Part 1 of 3A tennis ball is dropped from 1.2 m above

the ground. It rebounds to a height of 1 m.The acceleration of gravity is 9.8 m/s2 .With what velocity does it hit the ground?

(Let down be negative.)

Part 2 of 3With what velocity does it leave the ground?

Part 3 of 3If the tennis ball were in contact with theground for 0.01 s, find the acceleration givento the tennis ball by the ground.

Dropped vs Thrown Balloons02:07, highSchool, numeric, > 1 min, normal.

You and your friend throw balloons filledwith water from the roof of a several storyapartment house. You simply drop a bal-loon from rest. A second balloon is throwndownward by your friend 2 s later with an ini-tial speed of 39.2 m/s. They hit the groundsimultaneously.

The acceleration of gravity is 9.8 m/s2 .Youcan neglect air resistance.

How high is the apartment house?

Free Fall 12 I202:07, highSchool, numeric, < 1 min, normal.

In order to open the clam it catches, aseagull will drop the clam repeatedly onto ahard surface from high in the air until the


shell cracks.The acceleration of gravity is 9.8 m/s2 .If a seagull flies to a height of 25 m, how

long will the clam take to fall?


Suppose that a freely falling object weresomehow equipped with an odometer.

Would the readings of distance fallen eachsecond indicate equal or different falling dis-tances for successive seconds?

1. Greater distances fallen in successive sec-onds

2. Smaller distances fallen in successive sec-onds

3. Equal distances fallen in successive sec-onds

4. Initially equal distances fallen in succes-sive seconds, then greater distances fallen insuccessive seconds

5. All are wrong.


If air resistance can be neglected, how doesthe acceleration of a ball that has been tossedstraight upward compare with its accelerationif simply dropped?

1. A ball tossed upward has a greater accel-eration.

2. A ball tossed upward has a smaller accel-eration.

3. The accelerations are the same; bothgreater than g.

4. The accelerations are the same; both

smaller than g.

5. Both accelerations equal g.


Someone standing at the edge of a cliffthrows a ball straight up at a certain speed,and another ball straight down with the sameinitial speed.

If the air resistance is negligible, which ballwill have the greater speed when it strikes theground below?

1. The ball thrown up

2. The ball thrown down

3. Both balls will have the same speed.

4. It depends on the height of the cliff.



If you drop an object, its acceleration to-ward the ground is 10 m/s2.

If you throw it down instead, what is itsacceleration?

1. Greater than 10 m/s2

2. Smaller than 10 m/s2

3. 10 m/s2

4. It depends on the force of throwing.

5. All are wrong.


Part 1 of 2


A ball is thrown straight up with an initialspeed of 30 m/s.

How high does it go? Assume the accelera-tion of gravity is 10 m/s2 .

Part 2 of 2How long is it in the air?

Hewitt CP9 03 P05b02:07, highSchool, numeric, > 1 min, normal.

Part 1 of 3The acceleration of gravity is 9.8 m/s2 .What is the instantaneous velocity of a

freely falling object 10 s after it is releasedfrom a position of rest?

Part 2 of 3What is its average velocity during this 10 sinterval? g = 9.8 m/s2.

Part 3 of 3How far will it fall during this time?

Hewitt CP9 03 P0902:07, highSchool, numeric, > 1 min, normal.

The acceleration of gravity is 10 m/s2 .If there were no air resistance, with what

speed would drops hit the Earth if they fellfrom a cloud 1234 m above the Earth’s sur-face?


When you jump upward, your hang time isthe time your feet are off the ground.

Does hang time depend on the vertical com-ponent of velocity when you jump, the hori-zontal component of velocity, or both?

1. The vertical component of your lift-offvelocity

2. The horizontal component of your lift-offvelocity

3. Both components


Holt SF 02F 0102:07, highSchool, numeric,> 1min, wording-variable.

Part 1 of 2A robot probe drops a camera off the rim of

a 239 m high cliff on Mars, where the free-fallacceleration is −3.7 m/s2.

a) Find the velocity with which it hits theground.

Part 2 of 2b) Find the time required for the camera toreach the ground.


Part 1 of 2A flowerpot falls from a windowsill 25.0 m

above the sidewalk.a) What is the velocity of the flowerpot

when it strikes the ground?

Part 2 of 2b) How much time does a passerby on thesidewalk below have to move out of the waybefore the flowerpot hits the ground?


Part 1 of 2A tennis ball is thrown vertically upward

with an initial velocity of +8.0 m/s.a) What will the ball’s velocity be when it

returns to its starting point?

Part 2 of 2b) How long will the ball take to reach itsstarting point?



Part 1 of 2Stephanie serves a volleyball from a height

of 0.80 m and gives it an initial velocity of+7.5 m/s straight up.

a) How high will the volleyball go?

Part 2 of 2b) How long will it take the ball to reach itsmaximum height?


Part 1 of 2Maria throws an apple vertically upward

from a height of 1.3 m with an initial velocityof +3.0 m/s.

a) Will the apple reach a friend in a treehouse 1.9 m above the ground?

1. No, the apple will reach 0.141284 mbelow the tree house

2. Yes, the apple will reach 0.141284 mabove the tree house

3. Yes, the apple will reach 1.6211 m abovethe tree house

4. Yes, the apple will reach 1.43761 m abovethe tree house

5. No, the apple will reach 1.6211 m belowthe tree house

6. No, the apple will reach 1.43761 m belowthe tree house

Part 2 of 2b) If the apple is not caught, how long will itbe in the air before it hits the ground?

Holt SF 02Rev 3802:07, highSchool, numeric,> 1min, wording-

variable.

A worker drops a wrench from the top of atower 80.0 m tall.

What is the velocity when the wrenchstrikes the ground?


A ball is thrown upward from the groundwith an initial speed of 25 m/s; at the sameinstant, a ball is dropped from rest from abuilding 15 m high.

After how long will the balls be at the sameheight?


Part 1 of 2A ball is thrown vertically upward with a

speed of 25.0 m/s from a height of 2.0 m.a) How long does it take to reach its highest

point?

Part 2 of 2b) How long does the ball take to hit theground after it reaches its highest point?


Part 1 of 4Suppose you are on another planet where

the acceleration of gravity is different thanthat on Earth; e.g., g 6= 9.8 m/s2 .

A ball is thrown directly upward into theair. A continuous measurement is made ofthe vertical position of the ball with respectto time. The result is a curve shown in thefigure below.


0 0.1 0.2 0.3 0.40

0.05

0.10

0.15

0.20

time (s)

position(m

)

How much time does the ball take to reachits maximum height of 0.2 m? (The requiredprecision of your answer is decreased becauseof graphical resolution in the figure.)

Part 2 of 4How much time does the ball take to reachone-half of its maximum height h = 0.1 m?

Part 3 of 4Estimate the slope of the position vs timegraph at several places; e.g., the first one-half height (h = 0.1 m), the full height (h =0.2 m), and the second one-half height (h =0.1 m).

Hint: Draw a velocity vs time graph. Youshould see a straight line. The acceleration ofgravity on your planet is the slope of this line.

What is the slope of the velocity vs timegraph?

Part 4 of 4What was the velocity of the ball when it wasinitially thrown upward?


A rocket moves upward, starting from restwith an acceleration of 29.4 m/s2 for 3.98 s.It runs out of fuel at the end of the 3.98 s, butdoes not stop.

How high does it rise above the ground?


Part 1 of 2A small first-aid kit is dropped by a rock

climber who is descending steadily at 1.3 m/s.a) After 2.5 s, what is the velocity of the

first-aid kit?

Part 2 of 2b) How far is the kit below the climber afterthe 2.5 s?


Part 1 of 2A small fish is dropped by a pelican that is

rising steadily at 0.50 m/s.a) After 2.5 s, what is the velocity of the

fish?

Part 2 of 2b) How far below the pelican is the fish afterthe 2.5 s?


Part 1 of 2A parachutist descending at a speed of 10.0

m/s loses a shoe at an altitude of 50.0 m.a) What is the velocity of the shoe just

before it hits the ground?

Part 2 of 2b) When does the shoe reach the ground?


Part 1 of 4A mountain climber stands at the top of a

50.0 m cliff hanging over a calm pool of water.The climber throws two stones vertically 1.0s apart and observes that they cause a singlesplash when they hit the water. The firststone has an initial velocity of +2.0 m/s.


a) What will the velocity of the first stonebe at the instant both stones hit the water?

Part 2 of 4b) How long after the release of the first stonewill the two stones hit the water?

Part 3 of 4c) What is the initial velocity of the secondstone when it is thrown?

Part 4 of 4d) What will the velocity of the second stonebe the instant both stones hit the water?


Part 1 of 3A model rocket is launched straight upward

with an initial speed of 50.0 m/s. It acceler-ates with a constant upward acceleration of2.00 m/s2 until its engines stop at an altitudeof 150 m.

a) What is the maximum height reached bythe rocket?

Part 2 of 3b) When does the rocket reach maximumheight?

Part 3 of 3c) How long is the rocket in the air?

Kinematics02:07, highSchool, multiple choice, < 1 min,fixed.

If you drop an object in the absence ofair resistance, it accelerates downward at 9.8m/s2.

If instead you throw it downward, its down-ward acceleration after release is

1. less than 9.8 m/s2.

2. equal to 9.8 m/s2.

3. more than 9.8 m/s2.

Kinematics302:07, highSchool, multiple choice, < 1 min,fixed.

You are throwing a ball straight up in theair. At the highest point, the ball’s velocityand acceleration are

1. velocity is zero, acceleration is zero

2. velocity is not zero, acceleration is zero

3. velocity is zero, acceleration is not zero

4. velocity is not zero, acceleration is notzero

Rock Tossed Upward02:07, highSchool, multiple choice, < 1 min,fixed.

Henry has tossed a rock upward. It hasalready been released and is moving upwardat time t = 0, turns around at time t ≈ t1,and hits the ground at time t ≈ t2.

Which of the following curves could de-scribes the acceleration of the rock?

1. t

a

t1t2

2.

ta t1t2

3.t

a

t1

t2


4.

ta t1t2

5.t

a

t1

t2

6.ta

t1

t2

7.t

a

t1 t2

8.

ta t1 t2


Velocity vs Time 1802:07, highSchool, numeric, > 1 min, fixed.

An object was suspended in a fixed placeand then allowed to drop in a free fall.

Taking down as the positive vertical di-rection, which graph correctly represents itsmotion as vertical velocity vs time?

1. t

y

2. t

y

3. t

y

4. t

y

5. t

y

6. t

y

7. t

y

8. t

y

Chapter 2, section 9, Relative Velocities 88

Approaching Cars02:09, highSchool, numeric, > 1 min, normal.

Part 1 of 3Two cars approach each other; both cars

are moving westward, one at 78 km/h, theother at 64 km/h.

What is the magnitude of the velocity of thefirst car relative to (in the frame of referenceof) the second car?

Part 2 of 3What is the direction of the resultant veloc-ity?

1. westward

2. eastward


Part 3 of 3After they pass, how will their relative veloc-ity change?

1. Less than before.

2. Greater than before.

3. No change.


Chapter 3, section 2, Vector and Scalar Quantities 89


Which of the following are scalar quantities,which are vector quantities?a) velocity.b) age.c) speed.d) acceleration.e) temperature.

1. Vectors: velocity, acceleration; Scalars:age, temperature, speed

2. Vector: velocity; Scalars: age, tempera-ture, speed, acceleration

3. Vectors: age, temperature, speed;Scalars: velocity, acceleration

4. All are vectors.

5. All are scalars.

Chapter 3, section 3, Some Properties of Vectors 90


When two vectors sum to zero, how mustthey be related?

1. The magnitudes are the same; the direc-tions are opposite.

2. Both magnitude and direction are thesame.

3. The magnitudes are different; the direc-tions are opposite.

4. The magnitudes are different; the direc-tions are the same.

5. All are wrong.

Chapter 3, section 5, Graphical Addition of Vectors 91

Holt SF 03B 05 graph03:05, highSchool, numeric,> 1min, wording-variable.

Part 1 of 2A superhero flies 225 m from the top of

a tall building at an angle of 25◦ below thehorizontal.

Draw the vectors to scale on a graph todetermine the answer.

a) What is the horizontal component of thesuperhero’s displacement?

Part 2 of 2b) What is the vertical component of the su-perhero’s displacement?

Holt SF 03Rev 50 graph03:05, highSchool, numeric,> 1min, wording-variable.

A hunter wishes to cross a river that is1.5 km wide and that flows with a speed of5.5 km/h. The hunter uses a small powerboatthat moves at a maximum speed of 13 km/hwith respect to the water.

What is the time necessary for crossingif the boat moves directly across the river?Draw the vectors to scale on a graph to deter-mine the answer.

Sum of Three Vectors 01 graph03:05, highSchool, numeric,> 1min, wording-variable.

Part 1 of 2Consider three force vectors ~F1, ~F2, and

~F3. The vector ~F1 has magnitude F1 = 87 Nand direction θ1 = 170◦; the vector ~F2 hasmagnitude F2 = 48 N and direction θ2 = 330◦;and the vector ~F3 has magnitude F3 = 65 Nand direction θ3 = 50◦.

All the direction angles θ are measured fromthe positive x axis: counter-clockwise for θ >0 and clockwise for θ < 0.


What is the magnitude of the resultant vec-

tor ‖~F‖, where ~F = ~F1 + ~F2 ?

Part 2 of 2Note: Give the angle in degrees, use coun-terclockwise as the positive angular direction,between the limits of −180◦ and +180◦ fromthe positive x axis.

What is the direction of this resultant vec-tor ~F?

Sum of Two Vectors 01 graph03:05, highSchool, numeric,> 1min, wording-variable.

Part 1 of 2Given two vectors ~F1, and ~F2. Where the

magnitude of these vectors are F1 = 53 N ,and F2 = 66 N . And where θ1 = 240◦ , andθ2 = 25◦ .

The angles are measure from the positive xaxis with the counter-clockwise angular direc-tion as positive.


What is the magnitude of the resultant vec-tor ‖~F‖, where ~F = ~F1 + ~F2 ?



Sum of Two Vectors 02 graph03:05, highSchool, multiple choice, > 1 min,wording-variable.

Part 1 of 2Given two vectors ~F1, and ~F2. Where the

magnitude of these vectors are F1 = 53 N ,and F2 = 66 N . And where θ1 = 240◦ , andθ2 = 25◦ .

The angles are measure from the positive xaxis with the counter-clockwise angular direc-tion as positive.


Chapter 3, section 5, Graphical Addition of Vectors 92

What is the magnitude of the resultant vec-tor ‖~F‖, where ~F = ~F1 + ~F2 ?

1. 37.871 N

2. 85.5559 N

3. 132.714 N

4. 101.602 N

5. 63.8812 N

6. 108.789 N

7. 79.9939 N

8. 44.5851 N



1. −28.39◦

2. −138.325◦

3. 44.2271◦

4. 119.588◦

5. −174.157◦

6. −111.061◦

7. −68.1394◦

8. −2.21563◦

Chapter 3, section 6, Components of a Vector 93

Holt SF 03B 01 0203:06, highSchool, numeric, < 1 min, normal.

Part 1 of 2A truck travels beneath an airplane that is

moving 105 km/h at an angle of 25◦ to theground.

a) How fast must the truck travel to staybeneath the airplane?

Part 2 of 2b) What is the magnitude of the vertical com-ponent of the velocity of the plane?

Holt SF 03B 0303:06, highSchool, numeric, < 1 min, normal.

Part 1 of 2A truck travels up a hill with a 15◦ incline.

The truck has a constant speed of 22 m/s.a) What is the horizontal component of the

truck’s velocity?

Part 2 of 2b) What is the vertical component of thetruck’s velocity?


Part 1 of 2A cat climbs 5 m directly up a tree.a) What is the horizontal component of the

cat’s displacement?

Part 2 of 2b) What is the vertical component of the cat’sdisplacement?


Part 1 of 2A superhero flies 225 m from the top of

a tall building at an angle of 25◦ below thehorizontal.

a) What is the horizontal component of the

superhero’s displacement?

Part 2 of 2b) What is the vertical component of the su-perhero’s displacement?


Part 1 of 2A child rides a toboggan down a hill that

descends at an angle of 30.5◦ to the horizontal.The hill is 23.0 m long.

a) What is the horizontal component of thechild’s displacement?

Part 2 of 2b) What is the vertical component of thechild’s displacement?


Part 1 of 2A skier squats low and races down a(n) 18◦

ski slope. During a 5 s interval, the skieraccelerates at 2.5 m/s2.

a) What is the horizontal component ofthe skier’s acceleration (perpendicular to thedirection of free fall)?

Part 2 of 2b) What is the vertical component of theskier’s acceleration?


Part 1 of 2A submarine dives 110.0 m at an angle of

10.0◦ below the horizontal.a) What is the horizontal component of the

submarine’s displacement?

Part 2 of 2

Chapter 3, section 6, Components of a Vector 94

b) What is the vertical component of the sub-marine’s displacement?


Part 1 of 2A person walks 25.0◦ north of east for 3.10

km. Another person walks due north and dueeast to arrive at the same location.

a) How large is the east component of thissecond path?

Part 2 of 2b) How large is the north component of thissecond path?


Part 1 of 2A roller coaster travels 41.1 m at an angle

of 40.0◦ above the horizontal.a) How far does it move horizontally?

Part 2 of 2b) How far does it move vertically?

Chapter 3, section 7, Adding Vector Components 95


Part 1 of 3A girl delivering newspapers travels 5

blocks west, 8 blocks north, then 9 blockseast.

a) What is the magnitude of her resultantdisplacement?

Part 2 of 3b) Find the direction (measured from dueeast, with counterclockwise positive) of herdisplacement.

Part 3 of 3c) What is the total distance she travels?

RandomWalk 0203:07, highSchool, multiple choice, > 1 min,wording-variable.

All angles are measured in a counter-clockwise direction from the positive x-axis.

A hiker makes four straight-line walks (A,B, C, and D) in random directions andlengths starting at position (41 km, 41 km) ,listed below and shown below in the plot.

A 23 km at 79 ◦

B 12 km at 221 ◦

C 33 km at 248 ◦

D 26 km at 119 ◦

A

B

C

D

Scale: 10 km =

Figure: Drawn to scale.

Select the vector which will return the hikerto the starting point by identifying the vectorE (described below) with the diagram above.

1. ‖~E‖ = 30.4158 km , θe = 346.989 ◦

2. ‖~E‖ = 55.4945 km , θe = 89.3401 ◦

3. ‖~E‖ = 23.7827 km , θe = 103.694 ◦

4. ‖~E‖ = 57.0787 km , θe = 186.821 ◦

5. ‖~E‖ = 10.8179 km , θe = 275.905 ◦

6. ‖~E‖ = 20.5301 km , θe = 188.519 ◦

7. ‖~E‖ = 24.453 km , θe = 117.987 ◦

8. ‖~E‖ = 64.2649 km , θe = 299.548 ◦

9. ‖~E‖ = 46.6311 km , θe = 234.463 ◦

10. ‖~E‖ = 21.7927 km , θe = 272.92 ◦


All angles are measured in a counter-


clockwise direction from the positive x-axis.A hiker makes four straight-line walks (A,

B, C, and D) in random directions andlengths starting at position (41 km, 41 km) ,listed below and shown below in the plot.

A 11 km at 109 ◦

B 22 km at 151 ◦

C 33 km at 108 ◦

D 22 km at 279 ◦

Select the vector diagram which best repre-sents this hike.

1.

A

B

C

D

Scale: 10 km =

2.

A

BC

D

Scale: 10 km =

3.

AB

C

D

Scale: 10 km =

4.

A

B

C

D

Scale: 10 km =

5. A

B

C

D

Scale: 10 km =


6.

A

B

C

D

Scale: 10 km =



A hiker makes four straight-line walks (A,B, C, and D) in random directions andlengths starting at position (41 km, 41 km) ,listed below and shown below in the plot.

A 11 km at 109 ◦

B 22 km at 151 ◦

C 33 km at 108 ◦

Select the vector diagram which best repre-sents this hike.

1.

A

B

C

Scale: 10 km =

2.

A

B

C

Scale: 10 km =

3.

A

B

C

Scale: 10 km =

4.A

B

C

Scale: 10 km =


5.

AB

C

Scale: 10 km =

6.

A

B

C

Scale: 10 km =



A hiker makes three straight-line walks (A,B, and C) in random directions and lengthsstarting at position (41 km, 41 km) , listedbelow and shown below in the plot.

A 23 km at 79 ◦

B 12 km at 221 ◦

C 26 km at 242 ◦

A

B

C

Scale: 10 km =

Figure: Drawn to scale.

Select the vector which will return the hikerto the starting point by identifying the vectorD (described below) with the diagram above.

1. ‖~D‖ = 18.7838 km , θd = 26.06 ◦

2. ‖~D‖ = 17.8326 km , θd = 288.713 ◦

3. ‖~D‖ = 43.2406 km , θd = 215.54 ◦

4. ‖~D‖ = 48.7427 km , θd = 331.382 ◦

5. ‖~D‖ = 17.5237 km , θd = 100.625 ◦

6. ‖~D‖ = 43.9169 km , θd = 18.6803 ◦

7. ‖~D‖ = 38.5343 km , θd = 327.858 ◦

8. ‖~D‖ = 29.4472 km , θd = 252.107 ◦

9. ‖~D‖ = 33.7445 km , θd = 122.114 ◦

10. ‖~D‖ = 49.4222 km , θd = 3.51645 ◦

Vectors 0103:07, highSchool, multiple choice, > 1 min,wording-variable.

Vectors ~A, ~B, ~C, ~D, and ~E are shown in


the figure below. For convenience, the tails ofeach vector are arbitrarily located at (0,0).

y

−5 −3 −1 0 1 2 3 4 5

x

−5−4−3−2−101

23

45

A

B

C

D

E

Select the figure showing the resultant vec-tor ~R, where

~R = −~A+ ~B − ~C + ~D − ~E .

1.

y

−5 −3 −1 0 1 2 3 4 5

x

−5−4−3−2−1012345

R

2.

y

−5 −3 −1 0 1 2 3 4 5

x

−5−4−3−2−1012345

R

3.

y

−5 −3 −1 0 1 2 3 4 5

x

−5−4−3−2−1012345

R

4.

y

−5 −3 −1 0 1 2 3 4 5

x

−5−4−3−2−1012345

R

5. None of these figures is correct.


Vectors ~A, ~B, ~C, and ~D are shown in thefigure below. For convenience, the tails ofeach vector are arbitrarily located at (0,0).


y

−5 −3 −1 0 1 2 3 4 5

x

−5−4−3−2−101

23

45

AB

C

D


~R = −~A+ ~B − ~C + ~D .

1.

y

−5 −3 −1 0 1 2 3 4 5

x

−5−4−3−2−1012345

R

2.

y

−5 −3 −1 0 1 2 3 4 5

x

−5−4−3−2−101

23

45

R

3.

y

−5 −3 −1 0 1 2 3 4 5

x

−5−4−3−2−101

23

45

R

4.

y

−5 −3 −1 0 1 2 3 4 5

x

−5−4−3−2−1012345

R



Vectors ~A, ~B, and ~C are shown in thefigure below. For convenience, the tails ofeach vector are arbitrarily located at (0,0).


y

−5 −3 −1 0 1 2 3 4 5

x

−5−4−3−2−101

23

45

A

B

C


~R = −~A+ ~B − ~C .

1.

y

−5 −3 −1 0 1 2 3 4 5

x

−5−4−3−2−1012345

R

2.

y

−5 −3 −1 0 1 2 3 4 5

x

−5−4−3−2−101

23

45

R

3.

y

−5 −3 −1 0 1 2 3 4 5

x

−5−4−3−2−101

23

45

R

4.

y

−5 −3 −1 0 1 2 3 4 5

x

−5−4−3−2−1012345 R



Vectors ~A and ~B are shown in the figurebelow. For convenience, the tails of eachvector are arbitrarily located at (0,0).


y

−5 −3 −1 0 1 2 3 4 5

x

−5−4−3−2−101

23

45

AB


~R = −~A+ ~B .

1.

y

−5 −3 −1 0 1 2 3 4 5

x

−5−4−3−2−1012345

R

2.

y

−5 −3 −1 0 1 2 3 4 5

x

−5−4−3−2−101

23

45

R

3.

y

−5 −3 −1 0 1 2 3 4 5

x

−5−4−3−2−101

23

45

R

4.

y

−5 −3 −1 0 1 2 3 4 5

x

−5−4−3−2−1012345

R


Vectors 0503:07, highSchool, multiple choice, < 1 min,normal.

Vectors ~A and ~B are shown in the figurebelow. For convenience, the tails of eachvector are arbitrarily located at (0,0).


y

−5 −3 −1 0 1 2 3 4 5

x

−5−4−3−2−101

23

45 A

B


~R = ~A+ ~B .

1.

y

−5 −3 −1 0 1 2 3 4 5

x

−5−4−3−2−1012345

R

2.

y

−5 −3 −1 0 1 2 3 4 5

x

−5−4−3−2−101

23

45

R

3.

y

−5 −3 −1 0 1 2 3 4 5

x

−5−4−3−2−101

23

45

R

4.

y

−5 −3 −1 0 1 2 3 4 5

x

−5−4−3−2−1012345

R


Chapter 3, section 9, Vector Kinematics 104


Part 1 of 2A truck driver attempting to deliver some

furniture travels 8 km east, turns around andtravels 3 km west, and then travels 12 km eastto his destination.

a) What distance has the driver traveled?

Part 2 of 2b) What is the magnitude of the driver’s totaldisplacement?


Part 1 of 2While following the directions on a treasure

map, a pirate walks 45.0 m north, then turnsand walks 7.5 m east.

a) What is the magnitude of the sin-gle straight-line displacement that the piratecould have taken to reach the treasure?

Part 2 of 2b) At what angle with the north would hehave to walk?


Part 1 of 2Emily passes a soccer ball 6.0 m directly

across the field to Kara, who then kicks theball 14.5 m directly down the field to Luisa.

a) What is the magnitude of the ball’s totaldisplacement as it travels between Emily andLuisa?

Part 2 of 2b) How many degrees to the side of straightdown the field is the ball’s total displace-ment?

Holt SF 03A 04


Part 1 of 2A hummingbird flies 1.2 m along a straight

path at a height of 3.4 m above the ground.Upon spotting a flower below, the humming-bird drops directly downward 1.4 m to hoverin front of the flower.

a) What is the magnitude of the humming-bird’s total displacement?

Part 2 of 2Howmany degrees below the horizontal is thistotal displacement?


Part 1 of 2A plane travels 2.5 km at an angle of 35◦ to

the ground, then changes direction and travels5.2 km at an angle of 22◦ to the ground.

a) What is the magnitude of the plane’stotal displacement?

Part 2 of 2b) At what angle above the horizontal is theplane’s total displacement?

Holt SF 03C 0303:09, highSchool, numeric,< 1min, wording-variable.

Part 1 of 2During the rodeo, a clown runs 8.0 m north,

turns 35◦ east of north, and runs 3.5 m. Then,after waiting for the bull to come near, theclown turns due east and runs 5.0 m to exitthe arena.

a) What is the magnitude of the clown’stotal displacement?

Part 2 of 2b) How many degrees east of north is theclown’s total displacement?

Holt SF 03C 04



Part 1 of 2An airplane flying parallel to the ground

undergoes two consecutive displacements.The first is 75 km at 30.0◦ west of north,and the second is 155 km at 60.0◦ east ofnorth.

a) What is the magnitude of the plane’stotal displacement?

Part 2 of 2b) At what angle east of north is the plane’stotal displacement?


Part 1 of 2A golfer takes two putts to sink his ball in

the hole once he is on the green. The firstputt displaces the ball 6.00 m east, and thesecond putt displaces it 5.40 m south.

a) How large a displacement would put theball in the hole in one putt?

Part 2 of 2b) What is the direction (measured from dueeast, with counterclockwise positive) of thedisplacement?


A quarterback takes the ball from the lineof scrimmage, runs backward for 10.0 yards,then runs sideways parallel to the line ofscrimmage for 15.0 yards. At this point, hethrows a 50.0 yard forward pass straight downthe field.

What is the magnitude of the football’sresultant displacement?


Part 1 of 4Note: You are not given the direction

moved after any of the 90◦ turns, so therecould be more than one answer.

A shopper pushing a cart through a storemoves 40.0 m south down one aisle, thenmakes a 90◦ turn and moves 15.0 m. Hethen makes another 90◦ turn and moves 20.0m.

a) What is the magnitude of the small-est possible displacement the shopper couldhave?

Part 2 of 4b) At how many degrees from due south isthis displacement?

Part 3 of 4c) What is the magnitude of the largest pos-sible displacement the shopper could have?

Part 4 of 4d) At how many degrees from due south isthis displacement?


Part 1 of 2A person walks the path shown. The total

trip consists of four straight-line paths.

S

N

W E

100 m

300m

30.0◦

150m

200m

60.0◦

Note: Figure is not drawn to scale.a) At the end of the walk, what is the mag-

nitude of the person’s resultant displacementmeasured from the starting point?


Part 2 of 2b) What is the direction (measured from duewest, with counterclockwise positive) of theperson’s resultant displacement?


The eye of a hurricane passes over GrandBahama Island. It is moving in a direction60.0◦ north of west with a speed of 41.0 km/h.Exactly 3.00 hours later, the course of thehurricane shifts due north, and its speed slowsto 25.0 km/h, as shown.

How far from Grand Bahama is the hurri-cane 4.50 h after it passes over the island?

Chapter 4, section 1, Position and Displacement 107


Part 1 of 2A football player runs directly down the

field for 35 m before turning to the right atan angle of 25 ◦ from his original directionand running an additional 15 m before beingtackled.

a) What is the magnitude of the runner’stotal displacement?

Part 2 of 2b) At what angle to his original displacementis his total displacement (with counterclock-wise positive)?

Chapter 4, section 3, Average and Instantaneous Acceleration 108

Accelerations Along a Trajectory04:03, highSchool, multiple choice, < 1 min,fixed.

Part 1 of 3A boy throws a ball upward. Compare the

magnitudes of the gravitational accelerationsat three points along the path of the ball.Point A is before the ball reaches the top.

a) Point A on the way up.b) Point B is at the top.c) Point C is after it has passed the top andon the way down.

B

A

C

The magnitudes of the acceleration are re-lated as

1. aA= g .

2. aA< a

B.

Part 2 of 3The magnitudes of the acceleration are re-lated as

1. aB= 0 .

2. aB= a

A.

3. aB> a

C.

Part 3 of 3The magnitudes of the acceleration are re-lated as

1. aC< a

Band a

A< a

B.

2. aC= a

B= a

A.

Hewitt CP9 03 E17


Suppose that three balls are rolled simulta-neously from the top of a hill along the slopesas shown below.

1 2 3

Which one reaches the bottom first?

1. 1

2. 2

3. 3

4. They reach the bottom at the sametime.

5. 1 and 2

6. 2 and 3

7. 1 and 3

Chapter 4, section 5, Graphical Solutions 109

Walking on a Ship 01 graph04:05, highSchool, numeric,> 1min, wording-variable.

Part 1 of 2A ship cruises forward at vs = 4 m/s rel-

ative to the water. On deck, a man walksdiagonally toward the bow such that his pathforms an angle θ = 22◦ with a line perpen-dicular to the boat’s direction of motion. Hewalks at vm = 3 m/s relative to the boat.


θ

vs

vm

At what speed does he walk relative to thewater?

Part 2 of 2At what angle to his intended path does theman walk with respect to the water?

Walking on a Ship 02 graph04:05, highSchool, numeric,> 1min, wording-variable.

A ship cruises forward at vs = 4 m/s rel-ative to the water. On deck, a man walksdiagonally toward the bow such that his pathforms an angle θ = 22◦ with a line perpen-dicular to the boat’s direction of motion. Hewalks at vm = 3 m/s relative to the boat.


θ

vs

vm

At what speed does he walk relative to thewater?

Chapter 4, section 6, Projectile Motion 110

Ball Falling from an Airliner04:06, highSchool, multiple choice, < 1 min,wording-variable.

A bowling ball accidentally falls out of thecargo bay of an airliner as it flies along in ahorizontal direction.

Z

Y

X

W

U

V

As observed by a person standing on theground and viewing the plane as in the fig-ure, which path would the bowling ball mostclosely follow after leaving the airplane?

1.W

2. Z

3. Y

4. X

5. U

6. V

Baseball Toss v204:06, highSchool, numeric, > 1 min, normal.

A man can throw a ball a maximum hori-zontal distance of 75 m.

The acceleration of gravity is 9.8 m/s2 .How far can he throw the same ball verti-

cally upward with the same initial speed?

Concept 05 E3204:06, highSchool, multiple choice, > 1 min,fixed.

If you are standing in a bus that moves atconstant velocity and drop a ball from youroutstretched hand, you will see its path as avertical straight line.

How will the path appear to a friend stand-ing at the side of the road?

1. The path is a straight line orientatedvertically.

2. The path curves downward.

3. The path curves upward.

4. The path is a straight line slanteddown.

Conceptual 03 0404:06, highSchool, numeric, > 1 min, normal.

Someone in a car going past you at thespeed of 20 m/s drops a small rock from aheight of 2 m.

How far from the point of the drop will therock hit the ground? The acceleration due togravity is 9.8 m/s2.

Figuring Physics 2704:06, highSchool, multiple choice, < 1 min,fixed.

A projectile is fired from a horizontalspring-loaded gun aimed directly (along theline of sight) at a distant bull’s eye. Becauseof the pull of gravity during flight, the pro-jectile misses and hits a point at distance ybeneath the bull’s eye. To hit the bull’s eye,the gun should be aimed along a line of sightabove the bull’s eye, a vertical distance

1. of y, exactly.

2. slightly lower than y.

3. slightly higher than y.



A heavy crate accidentally falls from a high-flying airplane just as it flies directly above ashiny red Camaro parked in a parking lot.

Relative to the Camaro, where will thecrate crash?

1. The crate will hit the Camaro.

2. The crate will not hit the Camaro, butwill crash a distance beyond it determined bythe height and speed of the plane.

3. The crate will continue to fly and will notcrash.

4. The crate will hit the front part of thecar.


How does the vertical component of a pro-jectile’s motion compare with the motion ofvertical free fall when air resistance is negligi-ble?

1. Greater than that of free fall

2. Less than that of free fall

3. Identical to that of free fall



At what point in its trajectory does a bat-ted baseball have its minimum speed?

1. at the top

2. somewhere at the middle height

3. at the beginning point

4. at the end point


When a rifle fires at a distant target, whereshould the barrel be pointing?

1. directly at the target

2. above the target

3. below the target

4. to the left of the target

5. to the right of the target

6. diagonally from the target


An autographed baseball rolls off of a 0.70m high desk and strikes the floor 0.25 m awayfrom the desk.

The acceleration of gravity is 9.81 m/s2 .How fast was it rolling on the desk before it

fell off?


A cat chases a mouse across a 1.0 m hightable. The mouse steps out of the way, andthe cat slides off the table and strikes the floor2.2 m from the edge of the table.

The acceleration of gravity is 9.81 m/s2 .What was the cat’s speed when it slid off

the table?

Holt SF 03D 03 04



Part 1 of 2A pelican flying along a horizontal path

drops a fish from a height of 5.4 m. The fishtravels 8.0 m horizontally before it hits thewater below.

The acceleration of gravity is 9.81 m/s2 .a) What was the pelican’s initial speed?

Part 2 of 2b) If the pelican was traveling at the samespeed but was only 2.7 m above the water,how far would the fish travel horizontally be-fore hitting the water below?


In a scene in an action movie, a stunt manjumps from the top of one building to thetop of another building 4.0 m away. After arunning start, he leaps at an angle of 15◦ withrespect to the flat roof while traveling at aspeed of 5.0 m/s.

The acceleration of gravity is 9.81 m/s2 .To determine if he will make it to the other

roof, which is 2.5 m shorter than the build-ing from which he jumps, find his verticaldisplacement upon reaching the front edge ofthe lower building with respect to the tallerbuilding.


A golfer can hit a golf ball a horizontaldistance of over 300 m on a good drive.

What maximum height will a 310.0 m drivereach if it is launched at an angle of 25.0◦ tothe ground?


Part 1 of 2A baseball is thrown at an angle of 25◦

relative to the ground at a speed of 23.0 m/s.The ball is caught 41.3 m from the thrower.

The acceleration of gravity is 9.81 m/s2 .a) How long is it in the air?

Part 2 of 2b) How high is the tallest spot in the ball’spath?


Salmon often jump waterfalls to reach theirbreeding grounds.

The acceleration of gravity is 9.81 m/s2 .Starting 2.00 m from a waterfall 0.550 m

in height, at what minimum speed must asalmon jumping at an angle of 32.0◦ leave thewater to continue upstream?


Part 1 of 2A quarterback throws the football to a sta-

tionary receiver who is 31.5 m down the field.The football is thrown at an initial angle of40.0◦ to the ground.

The acceleration of gravity is 9.81 m/s2 .a) At what initial speed must the quarter-

back throw the ball for it to reach the receiver?

Part 2 of 2b) What is the ball’s highest point during itsflight?


The fastest recorded pitch in Major LeagueBaseball was thrown by Nolan Ryan in 1974.If this pitch were thrown horizontally, the ballwould fall 0.809 m (2.65 ft) by the time itreached home plate, 18.3 m (60 ft) away.



How fast was Ryan’s pitch?


Part 1 of 2A shell is fired from the ground with an

initial speed of 1.70×103 m/s (approximatelyfive times the speed of sound) at an initialangle of 55.0◦ to the horizontal.

The acceleration of gravity is 9.81 m/s2 .a) Neglecting air resistance, find the shell’s

horizontal range.

Part 2 of 2b) How long is the shell in motion?


Part 1 of 2A person standing at the edge of a seaside

cliff kicks a stone over the edge with a speedof 18 m/s. The cliff is 52 m above the water’ssurface, as shown.


18 m/s

52m

Note: Figure not drawn to scalea) How long does it take for the stone to fall

to the water?

Part 2 of 2b) With what speed does the stone strike thewater?

Holt SF 03Rev 37


A spy in a speed boat is being chased downa river by government officials in a faster craft.Just as the officials’ boat pulls up next to thespy’s boat, both boats reach the edge of a 5.0m waterfall. The spy’s speed is 15 m/s andthe officials’ speed is 26 m/s.

The acceleration of gravity is 9.81 m/s2 .How far apart will the two vessels be when

they land below the waterfall?


Part 1 of 2A place kicker must kick a football from a

point 36.0 m (about 39 yd) from the goal. Asa result of the kick, the ball must clear thecrossbar, which is 3.05 m high. When kicked,the ball leaves the ground with a speed of 20.0m/s at an angle of 53◦ to the horizontal.

The acceleration of gravity is 9.81 m/s2 .a) To determine if the ball clears the cross-

bar, what is its height with respect to thecrossbar when it reaches the plane of thecrossbar?

Part 2 of 2b) To determine if the ball approaches thecrossbar while still rising or while falling, whatis its vertical velocity at the crossbar?


A daredevil is shot out of a cannon at 45.0◦

to the horizontal with an initial speed of 25.0m/s. A net is positioned at a horizontal dis-tance of 50.0 m from the cannon from whichthe daredevil is shot.

The acceleration of gravity is 9.81 m/s2 .At what height above the cannon’s mouth

should the net be placed in order to catch thedaredevil?



Part 1 of 2When a water gun is fired while being

held horizontally at a height of 1.00 m aboveground level, the water travels a horizontaldistance of 5.00 m.

The acceleration of gravity is 9.81 m/s2 .a) Find the initial velocity of the water.

Part 2 of 2A child, who is holding the same gun in ahorizontal position, is sliding down a 45.0◦

incline at a constant speed of 2.00 m/s. Thechild fires the gun when it is 1.00 m above theground and the water takes 0.329 s to reachthe ground.

b) How far will the water travel horizon-tally?


Part 1 of 2A ship maneuvers to within 2.50 × 103 m

of an island’s 1.80 × 103 m high mountainpeak and fires a projectile at an enemy ship6.10 × 102 m on the other side of the peak,as illustrated. The ship shoots the projectilewith an initial velocity of 2.50 × 102 m/s atan angle of 75.0◦.


250m/s

75◦

2500 m610 m

1800 m

Note: Figure is not drawn to scalea) How close to the enemy ship does the

projectile land?

Part 2 of 2b) How close (vertically) does the projectilecome to the peak?


Part 1 of 3A ball player hits a home run, and the

baseball just clears a wall 7.00 m high located130.0 m from home plate. The ball is hit atan angle of 35.0◦ to the horizontal, and airresistance is negligible. Assume the ball is hitat a height of 1.0 m above the ground.

The acceleration of gravity is 9.81 m/s2 .a) What is the initial speed of the ball?

Part 2 of 3b) How much time does it take for the ball toreach the wall?

Part 3 of 3c) Find the speed of the ball when it reachesthe wall.


Part 1 of 2A daredevil jumps a canyon 12 m wide. To

do so, he drives a car up a 15◦ incline.The acceleration of gravity is 9.81 m/s2 .a) What minimum speed must he achieve

to clear the canyon?

Part 2 of 2b) If the daredevil jumps at this minimumspeed, what will his speed be when he reachesthe other side?


A 2.00 m tall basketball player attempts agoal 10.00 m from the basket (3.05 m high).



2 m3.05 m

10 m

v 045◦

If he shoots the ball at a 45.0◦ angle, atwhat initial speed must he throw the basket-ball so that it goes through the hoop withoutstriking the backboard?


A ball is thrown straight upward and re-turns to the thrower’s hand after 3.00 s in theair. A second ball is thrown at an angle of30.0◦ with the horizontal.

The acceleration of gravity is 9.81 m/s2 .At what speed must the second ball be

thrown so that it reaches the same height asthe one thrown vertically?


A 80 g autographed baseball rolls off ofa 1.2 m high table and strikes the floor ahorizontal distance of 0.8 m away from thetable.

The acceleration of gravity is 9.81 m/s2 .See the figure below.

1.2m

0.8 m

How fast was it rolling on the table beforeit fell off?

Holt SF 03Rev 58A04:06, highSchool, numeric, > 1 min, normal.

Part 1 of 2A 80 g autographed baseball slides off of

a 1.2 m high table and strikes the floor ahorizontal distance of 0.9 m away from thetable.

The acceleration of gravity is 9.81 m/s2 .See the figure below.

1.2m

0.9 m

How fast was it rolling on the table beforeit fell off?

Part 2 of 2What was the direction of the ball’s velocityjust before it hit the floor?

That is, at what angle (in the range−90◦ to+90◦ relative to the horizontal directed away


from the table) did the ball hit the floor?


Part 1 of 2A car is parked on a cliff overlooking the

ocean on an incline that makes an angle of24.0◦ below the horizontal. The negligentdriver leaves the car in neutral, and the emer-gency brakes are defective. The car rolls fromrest down the incline with a constant acceler-ation of 4.00 m/s2 and travels 50.0 m to theedge of the cliff. The cliff is 30.0 m above theocean.

The acceleration of gravity is 9.81 m/s2 .a) How long is the car in the air?

Part 2 of 2b) What is the car’s position relative to thebase of the cliff when the car lands in theocean?


Part 1 of 2A golf ball with an initial angle of 34◦

lands exactly 240 m down the range on alevel course.

The acceleration of gravity is 9.81 m/s2 .a) Neglecting air friction, what initial speed

would achieve this result?

Part 2 of 2b) Find the maximum height reached by theball.


Part 1 of 2A person can jump a horizontal distance of

3.0 m on Earth.a) How far could the person jump on the

moon, where the free-fall acceleration is g/6

and g = 9.81 m/s2?

Part 2 of 2b) How far could the person jump on Mars,where the acceleration due to gravity is0.38g?


A science student riding on a flatcar of atrain moving at a constant speed of a 10.0m/s throws a ball toward the caboose alonga path that the student judges as makingan initial angle of 60.0◦ with the horizontal.The teacher, who is standing on the groundnearby, observes the ball rising vertically.

The acceleration of gravity is 9.81 m/s2 .How high does the ball rise?


A football is thrown toward a receiver withan initial speed of 18.0 m/s at an angle of35.0◦ above the horizontal. At that instant,the receiver is 18.0 m from the quarterback.

The acceleration of gravity is 9.81 m/s2 .With what constant speed should the re-

ceiver run to catch the football at the level atwhich it was thrown?


Part 1 of 3A rocket is launched at an angle of 53◦

above the horizontal with an initial speed of75 m/s, as shown. It moves for 25 s alongits initial line of motion with an overall accel-eration of 25 m/s2. At this time its enginesfail and the rocket proceeds to move as a freebody.

The acceleration of gravity is 9.81 m/s2 .a) What is the rocket’s maximum altitude?


Part 2 of 3b) What is the rocket’s total time of flight?

Part 3 of 3c) What is the rocket’s horizontal range?


A person tosses a ball from the ground upinto the air at an initial speed of 10 m/sec andan initial angle of 43◦ off the ground.

After the ball is released, what is the totalacceleration vector acting on the ball whenthe ball is at the top of its arc?

1. zero

2. 9.8 m/s2, down

3. 9.8 m/s2, in the horizontal direction

4. 9.8 m/s2, up

5. None of these


A person tosses a ball from the ground upinto the air at an initial speed of 10 m/sec andan initial angle of 43◦ off the ground.

What is the component of the velocity ofthe ball in the horizontal direction just beforethe ball hits the ground? Assume that bothvelocity components were positive when theball was first thrown.

1. 10 m/s

2. zero

3. -7.3 m/s

4. 7.3 m/s

5. None of these

Projectile Cat04:06, highSchool, numeric,> 1min, wording-variable.

A cat chases a mouse across a 1.0 m hightable. The mouse steps out of the way, andthe cat slides off the table and strikes the floor2.2 m from the edge of the table.

The acceleration of gravity is 9.81 m/s2 .What was the cat’s speed when it slid off

the table?

Chapter 4, section 7, Uniform Circular Motion 118

Circular Track04:07, highSchool, multiple choice, < 1 min,fixed.

A mass slides with negligible friction on acircular track of 1 m radius oriented vertically.Its speed at the position shown in the figureis 3.13 m/s. The acceleration of gravity is 9.8m/s2.

v

At the position shown in the figure, whichof the labeled arrows best represents the di-rection of the acceleration of the mass?

1.

2.

3.

4.

5.

6.

7.

8.

9. The mass is traveling at a constant veloc-ity, therefore it has no acceleration.


Part 1 of 2

Imagine that a new asteroid is discoveredin the solar system with a circular orbit andan orbital period of 8 years.

What is the average distance of this objectfrom the Sun in Earth units?

Part 2 of 2Between which planets would this new aster-oid be located?

1. Mars and Earth

2. Mars and Jupiter

3. Jupiter and Pluto


Calculate the speed at the edge of a discof radius 6 cm that rotates at the rate of3.5 rev/s.

Conceptual 07 0104:07, highSchool, multiple choice, < 1 min,fixed.

What is the frequency of the minute handof a clock?

1. 0.0167Hz

2. 60Hz

3. 3600Hz

4. 0.000278Hz

5. 1Hz

6. 24Hz

7. 12Hz

8. 0.0000116Hz



A dragster maintains a speedometer read-ing of 100 km/h and passes through a curvewith a constant radius.

Which statement is true?

1. The dragster rounded the curve at a con-stant velocity of 100 km/h.

2. The dragster rounded the curve at achanging velocity of 100 km/h.

3. The dragster rounded the curve at achanging speed of 100 km/h.

4. The dragster moved along a straight lineat a constant velocity of 100 km/h.

5. All are wrong.

Holt SF 07G 0304:07, highSchool, numeric,> 1min, wording-variable.

Part 1 of 2A dog sits 1.5 m from the center of a merry-

go-round.a) If the dog undergoes a 1.5 m/s2 cen-

tripetal acceleration, what is the dog’s linearspeed?

Part 2 of 2b) What is the angular speed of the merry-go-round?

Holt SF 07G 0404:07, highSchool, numeric,< 1min, wording-variable.

A race car moves along a circular track atan angular speed of 0.512 rad/s.

If the car’s centripetal acceleration is 15.4m/s2, what is the distance between the carand the center of the track?


A piece of clay sits 0.20 m from the centerof a potter’s wheel.

If the potter spins the wheel at an angularspeed of 20.5 rad/s, what is the magnitudeof the centripetal acceleration of the piece ofclay on the wheel?


Part 1 of 2The radius of the Earth is about

6.37× 106 m.a) What is the centripetal acceleration of a

point on the equator?

Part 2 of 2b) What is the centripetal acceleration of apoint at the North Pole?

Planet Rotation 0104:07, highSchool, numeric, > 1 min, normal.

If the rotation of a planet of radius6.37×106 m and free-fall acceleration 9.8 m/s2

increased to the point that the centripetal ac-celeration was equal to the gravitational ac-celeration at the equator, what would be thetangential speed of a person standing at theequator?


Consider a too-small space habitat thatconsists of a rotating cylinder of radius 4 m.If a man standing inside is 2 m tall and his


feet are at 1 g, what is the g force at the eleva-tion of his head? (Do you see why projectionscall for large habitats?)

1. 0.25 g

2. 0.5 g

3. 2 g

4. 4 g

Problems 08 0804:07, highSchool, multiple choice, < 1 min,normal.

If the variation in g between one’s head and

feet is to be less thang

90, then compared to

one’s height, what should be the minimumradius of the space habitat? (Assume that aperson’s height is 2 m.)

Chapter 4, section 8, Tangential and Radial Acceleration 121


A girl sits on a tire that is attached toan overhanging tree limb by a rope. Thegirl’s father pushes her so that her centripetalacceleration is 3.0 m/s2.

If the length of the rope is 2.1 m, what isthe girl’s tangential speed?


A young boy swings a yo-yo horizontallyabove his head so that the yo-yo has a cen-tripetal acceleration of 250 m/s2.

If the yo-yo’s string is 0.50 m long, what isthe yo-yo’s tangential speed?


A building superintendent twirls a set ofkeys in a circle at the end of a cord.

If the keys have a centripetal accelerationof 145 m/s2 and the cord has a length of 0.34m, what is the tangential speed of the keys?


A sock stuck to the side of a clothes-dryerbarrel has a centripetal acceleration of 28m/s2.

If the dryer barrel has a radius of 27 cm,what is the tangential speed of the sock?

Problems 08 0204:08, highSchool, numeric, < 1 min, normal.

What is the tangential speed of a passengeron a Ferris wheel that has a radius of 10 mand rotates once in 30 sec?

Chapter 4, section 9, Relative Velocity 122


While running at 10 mph directly towardPatrick, Lisa passes a basketball to him.Patrick is stationary when he receives theball, which is moving at a speed of 35 mph.

How fast did Lisa throw the ball?


Giselle is travelling on her bicycle at a speedof 10 mph when a car passes her. From herframe of reference, she estimates that the caris going 45 mph toward her and 45 mph awayfrom her.

What is the speed of the car from theframe of reference of someone standing onthe ground?


Part 1 of 3You are traveling 80 km/h and you throw a

ball 40 km/h with respect to yourself.What is the ball’s apparent speed to a friend

standing by the road when the ball is thrownstraight ahead?

Part 2 of 3What is the ball’s apparent speed to the samefriend when the ball is thrown sideways?

Part 3 of 3What is the ball’s apparent speed to the samefriend when the ball is thrown backwards?


Vertically falling rain makes slanted streakson the side windows of a moving automobile.

If the streaks make an angle of 45◦, whatdoes this tell you about the relative speed ofthe car and the falling rain?

1. The speed of the car is the same as thatof the falling rain.

2. The speed of the car is half of that of thefalling rain.

3. The speed of the car is two times greaterthan that of the falling rain.

4. The speed of the car is three times greaterthan that of the falling rain.

5. All are wrong.


A passenger at the rear of a train travelingat 15 m/s relative to Earth throws a base-ball with a speed of 15 m/s in the directionopposite the motion of the train.

What is the velocity of the baseball relativeto Earth as it leaves the thrower’s hand?


A spy runs from the front to the back of anaircraft carrier at a velocity of 3.5 m/s. Theaircraft carrier is moving forward at 18.0 m/s.

How fast does the spy appear to be run-ning when viewed by an observer on a nearbystationary submarine (forward is positive)?


Part 1 of 2A ferry is crossing a river. The ferry is

headed due north with a speed of 2.5 m/srelative to the water and the river’s velocityis 3.0 m/s to the east.

a) What is magnitude of the boat’s velocityrelative to Earth?


Part 2 of 2b) Find the direction in which the ferry ismoving (measured from due east, with coun-terclockwise positive).


Part 1 of 2A pet store supply truck moves at 25.0 m/s

north along a highway. Inside, a dog moves at1.75 m/s at an angle of 35.0◦ east of north.

a) What is the magnitude of the dog’s ve-locity relative to the road?

Part 2 of 2b) At how many degrees east of north is thedog actually moving?


The pilot of a plane measures an air velocityof 165 km/h south. An observer on the groundsees the plane pass overhead at a velocity of145 km/h toward the north.

What is the velocity of the wind that isaffecting the plane? Let north be positive.


Part 1 of 3A river flows due east at 1.50 m/s. A

boat crosses the river from the south shoreto the north shore by maintaining a constantvelocity of 10.0 m/s due north relative to thewater.

a) What is the magnitude of the velocity ofthe boat as viewed by an observer on shore?

Part 2 of 3b) How many degrees off course is the boatforced by the current?

Part 3 of 3

c) If the river is 325 m wide, how far down-stream is the boat when it reaches the northshore?


Part 1 of 2The pilot of an aircraft wishes to fly due

west in a 50.0 km/h wind blowing toward thesouth. The speed of the aircraft in the absenceof a wind is 205 km/h.

a) How many degrees from west should theaircraft head? Let clockwise be positive.

Part 2 of 2b) What should the plane’s speed be relativeto the ground?


A hunter wishes to cross a river that is1.5 km wide and that flows with a speed of5.5 km/h. The hunter uses a small powerboatthat moves at a maximum speed of 13 km/hwith respect to the water.

What is the time necessary for crossing ifthe boat goes directly across the river?


Part 1 of 2A swimmer can swim in still water at a

speed of 9.50 m/s. He intends to swim directlyacross a river that has a downstream currentof 3.75 m/s.

a) How many degrees from straight acrossthe river should he head? Let upstream be apositive angle.

Part 2 of 2b) What is the magnitude of the swimmer’svelocity relative to the bank?



Part 1 of 3A motorboat heads due east at 12.0 m/s

across a river that flows toward the south at aspeed of 3.5 m/s.

a) What is the magnitude of the resultantvelocity relative to an observer on the shore?

Part 2 of 3b)What is the angle from the original heading(with counterclockwise positive) of the boat’sdisplacement?

Part 3 of 3c) If the river is 1360 m wide, how long doesit take the boat to cross?


Part 1 of 2An escalator is 20.0 m long. If a person

stands on the escalator, it takes 50.0 s to ridefrom the bottom to the top.

a) If a person walks up the moving escalatorwith a speed of 0.500 m/s relative to theescalator, how long does it take the person toget to the top?

Part 2 of 2b) If a person walks down the “up” escala-tor with the same relative speed as in thefirst part, how long does it take to reach thebottom?

Holt SF 03Rev 57 shortened04:09, highSchool, numeric,> 1min, wording-variable.

An escalator is 20.0 m long. If a personstands on the escalator, it takes 50.0 s to ridefrom the bottom to the top.

If a person walks up the moving escalatorwith a speed of 0.500 m/s relative to theescalator, how long does it take the person to

get to the top?


A boat moves through a river at 7.5 m/srelative to the water, regardless of the boat’sdirection.

If the water in the river is flowing at 1.5m/s, how long does it take the boat to make around trip consisting of a 250 m displacementdownstream followed by a 250 m displacementupstream?


Part 1 of 4A water spider maintains an average po-

sition on the surface of a stream by dartingupstream (against the current), then driftingdownstream (with the current) to its origi-nal position. The current in the stream is0.500 m/s relative to the shore, and the waterspider darts upstream 0.560 m (relative to aspot on shore) in 0.800 s during the first partof its motion. Use upstream as the positivedirection.

a) Find the velocity of the water spiderrelative to the water during its dash upstream.

Part 2 of 4b) What is its velocity (relative to the water)during its drift downstream?

Part 3 of 4c) How far upstream relative to the water doesthe water spider move during one cycle of thisupstream and downstream motion?

Part 4 of 4d) What is the average velocity of the waterspider relative to the water for one completecycle?

Holt SF 03Rev 6504:09, highSchool, numeric,> 1min, wording-


variable.

Part 1 of 2A car travels due east with a speed of 50.0

km/h. Rain is falling vertically with respectto Earth. The traces of the rain on the sidewindows of the car make an angle of 60.0◦

with the vertical.a) Find the magnitude of the velocity of the

rain with respect to the car.

Part 2 of 2b) Find the magnitude of the rain’s velocitywith respect to Earth.


A shopper in a department store can walkup a stationary (stalled) escalator in 30.0 s.

If the normally functioning escalator cancarry the standing shopper to the next floorin 20.0 s, how long would it take the shopperto walk up the moving escalator? Assume thesame walking effort for the shopper whetherthe escalator is stalled or moving.

Rowing Speed04:09, highSchool, multiple choice, > 1 min,wording-variable.

Part 1 of 6Assume: The water has uniform velocity

represented by the vector ~P in the diagrambelow. The shore lines are on the left- andright-hand side of the diagram.

A river is crossed by a girl rowing a boat.The rowing speed of the girl’s boat and a setof possible orientations of her boat (relativeto still water) are also shown in the diagram.

River

Velocity P

H

K

Z

S

J

N

G

Rowing Speed andDirection ofBoat

For an observer on shore, the speed of theboat for direction ~H is greater than for direc-tion ~K.

1. true

2. false

Part 2 of 6To land directly across the river, she must rowin direction ~N .

1. true

2. false

Part 3 of 6To get across the river in the shortest time,she must row in direction ~N .

1. false

2. true

Part 4 of 6Time to row across for direction ~H is equal tothat for direction ~G.

1. true

2. false

Part 5 of 6Time to row across for direction ~N is less that


for direction ~G.

1. true

2. false

Part 6 of 6The total distance traveled in crossing fordirection ~G is greater than for direction ~H.

1. false

2. true

Chapter 5, section 1, The Concept of Force 127

Conceptual forces 0405:01, highSchool, multiple choice, < 1 min,fixed.

Part 1 of 2A book is at rest on an incline as shown

below. A hand, in contact with the top ofthe book, produces a constant force Fhand

vertically downward.

Fhand

Book

The following figures show several attemptsat drawing free-body diagrams for the book.

Which figure has the correct directions foreach force? The magnitudes of the forces arenot necessarily drawn to scale.

1.

weightforce

frictionnormal

2.

weightforce

normalfriction

3.

normalfriction weight

force

4.

normal

force

frictionweight

5.

weightfriction

forcenormal

6.

weightfriction

normalforce

7.

weightforce normal

friction

8.

weightnormal

frictionforce

Part 2 of 2For the normal force exerted on the bookby the wedge in the diagram, which force(s)complete(s) the force pair for Newton’s thirdlaw (action-reaction)?

1. the normal force exerted on the wedge bythe book

2. the pull of the book on the earth

3. the component of gravity pointing per-pendicular to the surface of the incline


4. the component of gravity pointing parallelto the surface of the incline

5. the component of Fhand pointing perpen-dicular to the surface of the incline

6. the pull of the earth on the book

7. the sum of the component of gravity per-pendicular to the surface of the incline andthe component of Fhand perpendicular to thesurface of the incline


Part 1 of 2The velocity of a transverse wave traveling

along a string depends on the tension F = maof the string and its mass per unit length µ.

Assume v = F xµy. The powers of x andy may be determined based on dimensionalanalysis. By equating the powers of mass,length, and time, one arrives correspondinglyat a set of three equations.

Choose the correct expressions for x and y.

1. 0 = x+ y, 1 = x− y, −1 = −2x

2. 0 = x+ y, 1 = x+ y, −1 = −2x

3. 0 = x− y, 1 = x+ y, −1 = −2x

4. 0 = x− y, 1 = x− y, −1 = −2x

5. 0 = x+ y, 1 = x− y, 1 = −2x

6. 0 = x+ y, 1 = x+ y, 1 = −2x

7. 0 = x− y, 1 = x+ y, 1 = −2x

8. 0 = x− y, 1 = x− y, 1 = −2x

9. 0 = x+ y, 0 = x− y, 1 = −2x

10. 1 = x+ y, 1 = x− y, 1 = −2x

Part 2 of 2The values of x and y for this problem are

1. x =1

2, y = −1

2

2. x = −1

2, y = −1

2

3. x =1

2, y =

1

2

4. x = −1

2, y =

1

2

5. x = −1 , y = 1

6. x = 1 , y = −1

7. x = −1 , y = −1

8. x = 1 , y = 1

9. x = 0 , y = 1

10. x = 1 , y = 0

Dimensional Analysis 04b05:01, highSchool, multiple choice, > 1 min,fixed.

The velocity of a transverse wave travelingalong a string depends on the tension F = maof the string and its mass per unit length µ.

Assume v = F xµy. The powers of x andy may be determined based on dimensionalanalysis. By equating the powers of mass,length, and time, one arrives correspondinglyat a set of three equations.

Choose the correct expressions for x and y.

1. 0 = x+ y, 1 = x− y, −1 = −2x

2. 0 = x+ y, 1 = x+ y, −1 = −2x

3. 0 = x− y, 1 = x+ y, −1 = −2x

4. 0 = x− y, 1 = x− y, −1 = −2x

5. 0 = x+ y, 1 = x− y, 1 = −2x

6. 0 = x+ y, 1 = x+ y, 1 = −2x


7. 0 = x− y, 1 = x+ y, 1 = −2x

8. 0 = x− y, 1 = x− y, 1 = −2x

9. 0 = x+ y, 0 = x− y, 1 = −2x

10. 1 = x+ y, 1 = x− y, 1 = −2x

Dimensional Analysis 04 v105:01, highSchool, multiple choice, < 1 min,fixed.

The velocity of a transverse wave travelingalong a string depends on the tension F = maof the string and its mass per unit length µ.

Assume v = F xµy. The powers of x andy may be determined based on dimensionalanalysis.

The values of x and y for this problem are

1. x =1

2, y = −1

2

2. x = −1

2, y = −1

2

3. x =1

2, y =

1

2

4. x = −1

2, y =

1

2

5. x = −1 , y = 1

6. x = 1 , y = −1

7. x = −1 , y = −1

8. x = 1 , y = 1

9. x = 0 , y = 1

10. x = 1 , y = 0


Part 1 of 3Stokes law says

F = 6πrηv.

F = ma is a force, r the radius and v thevelocity.

The parameter η has the dimension of

1. [η] =M

T L

2. [η] =M

T 2 L

3. [η] =M

T 2 L2

4. [η] =M

T L2

5. [η] =M

T

6. [η] =T L

M

7. [η] =T 2 L

M

8. [η] =T L2

M

9. [η] =T 2 L2

M

10. [η] =T

M

Part 2 of 3Consider a simple pendulum which consists ofa string with a bob attached to its end. Itsperiod (i.e., the time interval taken for thebob to complete one cycle of motion) may bewritten in the form

T = kmx gy bz ,

where k is a dimensionless constant, g themagnitude of the gravitational acceleration,m the mass of the bob, and b the length of thestring.

The appropriate x, y, and z values are givenrespectively by

1. (x, y, z) =

(

0,−1

2,1

2

)

2. (x, y, z) =

(

0,1

2,−1

2

)

3. (x, y, z) =

(

0,1

2,1

2

)


4. (x, y, z) =

(

0,−1

2,−1

2

)

5. (x, y, z) = (0,−1, 1)

6. (x, y, z) =

(

1,−1

2,1

2

)

7. (x, y, z) =

(

1,1

2,−1

2

)

8. (x, y, z) =

(

1,−1

2,−1

2

)

9. (x, y, z) =

(

1,1

2,1

2

)

10. (x, y, z) = (1,−1, 1)

Part 3 of 3Consider a piece of string which is placedalong the x-axis. Let ∆m be the mass of asegment of the string and ∆x the length ofthis segment. The linear mass density, µ, of apiece of string is defined as

µ =∆m

∆x.


ρ =mass

volume


µ = ρxAy.

Use dimensional analysis to determine theequations for x and y.

1. x = 1, 2 y − 3x = −1

2. x = 1, 2 y + 3x = −1

3. x = 1, 3x+ 2 y = 1

4. x = 1, 2 y − 3x = 1

5. x = 1, −2 y − 3x = −1

6. x = −1, 2 y − 3x = −1

7. x = −1, 2 y + 3x = −1

8. x = −1, 3x+ 2 y = 1

9. x = −1, 2 y − 3x = 1

10. x = −1, −2 y − 3x = −1



F = 6πrηv .



1. [η] =M

T L

2. [η] =M

T 2 L

3. [η] =M

T 2 L2

4. [η] =M

T L2

5. [η] =M

T

6. [η] =T L

M

7. [η] =T 2 L

M

8. [η] =T L2

M

9. [η] =T 2 L2

M

10. [η] =T

M

Part 2 of 3Consider a simple pendulum which consists ofa string with a bob attached to its end. Itsperiod, (i.e., the time interval taken for thebob to complete one cycle of motion), may bewritten in the form

T = kmx gy bz ,




1. (x, y, z) =

(

0,−1

2,1

2

)

2. (x, y, z) =

(

0,1

2,−1

2

)

3. (x, y, z) =

(

0,1

2,1

2

)

4. (x, y, z) =

(

0,−1

2,−1

2

)

5. (x, y, z) = (0,−1, 1)

6. (x, y, z) =

(

1,−1

2,1

2

)

7. (x, y, z) =

(

1,1

2,−1

2

)

8. (x, y, z) =

(

1,−1

2,−1

2

)

9. (x, y, z) =

(

1,1

2,1

2

)

10. (x, y, z) = (1,−1, 1)

Part 3 of 3Consider a piece of string which is placedalong the x-axis. Let ∆m be the mass of asegment of the string and ∆x the length ofthis segment. The linear mass density, µ, of apiece of string is defined as

µ =∆m

∆x.


ρ =mass

volume


µ = ρxAy.

Use dimensional analysis to determine theequations for x and y.

1. x = 1, 2 y − 3x = −1

2. x = 1, 2 y + 3x = −1

3. x = 1, 3x+ 2 y = 1

4. x = 1, 2 y − 3x = 1

5. x = 1, −2 y − 3x = −1

6. x = −1, 2 y − 3x = −1

7. x = −1, 2 y + 3x = −1

8. x = −1, 3x+ 2 y = 1

9. x = −1, 2 y − 3x = 1

10. x = −1, −2 y − 3x = −1

Dimensional Analysis 17 0205:01, highSchool, multiple choice, > 1 min,fixed.

Stokes law says

F = 6πrηv .



1. [η] =M

T L

2. [η] =M

T 2 L

3. [η] =M

T 2 L2

4. [η] =M

T L2

5. [η] =M

T

6. [η] =T L

M

7. [η] =T 2 L

M

8. [η] =T L2

M


9. [η] =T 2 L2

M

10. [η] =T

M



F = 6πrηv .



1. [η] =M

T L

2. [η] =M

T 2 L

3. [η] =M

T 2 L2

4. [η] =M

T L2

5. [η] =M

T

6. [η] =T L

M

7. [η] =T 2 L

M

8. [η] =T L2

M

9. [η] =T 2 L2

M

10. [η] =T

M

Part 2 of 2Consider a simple pendulum which consists ofa string with a bob attached to its end. Itsperiod, (i.e., the time interval taken for thebob to complete one cycle of motion), may bewritten in the form

T = kmx gy bz ,



1. (x, y, z) =

(

0,−1

2,1

2

)

2. (x, y, z) =

(

0,1

2,−1

2

)

3. (x, y, z) =

(

0,1

2,1

2

)

4. (x, y, z) =

(

0,−1

2,−1

2

)

5. (x, y, z) = (0,−1, 1)

6. (x, y, z) =

(

1,−1

2,1

2

)

7. (x, y, z) =

(

1,1

2,−1

2

)

8. (x, y, z) =

(

1,−1

2,−1

2

)

9. (x, y, z) =

(

1,1

2,1

2

)

10. (x, y, z) = (1,−1, 1)


Tension is a force with [F ] =M L

T 2. The

velocity of a transverse wave traveling along astring depends on the tension F of the stringand its mass per unit length µ.

Assume: v = F x µy .The powers x and y may be determined basedon dimensional analysis.

What system of equations can be foundby equating the powers of mass, length, andtime?

1. 0 = x+ y, 1 = x− y, −1 = −2x

2. 0 = x+ y, 1 = x+ y, −1 = −2x


3. 0 = x− y, 1 = x+ y, −1 = −2x

4. 0 = x− y, 1 = x− y, −1 = −2x

5. 0 = x+ y, 1 = x− y, 1 = −2x

6. 0 = x+ y, 1 = x+ y, 1 = −2x

7. 0 = x− y, 1 = x+ y, 1 = −2x

8. 0 = x− y, 1 = x− y, 1 = −2x

9. 0 = x+ y, 0 = x− y, 1 = −2x

10. 1 = x+ y, 1 = x− y, 1 = −2x

Dimensional Analysis of Force05:01, highSchool, multiple choice, < 1 min,fixed.

A certain force(

[F ] =M L/overT 2)

isgiven by the equation

F =KM L2

T 4

, whereM is a mass, L is a length, T is a timeand K is a constant.

What are units of the constant K?

1. [K] = T 2/L

2. [K] = L/T 2

3. [K] =M2L2/T 6

4. [K] = T 6/M2L2

5. [K] =ML/T 2

5. [K] = T 2/ML


Part 1 of 2A dog pulls on a pillow with a force of 5 N

at an angle of 37◦ above the horizontala) What is the x component of this force?

Part 2 of 2b) What is the y component of this force?


One Newton is the force

1. of gravity on a 1 kg body.

2. of gravity on a 1 g body.

3. that gives a 1 g body an acceleration of1 cm/s2.

4. that gives a 1 kg body an acceleration of1 m/s2.

5. that gives a 1 kg body an acceleration of9.8 m/s2.

Office Chair05:01, highSchool, multiple choice, < 1 min,fixed.

An empty office chair is at rest on a floor.Consider the following forces:

1. A downward force of gravity,2. An upward force exerted by the floor, and3. A net downward force exerted by the air.Which of the forces is (are) acting on the

office chair?

1. 1 only.

2. 1 and 2.

3. 2 and 3.

4. 1, 2, and 3.

5. None of the forces act on the chair. (Sincethe chair is at rest there are no forces actingupon it.)

Tennis Ball05:01, highSchool, multiple choice, < 1 min,fixed.


Despite a very strong wind, a tennis playermanages to hit a tennis ball with her racquetso that the ball passes over the net and landsin her opponent’s court.

Consider the following forces:1. A downward force of gravity,2. A force by the hit, and3. A force exerted by the air.Which of the above forces is (are) acting on

the tennis ball after it has left contact withthe racquet and before it touches the ground?

1. 1 only.

2. 1 and 2.

3. 1 and 3.

4. 2 and 3.

5. 1, 2, and 3.

Universal Gravitation Units 0205:01, highSchool, multiple choice, > 1 min,fixed.

Newton’s law of universal gravitation is

F = GM m

r2.

Here, M and m are masses and r is the sep-aration distance. The dimension of force isspecified by the equation F = ma.

What are the SI units of the constant G?

1. [G] = m3/kg/s2

2. [G] = m2/kg

3. [G] = kg/m2/s2

4. [G] = m3/kg2/s2

5. [G] = m2/kg2/s2

6. [G] = Nm

7. [G] = Nm/s2

8. [G] = m/kg/s2

9. [G] = W/m3

10. [G] = J s/kg

Chapter 5, section 2, Newton’s First Law and Inertial Frames 135

Concept 05 E0705:02, highSchool, multiple choice, < 1 min,fixed.

Within a book on a table there are billionsof forces pushing and pulling on all of themolecules.

Why is it that these forces never by chanceadd up to a net force in one direction, causingthe book to accelerate “spontaneously” acrossthe table?

1. The forces cause the book to move acrossthe table spontaneously all the time, but themovement is too weak to observe.

2. The billions of force pairs are internal tothe book and exert no net force on the book.

3. These forces between molecules are muchsmaller than the friction between the bookand the table.

4. These forces are counteracted by grav-ity.


A heavily loaded freight train moves withconstant velocity.

What is the relationship between the netforce on the first car (F1) and the net force onthe last car (F2)?

1. F1 = F2

2. F1 < F2

3. F1 > F2


Conceptual 04 Q2405:02, highSchool, multiple choice, < 1 min,normal.

A female gymnast weighs 400 N.If she is hanging stationary from a high bar,

how many forces are acting on her?

1. one

2. two

3. three

4. four

5. five

Elevator Lifted at a Const Speed05:02, highSchool, multiple choice, < 1 min,fixed.

An elevator is being lifted up an el-evator shaft at a constant speed by asteel cable as shown in the figure be-low. All frictional effects are negligible.

steelcable

Elevator going upat constant speed

In this situation, forces on the elevator aresuch that

1. the upward force by the cable is greaterthan the downward force of gravity.

2. the upward force by the cable is equal tothe downward force of gravity.

3. the upward force by the cable is smallerthan the downward force of gravity.

4. the upward force by the cable is greaterthan the sum of the downward force of gravity


and a downward force due to the air.

5. None of these. (The elevator goes upbecause the cable is being shortened, not be-cause an upward force is exerted on the eleva-tor by the cable.)


A ball rolls across the top of a billiard tableand slowly comes to a stop.

How would Aristotle interpret this observa-tion? How would Galileo interpret it?

1. They both would say that the ball comesto rest because the ball seeks its natural stateof rest.

2. They both would say that it comes torest because of some forces acting on it; likelyfriction between the ball and table surface andwith the air.

3. Aristotle would say that the ball comes torest because the ball seeks its natural state ofrest. Galileo would likely have said it comes torest because of some forces acting on it; likelyfriction between the ball and table surface andwith the air.

4. Galileo would say that the ball comes torest because the ball seeks its natural stateof rest. Aristotle would likely have said itcomes to rest because of some forces acting onit; likely friction between the ball and tablesurface and with the air.

5. All are wrong.


Who first proposed the concept of inertia?

1. Newton a few years earlier than Galileo

2. Galileo a few years earlier than Newton

3. Galileo before Newton was even born

4. Galileo after Newton was born

5. They came up with the concept of inertiaabout the same time.


Your friend says that inertia is a force thatkeeps things in their places, either at rest ormotion.

Do you agree? Why or why not?

1. Agree; only forces can keep things in theirplaces.

2. Disagree; inertia is a force that keepsthings moving.

3. Agree; inertia is not a force that keepsthings moving.

4. Disagree; inertia is a property of matterto behave this way, not some kind of force.

5. All are wrong.


Start a ball rolling down a bowling alleyand you’ll find it moves slightly slower withtime.

Does this violate Newton’s law of inertia?Defend your answer.

1. Yes; no force acts upon it.

2. No; air resistance and friction act uponthe ball.

3. Yes; the air resistance cancels the frictionand the total force on the ball is zero.


4. No; the law of inertia can also be appliedto moving objects.

5. None of these


Can an object be in mechanical equilibriumwhen only a single force acts on it? Explain.

1.Yes; the object will act back with an equaland opposite force.

2. Yes; a single force is necessary to keep theobject in mechanical equilibrium.

3. No; at least one other force is needed tocancel the action of the first force.

4. No; even one force is too much. Thereshould be no forces acting on an object.

5. None of these


A hockey puck slides across the ice at aconstant speed.

Which of the following is true?

1. It is in equilibrium.

2. The puck is at rest.

3. The puck is moving and thus not in equi-librium.

4. The puck can be considered neither atrest nor in equilibrium.

5. None of these

Hewitt CP9 02 E3105:02, highSchool, multiple choice, < 1 min,

fixed.

Is it correct to say that no force acts on abody at rest?

1. No force acts on a body at rest; if at leastone force acted on it the body would move.

2. No force acts on a body at rest; all forcescancel each other.

3. No net force acts on a body at rest; whenthe net force is zero, the body is in staticequilibrium.

4. No net force acts on a body at rest; noforce acts on the body at all.

5. All are wrong.


Before the time of Galileo and Newton,some learned scholars thought that a stonedropped from the top of a tall mast of amoving ship would fall vertically and hit thedeck behind the mast by a distance equal tohow far the ship had moved forward while thestone was falling.

In light of your understanding of Newton’sfirst law, what is true?

1. If the ship speed is fast enough, the stonewill drop into the sea.

2. Everyone on the ship will see the stonefall vertically if released from rest.

3. The stone will have a horizontal motion;it will hit the deck in front of the mast.

4. The stone will fall in some trajectorydepending on the speed of the ship.

5. All are wrong.

Hewitt CP9 04 E01



What is the net force on a Mercedes con-vertible traveling along a straight road at asteady speed of 100 km/h?

1. 0 N

2. 10 N

3. 100 N

4. 200 N

5. All are wrong.


If an object is not accelerating, how manyforces act on it?

1. 0

2. 1

3. 2

4. 3



What is the net force on a 1-N apple whenyou hold it at rest above your head and whatis the net force on it after you release it?

1. 0 N, 1 N

2. 0 N, 0 N

3. 1 N, 0 N

4. 1 N, 1 N

5. All are wrong.


Part 1 of 2A man is pulling on a rope with a force

of 53 N directed at an angle of 32 ◦ to thehorizontal.

What is the x-component of this force?

Part 2 of 2What is the y-component of this force?

Holt SF 04A 01 graph05:02, highSchool, numeric,> 1min, wording-variable.

Part 1 of 2A man is pulling on a rope with a force

of 53 N directed at an angle of 32 ◦ to thehorizontal.

Draw the vectors to scale on a graph todeterime the answer.

a) What is the x-component of this force?

Part 2 of 2b) What is the y-component of this force?


Part 1 of 4A crate is pulled to the right with a force

of 82.0 N, to the left with a force of 115 N,upward with a force of 565 N, and downwardwith a force of 236 N.

a) What is the net external force in the xdirection?

Part 2 of 4b) What is the net external force in the ydirection?

Part 3 of 4c) What is the magnitude of the net external


force on the crate?

Part 4 of 4d) What is the direction of the net externalforce on the crate (measured from the positivex axis, with counterclockwise positive)?


Part 1 of 2A gust of wind blows an apple from a tree.

As the apple falls, the force of gravity on theapple is 9.25 N downward, and the force ofthe wind on the apple is 1.05 N to the right.

a) What is the magnitude of the net exter-nal force on the apple?

Part 2 of 2b) What is the direction of the net externalforce on the apple (measured from the down-ward vertical, so that the angle to the right ofdownward is positive)?


Part 1 of 2The wind exerts a force of 203 N North on

a sailboat, while the water exerts a force of95 N West on the sailboat.

What is the magnitude of the net externalforce on the sailboat?

Part 2 of 2How many degrees west of north is this netexternal force directed?

Holt SF 04A 04 graph05:02, highSchool, numeric,> 1min, wording-variable.

Part 1 of 2The wind exerts a force of 188 N North on

a sailboat, while the water exerts a force of122 N West on the sailboat.

Draw the vectors to scale on a graph to

determine the answer.a) What is the magnitude of the net exter-

nal force on the sailboat?

Part 2 of 2b) How many degrees west of north is this netexternal force directed?


Part 1 of 2Four forces act on a hot-air balloon, as

shown from the side.

868 N385 N

728N

323N

Note: Figure is not drawn to scalea) Find the magnitude of the resultant force

on the balloon.

Part 2 of 2b) Find the direction of the resultant force(in relation to the 868 N force, with up beingpositive).


Part 1 of 2Four forces act on a hot-air balloon, as

shown from the side.


868 N385 N

728N

323N

Note: Figure is not drawn to scaleDraw the vectors to scale on a graph to

determine the answer.a) Find the magnitude of the resultant force

on the balloon.

Part 2 of 2b) Find the direction of the resultant force(in relation to the 868 N force, with up beingpositive).


Part 1 of 2Two lifeguards pull on ropes attached to

a raft. If they pull in the same direction,the raft experiences a net external force of334 N to the right. If they pull in oppositedirections, the raft experiences a net externalforce of 106 N to the left.

a) Draw a free body diagram for each situ-ation and find the magnitude of the larger ofthe two individual forces.

Part 2 of 2b) What is the magnitude of the smaller ofthe individual forces?

Net Forces05:02, highSchool, numeric, > 1 min, normal.

Part 1 of 4You have two forces, 100 N and 75 N.What is their resultant if the first acts up-

ward and the second acts downward?

Part 2 of 4What is the direction of the resultant?

1. downward

2. upward

Part 3 of 4What is their resultant if they both act down-ward?

Part 4 of 4What is the direction of this resultant?

1. downward

2. upward

Tennis Player05:02, highSchool, multiple choice, < 1 min,fixed.

Despite a very strong wind, a tennis playermanages to hit a tennis ball with her racquetso that the ball passes over the net and landsin her opponents court.

Consider the following forces:1 - A downward force of gravity.2 - A force by the “hit”.3 - A force exerted by the air.Which of the above forces is (are) acting on

the tennis ball after it has left contact withthe racquet and before it touches the ground?

1. 1 only

2. 1 and 2

3. 1 and 3

4. 2 and 3

5. 1, 2 and 3

Chapter 5, section 3, Inertial Mass 141

Conceptual 04 0205:03, highSchool, multiple choice, < 1 min,wording-variable.

Which object has the greatest inertia?

1. an ocean liner

2. a mosquito

3. a VW bug

4. a car


Two identical spring-loaded dart guns aresimultaneously fired straight forward. Onefires a regular dart; the other a weighted dart.

Which dart goes farther?

1. The regular dart.

2. The weighted dart.

3. It’s a tie.


A space probe is carried by a rocket intoouter space where it continues to move on itsown in a straight line.

What keeps the probe moving?

1. a propeller

2. The gravitation forces from different starsand planets

3. Nothing specific; in the absence of forcesit would continue moving in a straight line.

4. Nothing; the probe will eventually stop.

5. None of these

Chapter 5, section 4, Newton’s Second Law 142

Conceptual 04 0305:04, highSchool, multiple choice, < 1 min,normal.

Part 1 of 3You are driving a car down a straight road

at a constant 55 miles per hour.Consider the following forces:I) air drag pushing back on the car;II) gravity pulling down on the car;III) the ground pushing up on the car;IV) friction pushing the wheels (and the car)

forward; andV) friction pushing the wheels (and the car)

back.Which force(s) act on the car?

1. I and II

2. I, III and V

3. II, III and IV

4. I, II and III

5. I, II, III and IV

Part 2 of 3Is there a net or unbalanced force acting on

the car?

1. Yes; a net force in the vertical direction.

2. Yes; a net force in the horizontal direc-tion.

3. No; the speed is constant.

4. No; the velocity is constant.

5. Cannot be determined

Part 3 of 3After a while, the car started to go around a

long bend, still maintaining its constant speedof 55 miles per hour.

Is there a net (unbalanced) force acting onthe car?

1. Yes; its direction is the same as the veloc-ity.

2. Yes; its direction is not the same as thevelocity.

3. No; the velocity of the car does notchange.

4.No; the speed of the car does not change.



Part 1 of 3Suzie (of mass 50 kg) is roller-blading down

the sidewalk going 20 miles per hour. Shenotices a group of workers down the walkwaywho have unexpectedly blocked her path, andshe makes a quick stop in 0.5 seconds.

What is Suzie’s average acceleration?

Part 2 of 3What force was exerted to stop Suzie?

Part 3 of 3Where did this force come from?

1. the gravity

2. the upward force exerted by the ground

3. the friction between the air and Suzie

4. the friction between the ground and theskates

5. All of these


Part 1 of 4Tracy (of mass 50 kg) and Tom (of mass

75 kg) are standing at rest in the center of theroller rink, facing each other, free to move.


Tracy pushes off Tom with her hands and re-mains in contact with Tom’s hands, applyinga constant force for 0.75 s. Tracy moves 0.5 mduring this time. When she stops pushing offTom, she moves at a constant speed.

What is Tracy’s constant acceleration dur-ing her time of contact with Tom?

Part 2 of 4What is Tracy’s final speed after this con-

tact?

Part 3 of 4What force was applied to Tracy during

this time?

Part 4 of 4What is correct about Tom’s motion?

1. The force acting on Tom is greater thanthe force acting on Tracy.

2. Tom’s final velocity is greater thanTracy’s.

3. Tom’s acceleration is greater.

4. Tom’s acceleration is smaller.

Conceptual 04 Q1505:04, highSchool, numeric, < 1 min, normal.

Five 10 N forces act on a 2 kg object asshown.

What is the acceleration of the object?


Two 20 N forces and a 40 N force act on ahanging box as shown.

20 N20 N

40 N

Will the box experience acceleration?

1. Yes; downward.

2. Yes; upward.

3. No; it is balanced.

4. Unable to determine without the an-gle.


When a rocket is launched, it carries aheavy load of fuel, which is burned duringthe ascent. The force needed to produce agiven acceleration just off the launching padis F1. The force needed to produce the sameacceleration a few minutes after launch is F2.

What relationship would F1 and F2 have?

1. F1 = F2

2. F1 > F2

3. F1 < F2


Constant Horizontal Force 0205:04, highSchool, numeric, > 1 min, normal.

A 6 kg block initially at rest is pulled to theright along a horizontal, frictionless surface


by a constant, horizontal force of 12 N.Find the speed of the block after it has

moved 3 m.

Force and Motion 0505:04, highSchool, multiple choice, < 1 min,fixed.

Part 1 of 2The following 2 questions refer to a coin

which is tossed straight up into the air. Af-ter it is released it moves upward, reaches itshighest point and falls back down again. In-dicate the force acting on the coin for each ofthe cases described below.

The coin is moving upward after it is re-leased.

1. The force is down and constant.

2. The force is down and increasing.

3. The force is down and decreasing.

4. The force is zero.

5. The force is up and constant.

6. The force is up and increasing.

7. The force is up and decreasing.

Part 2 of 2The coin is at its highest point.

1. The force is up and constant.

2. The force is down and increasing.

3. The force is down and decreasing.

4. The force is zero.

5. The force is down and constant.

6. The force is up and increasing.

7. The force is up and decreasing.

Force and Motion 1305:04, highSchool, multiple choice, < 1 min,wording-variable.

A car moves to the right along a horizontalline (the positive part of the distance axis).

car

vg

O +

The car moves toward the right and isslowing down at a steady rate (constant ac-celeration).

Choose the one force graph which couldallow the described motion of the car to con-tinue.

1. t

F

2. t

F

3. t

F

4. t

F


5. t

F

6. t

F

7. t

F

8. t

F

9. t

F



Each bone in the chain of bones formingyour spine is separated from its neighbors bydisks of elastic tissue.

What happens, then, when you jump heav-ily onto your feet from an elevated position?

1. The space between each disk will becomelarger because of Newton’s first law.

2. The discs tend to compress upon eachother because of Newton’s first law.

3. The space between each disk will becomelarger because of Newton’s second law.

4. The discs tend to compress upon eachother because of Newton’s second law.

5. All are wrong.


While rolling balls down an inclined plane,Galileo observed that the ball rolled 1 cubit(the distance from elbow to fingertip) as hecounted to ten.

How far had the ball rolled from its startingpoint when he had counted to twenty?


Two balls are released simultaneously fromrest at the left end of equal-length tracks asshown.

A

B

Which ball reaches the end of its track first?

1. A

2. B

3. They reach the end of the track at thesame time.

4. All are wrong.



An astronaut tosses a rock on the moon.What force(s) act on the the rock during its

curved path?

1. gravitation force

2. friction force

3. air drag

4. air push

5. All are wrong.


The acceleration of gravity is 10 m/s2 .What is the greatest acceleration a runner

can muster if the friction between her shoesand the pavement is 90% her weight?

Hewitt CP9 04 P0205:04, highSchool, multiple choice, < 1 min,normal.

What is the acceleration of a 10 kg block ofcement when pulled sideways with a net forceof 200 N?


If a mass of 1 kg is accelerated 1 m/s2 by aforce of 1 N, what would be the accelerationof a 2 kg mass acted on by a force of 2 N?


How much acceleration does a 747 jumbojet of mass 30000 kg experience in takeoffwhen the thrust for each of four engines is30000 N?

Hewitt CP9 04 P0605:04, highSchool, numeric,< 1min, wording-variable.

Two boxes are seen to accelerate at thesame rate when a force F is applied to thefirst and 4F is applied the second.

What is the mass ratio of the first box tothe second?


A firefighter of mass 80 kg slides down avertical pole with an acceleration of 4 m/s2.

The acceleration of gravity is 10 m/s2 .What is the friction force that acts on

him?


The acceleration of gravity is 10 m/s2 .What will be the acceleration of a skydiver

when air resistance builds up to 50% of herweight?


Sprinting near the end of a race, a runnerwith a mass 60 kg accelerates from a speedof 6 m/s to a speed of 7 m/s in 2 s. To gainspeed the runner produces a backward forceon the ground, so that the ground pushes therunner forward, providing the force necessaryfor the acceleration.

Calculate this average force.


Before going into orbit, an astronaut has amass of 55 kg. When in orbit, a measurementdetermines that a force of 66 N causes her tomove with an acceleration of 1.1 m/s2.

To regain her original weight, should shego on a diet or start eating more candy? Toanswer this, find her mass in orbit.



The net external force on the propeller of a3.2 kg model airplane is 7.0 N forward.

What is the acceleration of the airplane?

Holt SF 04B 0205:04, highSchool, numeric, > 1 min, normal.

The net external force on a golf cart is 390 Nnorth.

If the cart has a total mass of 270 kg, whatis the cart’s acceleration?


A car has a mass of 1.50× 103 kg.If the force acting on the car is 6.75× 103 N

to the east, what is the car’s acceleration?


A 2.0 kg otter starts from rest at the top ofa muddy incline 85 cm long and slides downto the bottom in 0.50 s.

What net external force acts on the otteralong the incline?


A soccer ball kicked with a force of 13.5 Naccelerates at 6.5 m/s2 to the right.

What is the mass of the ball?


What acceleration will you give to a 24.3 kgbox if you push it with a force of 85.5 N?


A freight train has a mass of 1.5× 107 kg.If the locomotive can exert a constant pull

of 7.5 × 105 N, how long would it take toincrease the speed of the train from rest to85 km/h? (Disregard friction.)


Part 1 of 3A 3.00 kg ball is dropped from the roof of

a building 176.4 m high. While the ball isfalling to Earth, a horizontal wind exerts aconstant force of 12.0 N on the ball.

The acceleration of gravity is 9.81 m/s2 .a) How long does it take to hit the ground?

Part 2 of 3b) How far from the building does the ball hitthe ground?

Part 3 of 3c)What is its speed when it hits the ground?


What net external force is required to givea 25 kg suitcase an acceleration of 2.2 m/s2 tothe right?


A 5.0 kg bucket of water is raised from awell by a rope.

The acceleration of gravity is 9.81 m/s2 .If the upward acceleration of the bucket is

3.0 m/s2, find the force exerted by the ropeon the bucket of water.


Part 1 of 3


A boat moves through the water with twoforces acting on it. One is a 2.10×103 Nforward push by the motor, and the other is a1.80×103 N resistive force due to the water.

a) What is the acceleration of the 1200 kgboat?

Part 2 of 3b) If it starts from rest, how far will it movein 12 s?

Part 3 of 3c) What will its speed be at the end of thistime interval?


Part 1 of 2A 1250 kg car is pulling a 325 kg trailer.

Together, the car and trailer have an acceler-ation of 2.15 m/s2.

a) What is the net force on the car?

Part 2 of 2b) What is the net force on the trailer?


Part 1 of 4The figure below shows a plot of the speed

of a person’s body during a chin-up versus

time.t v

0.00 s 0.000 m/s0.50 s 0.120 m/s1.00 s 0.240 m/s1.50 s 0.240 m/s2.00 s 0.000 m/s

All motion is vertical and the mass of theperson (excluding the arms) is 64.0 kg.

0 0.5 1.0 1.5 2.00

0.1

0.2

0.3

�

�

� �

�

Time (s)

Speed(m

/s)

Figure: The line through thepoints is only to guide the eye.

a) What is the magnitude of the averageforce exerted on the body by the arms duringthe first time interval?

Part 2 of 4b) What is the magnitude of the average forceexerted on the body by the arms during thesecond time interval?

Part 3 of 4c) What is the magnitude of the average forceexerted on the body by the arms during thethird time interval?

Part 4 of 4d) What is the magnitude of the average forceexerted on the body by the arms during thelast time interval?


Part 1 of 3A hockey puck is hit on a frozen lake and

starts moving with a speed of 12.0 m/s. Ex-actly 5.00 s later, its speed is 6.00 m/s.

The acceleration of gravity is 9.81 m/s2 .a) What is its average acceleration?


Part 2 of 3b) What is the coefficient of kinetic frictionbetween the puck and the ice?

Part 3 of 3c) How far does the puck travel during this5.00 s interval?

Simple Newton Law05:04, highSchool, multiple choice, < 1 min,fixed.

Which one of the follow expressions is oneof Newton’s Law?

1. F = ma

2. F = mb

3. F = mc

4. F = mx

5. F = my

6. F = mz

Chapter 5, section 5, Weight 150


Imagine standing on a bathroom scale andreading your weight. Now lift one foot andread your weight again.

Does the scale read more, less or the sameweight when you are standing on one foot?

1. The scale reads higher because the pres-sure on the scale is greater.

2. The scale reads lower because the liftedfoot doesn’t contribute to the measurement.

3. The readings are the same.

4. It depends on how high a foot is ele-vated.


How much force must be applied duringliftoff to accelerate a 20 kg satellite justenough to counter the Earth’s gravitationalacceleration of 9.8 m/s2?


Your weight is 150 lb.What do you weigh in Newtons?


Your weight is 150 lb.What is your mass in kilograms?


A bungee jumper feels weightless as shefalls toward the Earth.

What accounts for her weightless feeling

when she fall freely?

1. The force of gravity disappears when shehas jumped off a high platform.

2. Her weight becomes less when she hasjumped off.

3. The weightless feeling is because of thelack of a support force that balances gravity.

4. The platform is too high.


How is weight related to mass?

1. They are the same.

2.W = 9.8m

3.W = 1.6m

4.Weight is directly proportional to mass.

5. Weight is inversely proportional tomass.

6.W = 4.9m

7. None of these


Why do you weight less on the Moon thanon the Earth?

1. Your mass become less when you are onthe Moon.

2. The Moon is less massive than theEarth.

3. The Moon is smaller than the Earth.


4. The Moon is so much less massive thanthe Earth that you weigh less on the Moon.


How would your mass change if you took atrip to the space station?

1. decreases; you weigh less.

2. no change in mass

3. increases; you weigh more.


Part 1 of 3The mass of a hydrogen atom is 1.67 ×

10−27 kg.Calculate the weight of 2 hydrogen atoms

near the Earth’s surface. g = 9.8 m/s2

Part 2 of 3How many hydrogen atoms are there in 1 lbof hydrogen gas?

Part 3 of 3Suppose that every person in the world (about6 billion people in all) were employed as anatom counter. Each person would work a 40-hour week and be able to count one atom persecond.

How long would it take for 6 billion peo-ple to count the hydrogen atoms in 1 lb ofhydrogen?


What is the weight of a column of water 5 fthigh with a radius of 1 m?

The density of the water is 1000 kg/m3.

Elevator05:05, highSchool, multiple choice, < 1 min,fixed.

Consider a person of weight W standingin an elevator that is accelerating downward.An upward force N is exerted by the elevatorfloor on the person.

The relationship between N andW is

1. N >W.

2. N =W.

3. N <W.



What happens to the weight of a cup whena tea bag is dipped in it?

1. The cup is heavier when the tea bag isdipped.

2. The cup is lighter when the tea bag isdipped.

3. There is no change in the weight of thecup.

Forces05:05, highSchool, multiple choice, < 1 min,fixed.

Wa

Consider a girl standing in an elevator that


is accelerating upward. The upward normalforce N exerted by the elevator on the girl is

1. larger than

2. identical to

3. smaller than

the downward weightW of the girl.


What Aristotelian idea did Galileo discreditin his fabled Leaning Tower demonstration?

1. He discredited Aristotle’s idea that therate at which bodies fall is directly propor-tional to their weight.

2. He discredited Aristotle’s idea that therate at which bodies fall is not related to theirweight.

3. He discredited Aristotle’s idea that therate at which bodies fall is inversely propor-tional to their weight.

4. He discredited Aristotle’s idea of gravita-tion.

5. All are wrong.


Part 1 of 4Gravity on the surface of the moon is only

1

6as strong as gravity on the Earth.

The acceleration of gravity is 10 m/s2 .What is the weight of a 10 kg object on the

Earth?

Part 2 of 4What is the weight on the moon?

Part 3 of 4What is the mass on the earth?

Part 4 of 4What is the mass on the moon?


What happens to your weight when yourmass increases?

1. When the mass increases weight de-creases.

2. When the mass increases weight in-creases.

3. Your weight is independent of yourmass.


When you jump vertically off the ground,what is your acceleration when you reach yourhighest point? Up is positive.

1. −g

2. −g2

3. −g3

4. 0 m/s2

5. All are wrong.

6. g

7.g

2

8.g

3



The acceleration of gravity is 10 m/s2 .What is the acceleration of a 20 kg pail of

cement that is pulled upward (not sideways)with a force of 300 N?


Which of the following has more weight?

1. a liter of ice

2. a liter of water

3. They have same weight



Part 1 of 2A 2.26 kg book is dropped from a height of

1.5 m.The acceleration of gravity is 9.81 m/s2 .a) What is its acceleration?

Part 2 of 2b) What is its weight?


Part 1 of 2A 3.46 kg briefcase is sitting at rest on a

level floor.The acceleration of gravity is 9.81 m/s2 .a) What is its acceleration?

Part 2 of 2b) What is its weight?


An object placed on an equal arm balancerequires 12 kg to balance it. When placed ona spring scale, the scale reads 12 kg. Noweverything (balance, set of masses, scale, andobject) is transported to the moon, where the

force of gravity is1

6that on earth.

What are the new readings on the balanceand spring scale, respectively?

1. 12 kg, 12 kg

2. 2 kg, 2 kg

3. 12 kg, 2 kg

4. 2 kg, 12 kg

5. 12 kg, 72 kg

Motion and Force 0505:05, highSchool, multiple choice, > 1 min,wording-variable.

A ball of mass M is suspended by a thinstring (of negligible mass). An upward forceF pulls on the string as shown in the figurebelow. The relation between the tension inthe string T and the weight of the ball M g isgiven in each statement below.

M

T

F

While T < M g , the ball’s accelerationmust be downwards, with its velocity eitherupwards, downwards, or zero.

1. True

2. False

3. Cannot be determined.

Chapter 5, section 6, Contact and Normal Forces 154


What force pushes up on you when youjump vertically off the ground?

1. The ground pushes up on you.

2. Your feet push up on your body.

3. The force of gravitation

4. The force of air drag

5. All are wrong.

Chapter 5, section 7, Hooke’s Law 155

Hewitt CP9 12 4505:07, highSchool, numeric, < 1 min, normal.

If a certain spring stretches 14 cm when aload of 40 N is suspended from it, how muchwill the spring stretch if it is cut in half and240 N is suspended from it?


A mass of 0.55 kg attached to a verticalspring stretches the spring 36 cm from itsoriginal equilibrium position.

The acceleration of gravity is 9.81 m/s2 .What is the spring constant?


A load of 45 N attached to a spring thatis hanging vertically stretches the spring 0.14m.

What is the spring constant?

Holt SF 12A 03 0405:07, highSchool, numeric,> 1min, wording-variable.

Part 1 of 2A slingshot consists of a light leather cup

attached between two rubber bands. It takesa force of 32 N to stretch the bands 1.2 cm.

a) What is the equivalent spring constantof the rubber bands?

Part 2 of 2b) How much force is required to pull the cupof the slingshot 3.0 cm from its equilibriumposition?


Janet wants to find the spring constant of a

given spring, so she hangs the spring verticallyand attaches a 0.40 kg mass to the spring’sother end.

The acceleration of gravity is 9.81 m/s2 .If the spring stretches 3.0 cm from its

equilibrium position, what is the spring con-stant?


In preparing to shoot an arrow, an archerpulls a bow string back 0.400 m by exerting aforce that increases uniformly from 0 to 230N.

What is the equivalent spring constant ofthe bow?


In an arcade game, a 0.12 kg disk is shotacross a frictionless horizontal surface by be-ing compressed against a spring and then re-leased. The spring has a spring constant of230 N/m and is compressed from its equilib-rium position by 6.0 cm.

What is the magnitude of the spring forceon the disk at the moment it is released?


A child’s toy consists of a piece of plasticattached to a spring, as shown. The spring iscompressed against the floor a distance of 2.0cm and released.

If the spring constant is 85 N/m, what isthe magnitude of the spring force acting onthe toy at the moment it is released?

Chapter 5, section 7, Hooke’s Law 156


Part 1 of 2A 0.40 kg mass is attached to a spring with

a spring constant of 160 N/m so that the massis allowed to move on a horizontal frictionlesssurface. The mass is released from rest whenthe spring is compressed 0.15 m.

a) Find the force on the mass at the instantthe spring is released.

Part 2 of 2b) Find the acceleration of the mass at theinstant the spring is released.

Spring Constant 0105:07, highSchool, multiple choice, > 1 min,normal.

The force required to stretch a springvaries directly with the amount the springis stretched. A force of 27 pounds is neededto stretch a spring 50 inches, as shown in theright-hand figure below.

30′′

50′′

W

27 lbs

How much force is required to stretch thespring 30 inches?

Spring Constant 0205:07, highSchool, numeric, > 1 min, normal.

A common technique used to measure the

force constant k of a spring is the following:The spring is hung vertically and then a

mass m is attached to the lower end of thespring. The spring stretches a distance dfrom the equilibrium position under the ac-tion of the “load” mg. Since the spring forceis upward, it must balance the weight mgdownward when the system is at rest.


55 m

39 N

Find the spring constant k if the springis stretched 55 m by a suspended weight of39 N.

Chapter 5, section 9, Newton’s Third Law 157

Barefoot Kicker 0205:09, highSchool, numeric, > 1 min, normal.

A barefoot field-goal kicker imparts a speedof 35 m/s to a football initially at rest.

If the football has a mass of 0.5 kg and thetime of contact with the ball is 0.025 s, whatis the force exerted by the ball on the kicker’sfoot?


When you drop a rubber ball on the floor itbounces almost to its original height.

What causes the ball to bounce?

1. The ball attempts to return to its originalposition.

2. The force of the floor on the ball causes itto bounce upward.

3. Air forced out upon contact causes a tem-porary vacuum which sucks the ball up.

4. The floor pushes up on the ball harderthen the ball pushes down on the floor.


When an athlete holds a barbell overhead,the reaction force is the weight of the barbellon his hand.

How does this force vary for the case wherethe barbell is decelerated upward?

1. The force exerted by the athlete is smallerthan the weight of the barbell.

2. The force exerted by the athlete is greaterthan the weight of the barbell

3. The force exerted by the athlete is equalto the weight of the barbell.

4. It depends on the will of the athlete.


Consider a baseball bat hitting a ball.Which of the following is correct?

1. Both slow down.

2. The baseball bat slows down, and the ballspeeds up.

3. Both speed up.

4. The baseball bat speeds up, and the ballslows down.

5. None of these


Ken and Joanne are astronauts floatingsome distance apart in space. They are joinedby a safety cord whose ends are tied aroundtheir waists.

If Ken starts pulling on the cord, what willhappen?

1. Ken will move toward Joanne whileJoanne remains stationary.

2. Joanne will move toward Ken while Kenremains stationary.

3. The move toward each other.

4. Neither will move.


Consider a bird landing on a stretchedpower-line wire.


Which of the following is correct?

1. The tension in the wire will change; theadded tension is less than the bird’s weight.

2. The tension in the wire will change;the added tension is more than the bird’sweight.

3. The tension in the wire will change; theadded tension is equal to the bird’s weight.

4. The tension in the wire will not change.

5. None of these


Margie (of mass 45 kg) and Bill (of mass65 kg), both with brand new roller blades,are at rest facing each other in the parkinglot. They push off each other and move inopposite directions, with Margie moving at aconstant speed of 14 ft/s .

At what speed is Bill moving?


Part 1 of 2A fast-moving VW Beetle traveling at 60

mph hit a mosquito hovering at rest abovethe road.

Which bug experienced the largest force?

1. the insect

2. the VW

3. They experienced the same magnitude offorce.


Part 2 of 2Which bug experienced the greatest accelera-tion?

1. the insect

2. the VW

3. Their acceleration is same.



Consider the following situations:I) A pitcher throws a fast ball;II) A pencil rests on your desk;III) A car hits a tree;IV) The wind pushes a sailboat.In which situation(s) do(es) a pair of equal

forces acting in opposite directions exist?

1. III and IV only

2. I, III and IV only

3. II, III and IV only

4. I and II only

5. I and III only

6. I, II and IV only

7. II and IV only

8. None of these

9. All of these

10. Another combination


When you are moving up at constant speedin an elevator, there are two forces acting onyou: the floor pushing up on you (F1) andgravity pulling down (F2).


What’s the relation of the magnitude of F1

and F2?

1. F1 = F2 from Newton’s first law.

2. F1 = F2 from Newton’s third law.

3. F1 > F2 from Newton’s second law.

4. F1 < F2 from Newton’s second law.

5. It depends on which direction the elevatoris moving.


In modern physics, we often talk aboutforces in terms of an exchange of particlesbetween objects. To see how this might work,imagine the following situation. Two studentsare running side-by-side in a straight line tocatch a train. One is carrying a heavy suitcaseand halfway to the train he throws it over tohis friend.

Will the two students be able to keep thestraight line motion?

1. Yes; from Newton’s first law.

2. Yes; from Newton’s third law.

3. No; both students recoil in response tothe suitcase pushing on them.

4. No; only the one catching the suitcase ispushed to the side.



When you kick a soccer ball, you apply aforce F1 to the ball.

What force F2 does the soccer ball exert onyour foot?

1. F1 = F2, acting in opposite directions

2. F1 = F2, acting in the same direction

3. F1 < F2

4. F2 < F1

5. There is no force F2.


Consider a tug-of-war contest between twopeople. Assume the rope is light and does notslip in either person’s hands.

What relationship would the two forceshave? Who will win the contest?

1. The forces are not equal; the person whopulls harder usually wins.

2. The forces are equal; neither person canwin.

3. The forces are equal; usually the per-son who weighs more and has better footingwins.

4. The forces are not equal; luck, not force,determines the winner.


If a book is sitting on a table, the force ofgravity pulls it down.

Why doesn’t it fall?

1. The book is not heavy enough.

2. Gravity isn’t pulling hard enough.

3. The table is pushing up on it with a forceequal to the weight of the book.



The Earth exerts an 800 N gravitationalforce on a man.

What force does the man exert on theEarth?


Part 1 of 3Consider the following statement made re-

garding a book at rest on a level table:The two forces exerted on the

book are the normal force directedup and the weight of the book di-rected down. These are equal andopposite to one another. By New-ton’s third law they are an action-reaction pair, so the normal force isalways equal to the weight of thebook.

Do you agree with the statement?

1. Disagree; if an additional force acts downon the book, the normal force must alsocounter this extra force.

2. Agree; a normal force only exerts enoughforce to keep the object from falling through.The normal force and weight are always equal,even when other forces are present.

3. Agree; for every action there is an equaland opposite reaction (Newton’s third law).Since gravity pulls down on the book, to be“equal and opposite” the force of gravity mustequal the normal force.

4. Disagree; the weight must be slightlygreater than the normal force to keep the bookin contact with the table. However, the forcesare an action-reaction force pair because theyare acting on one object.

Part 2 of 3

Consider a book on top of a level table whilethe book is being pressed straight down witha force F by your hand.

Book

F


Which figure has the correct directions foreach force?

Note: The magnitude of the forces are notnecessarily drawn to scale.

1.normal

gravitational hand

2.gravitational

hand normal

3.hand

normal gravitational


4.

normal

gravitational hand

5.

gravitational

hand normal

6.

hand

normal gravitational

Part 3 of 3What forces change when comparing the freebody diagram before the hand was placed onthe book to after?

1. normal and Fhand

2. gravitational

3. normal

4. Fhand

5. gravitational and normal

6. gravitational and Fhand

7. None of these

8. gravitational, normal, and Fhand


A car headrest helps to guard againstwhiplash in rear-end collisions.

Which law applies here?

1. the law of inertia

2. Newton’s second law

3. Newton’s third law

4. the law of gravitation

5. All are wrong.


As you stand on a floor, the floor exerts anupward force on you.

Why are you not moved upward by thisforce?

1. The upward force is greater than yourweight, but air pressure pushes you down.Without the air, you would be lifted up.

2. The upward force is less than your weight,so you do not move up.

3. The upward force is equal to your weightand the two forces cancel each other.

4. The upward force is negligible.

5. None of these


A common saying goes, “It’s not the fallthat hurts you; it’s the sudden stop.”

Translate this into Newton’s laws of mo-tion.

1. Newton’s first law

2. Newton’s second law



4. Gravitation law

5. All are wrong.


Identify the action-reaction pairs when abaseball is in flight.

1. Action: Earth pulls down on ball. Re-action: Ball pulls up on Earth. Action: Airpushes ball. Reaction: Ball pushes air.

2. Action: Ball pulls down on Earth. Re-action: Earth pulls up on ball. Action: Airpushes ball. Reaction: Ball pushes air.

3. Action: Bat pushes ball forward. Reac-tion: Ball pulls up on Earth. Action: Ballpushes air. Reaction: Air pushes ball.

4. Action: Bat pushes ball backward. Reac-tion: Earth pulls down on ball. Action: Ballpushes air. Reaction: Air pushes ball.

5. All are wrong.


Identify the action-reaction pairs when abaseball is being hit.

1. Action: bat hits ball. Reaction: ball hitsthe player.

2. Action: bat hits ball. Reaction: ball hitsbat.

3. Action: ball hits bat. Reaction: bat hitsthe player.

4. Action: ball hits bat. Reaction: bat

pushes the arm of the player.

5. None of these


When the athlete holds the barbell on hishand, the reaction force is the weight of thebarbell on his hand.

How does this force vary for the case wherethe barbell is accelerated upward? Down-ward?

1. Upward: the reaction force is greaterthan the weight of the barbell; downward:the reaction force is less than the weight ofthe barbell.

2. Upward: the reaction force is greaterthan the weight of the barbell; downward:the reaction force is greater than the weightof the barbell.

3. Upward: the reaction force is less thanthe weight of the barbell; downward: thereaction force is greater than the weight ofthe barbell.

4.Upward: the reaction force is less than theweight of the barbell; downward: the reactionforce is less than the weight of the barbell.

5. All are wrong.


What statement is correct?

1. You can exert greater force on the pedalsof a bicycle if you pull up on the handlebars;you will exert smaller force on the pedals of abicycle if you push down on the handlebars.

2. You can exert greater force on the pedalsof a bicycle if you pull up on the handlebars;


you can exert greater force on the pedals of abicycle if you push down on the handlebars.

3. You will exert smaller force on the pedalsof a bicycle if you pull up on the handlebars;you can exert greater force on the pedals of abicycle if you push down on the handlebars.

4. You will exert smaller force on the pedalsof a bicycle if you pull up on the handlebars;you will exert smaller force on the pedals of abicycle if you push down on the handlebars.

5. All are wrong.


If a Mack truck and Honda Civic have ahead-on collision, upon which vehicle is theimpact force greater and which vehicle expe-riences the greater acceleration?

1. The forces are the same; the Civic experi-ences the greater acceleration.

2. The force on the truck is greater; theaccelerations are the same.

3. The forces are the same; the accelerationsare same.

4. The forces are the same; the truck expe-riences the greater acceleration.

5. All are wrong.


Consider a stone at rest on the ground.There are two interactions that involve thestone. One is between the stone and theEarth; Earth pulls down on the stone and thestone pulls up on the Earth.

What is the other interaction?

1. between the stone and the ground

2. between the ground and the Earth

3. between the ground and air

4. between the Earth and air

5. All are wrong.

Horse and Cart05:09, highSchool, multiple choice, < 1 min,fixed.

Imagine a horse pulling a cart; the horseand the cart move at the same velocity.Whether the horse and the cart are movingat a constant velocity or not is not impor-tant. Now, according to the laws of motion,the horse and the cart exert forces on eachother.

Which force is bigger?

1. Force exerted by the horse on the cart

2. Force exerted by the cart on the horse

3. Two forces are equal

4. Insufficient information to determine

Reaction Force 0205:09, highSchool, multiple choice, < 1 min,fixed.

A projectile moves along a parabolic pathnear the Earth’s surface.

What is the reaction to the Earth’s gravi-tational force?

1. The force exerted by the projectile on theEarth.

2. None of these

3. The weight of the projectile.

4. The force of air friction.


5. The mass of the projectile.

Chapter 5, section 10, Free Body Diagrams in Problem Solving 165


Consider a sailboat that changes direction.What provides the force that makes the

change?

1. the water

2. the rudder

3. the sailor

4. None of these


Part 1 of 2Four forces act on an object.

F1

F4

F2

F3

If the object is accelerating to the right,compare the forces.

1. F1 = F2, F3 < F4

2. F1 = F2, F3 > F4

3. F1 > F2, F3 < F4

4. F1 < F2, F3 < F4

5. F1 = F2, F3 = F4

Part 2 of 2If the object is accelerating upward and to

the right, compare F1 to F2 and F3 to F4.

1. F1 = F2, F3 < F4

2. F1 = F2, F3 > F4

3. F1 > F2, F3 < F4

4. F1 < F2, F3 < F4

5. F1 = F2, F3 = F4


Part 1 of 2A spherical mass rests upon two wedges,

as seen in the figure below. The sphere andthe wedges are at rest and remain at rest.There is no friction between the sphere andthe wedges.

M

The following figures show several attemptsat drawing free-body diagrams for the sphere.


1.

weight

normalnormal

2.weight


3. weight

normalnormal

4. normalnormal

weightweight

5.

weight

normal

6.

weightfriction friction

normalnormal

7. normal

weightweight

8. normalnormal

weightweight

9. Since the sphere is not moving, no forcesact on it.

Part 2 of 2The wedges themselves lie on a horizontaltable. There is friction between the table andthe wedges. The following figures show several

attempts at drawing free-body diagrams forthe left wedge.


1.normal

weight

friction

F sphere

2.normal

weightfriction

F sphere

3.normal

weight

friction

F sphere

4.normal

weightfriction

F sphere

5.normal

weightF sphere


6.normal

weight

F sphere

7.normal

weightFsphere

friction

8.normal

weightFsphere

friction


Conceptual forces 06 short05:10, highSchool, multiple choice, > 1 min,fixed.

A spherical mass rests upon two wedges, asseen in the figure below. The sphere and thewedges are at rest and stay at rest. There is nofriction between the sphere and the wedges.

M

The following figures show several attemptsat drawing free-body diagrams for the sphere.

Which figure has the correct directions foreach force?

Note: The magnitude of the forces are notnecessarily drawn to scale.

1.

weight

normalnormal

2.weight

3. weight

normalnormal

4. normalnormal

weightweight

5.

weight

normal

6.

weightfriction friction

normalnormal

7. normal

weightweight


8. normalnormal

weightweight


Elevator Free Body Diagram05:10, highSchool, multiple choice, > 1 min,fixed.

A man stands in an elevator in theuniversity’s administration building andis accelerating upwards. (During peakhours, this does not happen very often.)

Elevator Cable

Choose the correct free body diagram forthe man, where Fi,j is the force on the objecti, from the object j.

1.

F

F

man, floor

man, earth

2.

Fman, cable

3.

Fman, acceleration

4.

F

F

elevator, cable

man, earth

5.

Felevator, cableFman, elevator

6.

Fman, floorFelevator, cable

Fman, earth

Free Body Diagram of Balloon05:10, highSchool, multiple choice, < 1 min,fixed.

Part 1 of 2


A balloon is waiting to take off. As seen inthe figure below, the balloon’s basket sits ona platform. The balloon is pulling up on thebasket, but not hard enough to lift it off theplatform. The platform lies on the ground.

Balloon

GroundPlatform

Basket

Which of the following is the correct free-bodydiagram for the platform?

N.B. Vectors may be offset horizontally forclarity.

1.Fballoon on platform

Fgravity on platform

2.Fplatform on basket

Fplatform on groundFgravity on platform

3.

Fgravity on platform Fplatform on ground

Fballoon on platform

4.Fground on platform

Fbasket on platformFgravity on platform

5.


Fgravity on basket

Fballoon

Part 2 of 2What is the free-body diagram for the basket?

N.B. Vectors may be offset horizontally forclarity.

1.

Fplatform on basket Fballoon on basket

Fgravity on basket

2.Fballoon on basket

Fgravity on basket

3.

Fground on basket Fballoon on basket

Fgravity on basket

4.


Fgravity on basket

Fbasket on balloon

Fballoon on basket


5.

Fgravity on basket

Fbasket on balloonFbasket on platform

Chapter 5, section 11, Static Applications of Newton’s Law 171

Hewitt CP9 02 E2205:11, highSchool, numeric, > 1 min, normal.

A staging that weighs Wstaging supports apainter weighing 200 N. The reading on theleft scale is 400 N and the reading on the rightscale is 300 N.

400 N 300 N

What is the weight of the staging?


A staging that weighs 300 N supports twopainters, one 250 N and the other 300 N. Thereading in the left scale is F` = 400 N .

400 Fr

What is the reading Fr in the right handscale?

Hewitt CP9 02 E2505:11, highSchool, numeric, > 1 min, normal.

Part 1 of 2Harry the painter swings year after year

from his bosun’s chair. His weight is 500 Nand the rope, unknown to him, has a breakingpoint of 300 N.

Why doesn’t the rope break when he issupported as shown at the left above? Toanswer this, find the tension in the rope.

Part 2 of 2One day Harry is painting near a flagpole,and, for a change, he ties the free end of therope to the flagpole instead of to his chair asshown at the right.

Why did Harry end up taking his vacationearly? To answer this, find the tension in therope.


Two ropes support a lantern that weighs 50N.

Is the sum of the tensions in both ropes lessthan, equal to, or more than 50 N?

1. Less than, by the parallelogram rule.

2. Equal to, so the lantern is at equilib-rium.

3. More than, because the two ropes formtwo legs of a triangle.

4. It depends on the angle between the tworopes.

5. All are wrong.

Holt SF 04Rev 43



A 2.00 kg block is in equilibrium on anincline of 36.0◦.

The acceleration of gravity is 9.81 m/s2 .What is Fn of the incline on the block?


Part 1 of 2A block with a mass of 5.0 kg is held in

equilibrium on a frictionless incline of 25.0◦

by the horizontal force ~F , as shown.The acceleration of gravity is 9.81 m/s2 .

5 kg

F25◦

25◦

What is the magnitude of F?

Part 2 of 2What is the magnitude of the normal force?


A machine in an ice factory is capable ofexerting 3.00 × 102 N of force to pull largeblocks of ice up a slope. The blocks eachweigh 1.22× 104 N.

Assuming there is no friction, what is themaximum angle that the slope can make withthe horizontal if the machine is to be able tocomplete the task?


Part 1 of 2

Consider the 34 N weight held by two cablesshown below. The left-hand cable is horizon-tal.

34 N

41◦

a) What is the tension in the cable slantedat an angle of 41◦?

Part 2 of 2b) What is the tension in the horizontal ca-ble?


Part 1 of 2Consider the 34 N weight held by two cables

shown below. The left-hand cable is horizon-tal.

34 N

41◦


a) What is the tension in the cable slantedat an angle of 41◦?

Part 2 of 2b) What is the tension in the horizontal ca-ble?

Platform Held by Ropes05:11, highSchool, numeric, > 1 min, normal.

Part 1 of 2A 25 kg person stands on a 50 kg platform.

He pulls on the rope that is attached to the


platform via the frictionless lower-right pul-ley. He pulls the rope at an angle of 30◦ to thehorizontal, as shown in the figure below.

Assume: g = 9.8 m/s2 . Ignore friction.The platform remains level.

50 kg

30◦

25 kg

If he pulls the platform up at a steady rate,how much force is he pulling on the rope?

1. F = 245 N

2. F = 735 N

3. F = 367.5 N

4. F = 490 N

5. F = 294 N

6. F = 441 N

7. F = 183.75 N

8. F = 551.25 N


Part 2 of 2In Part 1 we assumed that the platform re-mains level. This is a bad assumption.

However, if the man were pulling straightup on the rope, the forces will be balancedand the platform should remain level.

1. This also is a bad assumption.

2. This is a good assumption.


Pulleys 0605:11, highSchool, numeric, > 1 min, normal.

In the pulley system, all pulleys are mass-less and frictionless.


22 N

T

Find the tension T .


A 777 g mass is attached to a pulley and a8 N weight is attached to a thin massless cord,as shown below.

The pulley is massless and frictionless.The acceleration of gravity is 9.8 m/s2 .

777 g

8 N

T

What is the tension T?


The system is in equilibrium, and the pul-leys are weightless and frictionless.

The acceleration of gravity is 32 m/s2 .


1 slug

10 lb

T

Find the tension T . Note: lb ≡ slugft

s2.


The system is in equilibrium, and the pul-leys are weightless and frictionless.


10 N

8 N

T3

T2

T

T3T2



The system is in equilibrium, and the pulleyis weightless and frictionless. The suspendedweight on the left is 20 N and the suspendedweight on the right is 6 N.


20 N

6 N

1

T


Pulleys 11


The system is in equilibrium and the pulleysare massless and frictionless. The suspendedmass is 99 slug.

The acceleration of gravity is 32 ft/s2 .

99 slug

T

Find the tension T . Note: lb ≡ slugft

s2.


The system is in equilibrium and the pulleysare weightless and frictionless. The suspendedweight is 55 N.


55 N

T


Pulleys 1305:11, highSchool, numeric,> 1min, wording-variable.

The system is in equilibrium and the pulleysare weightless and frictionless. The weightsare 20 N, 3 N, 4 N, and 1 N.



20 N

3 N

4 N

1 N T



The pulley system is in equilibrium and thepulleys are weightless and frictionless. Theweights are 130 N, 15 N, and 20 N.


130 N

15 N

20 N

T



The system is in equilibrium and the pulleysare weightless and frictionless. The suspended

mass is 7 kg and the weights are 5 N and 8 N.The acceleration of gravity is 9.8 m/s2 .

5 N

8 N

7 kg

T



The system is in equilibrium and the pulleysare weightless and frictionless. The weightsare 47 N, 5 N, 6 N, and 11 N.


5 N

47 N

6 N

11 N

T



The system is in equilibrium and the pulleysare weightless and frictionless. The suspendedmass is 22 kg .



22 kg

T


Springs and Pulleys 0105:11, highSchool, numeric, > 1 min, normal.

The pulley system is in equilibrium, and thepulleys are weightless and frictionless. Thespring constant is 3 N/cm and the suspendedmass is 12 kg.


12 kg

3 N/cm

How much will the spring stretch?

Springs and Pulleys 0205:11, highSchool, numeric, > 1 min, normal.

The pulley system is in equilibrium and thepulleys are weightless and frictionless. Thespring constant is 4 N/cm, the suspendedweights are 35 N and 15 N.


35 N 15 N

4 N/cm

How much will the spring stretch?

Static Equilibrium Requirements05:11, highSchool, multiple choice, > 1 min,fixed.

Part 1 of 2Consider an extended object (not a point),

with forces ~F acting on it, producing torques~τ .

Is it possible for a situation to exist in whichthe net force acting on the object (the netforce is the sum of all the individual forces act-ing on the object) is equal to zero

(

∑

~F = 0)

while the net torque about any axis (the nettorque is the sum of all the torques acting on

the object) is not equal to zero(

∑

~τ 6= 0)

?

1. Yes.

2. No.

Part 2 of 2Is it possible for a situation to exist in whichthe net torque acting on the object is zero(

∑

~τ = 0)

while the net force acting on the

object is not equal to zero(

∑

~F 6= 0)

?

1. Yes.

2. No.

Chapter 5, section 12, Dynamic Applications of Newton’s Law 177

Ascending worker05:12, highSchool, multiple choice, > 1 min,fixed.

The mass of the worker m1 = 50 kg. Themass of the block at the end of the rope,m2 = 100 kg.

�

T T

aam2

m1

Determine the acceleration.

1. a =m2

m1g = 2 g

2. a =m2 −m1

m1g = g

3. a =m2 −m1

m1 +m2g =

1

3g

Bead on Track05:12, highSchool, multiple choice, > 1 min,wording-variable.

Part 1 of 4A bead slides starting from rest at position

O on a frictionless wire. The gravitation fieldis in the −y direction.

x

y

Y

S

V

O

At which position(s) will the speed of thebead have a maximum value?

1. Point V .

2. Point Y .

3. Point S.

4. Points Y and V .

5.The bead remains stationary at pointO.

Part 2 of 4At which position(s) will the magnitude ofthe acceleration in the x direction of the beadhave a maximum value?

1. Point O.

2. Point V .

3. Point Y .

4. Point S.

5. Points Y and V .

Part 3 of 4At which position(s) will the speed of the beadhave a minimum value?

1. Point S.

2. Point V .

3. Point Y .

4. Points Y and V .

5. The bead’s speed is constant.

Part 4 of 4At which position(s) will the magnitude ofthe acceleration of the bead have a minimumvalue?

1. Points Y , S, and V .

2. Points Y and V .

3. Points Y and S.


4. Points S and V .

5. Point O.

6. Point S.

Block on Incline Graphs 0105:12, highSchool, multiple choice, > 1 min,wording-variable.

Given: The initial position of the block isthe origin; i.e., x = 0 at t = 0 . Consider up

the track to be the positive x-direction.A block with an initial velocity v0 slides up

and back down a frictionless incline.

v0

θ

Which graph best represents a descriptionthe position of the block versus time?

1. t

x

2. t

x

3. t

x

4. t

x

5. t

x

6. t

x

7. t

x

8. t

x

9. t

x

10. t

x


Given: The initial position of the block isthe origin; i.e., x = 0 at t = 0 . Consider down




v 0

θ

Which graph best represents a descriptionof the velocity of the block versus time?

1. t

v

2. t

v

3. t

v

4. t

v

5. t

v

6. t

v

7. t

v

8. t

v

9. t

v

10. t

v




and back down a frictionless incline.v0

θ

Which graph best represents a descriptionthe acceleration of the block versus time?


1. t

a

2. t

a

3. t

a

4. t

a

5. t

a

6. t

a

7. t

a

8. t

a

9. t

a

10. t

a





v0

θ

Which graph best represents a descriptionthe position of the block versus time?

1. t

x


2. t

x

3. t

x

4. t

x

5. t

x

6. t

x

7. t

x

8. t

x

9. t

x

10. t

x

Hewitt CP9 02 E3705:12, highSchool, numeric, < 1 min, fixed.

A child learns in school that the Earth istraveling faster than 100,000 kilometers perhour around the sun, and in a frightened toneasks why we aren’t swept off.

What statement is true?

1. We are traveling just as fast as theEarth.

2.We are traveling faster than the Earth.

3.We are traveling slower than the Earth.

4. The Earth rotates on its own axis.

5. All are wrong.


The chimney of a stationary toy train con-sists of a vertical spring gun that shoots steelballs a meter or so straight into the air – sostraight that the ball always falls back intothe chimney.

If the train is moving, under which condi-tion will the ball fall back into the chimney?

1. The train moves at constant speed alongthe straight track.

2. The train suddenly increases its speedwhen the ball is in the air.

3. The train suddenly decreases its speedwhen the ball is in the air.

4. The train moves at a constant speed on acircular track.


5. All are wrong.


Part 1 of 3Two forces, 450 N at 15◦ and 300 N at 26◦

are applied to a car in an effort to accelerateit.

3000 kg

450 N15

◦

300 N26◦

a) Find the resultant of these two forces.

Part 2 of 3b) Find the direction of the resultant force(in relation to forward, with counterclock-wise considered positive, with −180◦ < θ <+180◦).

Part 3 of 3Assume: There is no friction.

c) If the car has a mass of 3000 kg, whatacceleration does it have?


A 40.0 kg wagon is towed up a hill inclinedat 18.5◦ with respect to the horizontal. Thetow rope is parallel to the incline and exertsa force of 140 N on the wagon. Assume thatthe wagon starts from rest at the bottom ofthe hill, and disregard friction.

The acceleration of gravity is 9.81 m/s2 .How fast is the wagon going after moving

30.0 m up the hill?


Part 1 of 2

A shopper in a supermarket pushes a loaded32 kg cart with a horizontal force of 12 N.

The acceleration of gravity is 9.81 m/s2 .a) Disregarding friction, how far will the

cart move in 3.5 s, starting from rest?

Part 2 of 2b) How far will the cart move in the 3.5 s ifthe shopper places a(n) 85 N child in the cartbefore pushing it?


A 2.0 kg mass starts from rest and slidesdown an inclined plane 8.0×10−1 m long in0.50 s.

What net force is acting on the mass alongthe incline?


Part 1 of 5Three blocks are in contact with each other

on a frictionless horizontal surface. A 360 Nhorizontal force is applied to the block withmass of 2 kg as shown in the figure below.


2 kg 4 kg 6 kgF

a) What is the net force on the block withmass 2 kg?

Part 2 of 5b) What is the resultant force on the blockwith mass 4 kg?

Part 3 of 5c) What is the resultant force on the blockwith mass 6 kg?

Part 4 of 5d)What is the magnitude of the force betweenthe block with mass 4 kg and 6 kg?


Part 5 of 5e) What is the magnitude of the force betweenthe block with mass 2 kg and 4 kg?


A wrecking ball of massM is suspended bya thin cable (of negligible mass). The ball’sposition is recorded by three sequential pic-tures (labeled 1, 2, & 3) with a flash camera inintervals of 1.5 s. The vertical position (in me-ters) is recorded on the scale on either side ofthe pictures. Throughout the positions illus-trated below, the tension remains constant.The positive direction is upward.

1 2 3

5

4

3

2

1

0

[m]

Compare the tension in the cable T withthe weightM g of the ball.

1. T > M g

2. T =M g

3. T < M g



A wrecking ball of massM is suspended bya thin cable (of negligible mass). The ball’sposition is recorded by three sequential pic-tures (labeled 1, 2, & 3) with a flash camerain intervals of 1.5 s. The vertical position

(in meters) is recorded on the scale on eitherside of the pictures. Throughout the posi-tions illustrated below, the tension remainsconstant.

For each of the pictures below, the verticalposition y of the ball is described as a functionof time t by

y = y0 + v0 t+1

2a t2 .

y0 is the initial vertical height in the firstpicture. v0 is the initial vertical velocity inthe first picture. The positive direction isupward.

1 2 3

5

4

3

2

1

0

[m]

Select the correct values for a .

1. The acceleration is upward.

2. The acceleration is zero.

3. The acceleration is downward.


Motion and Force 0305:12, highSchool, numeric, > 1 min, normal.

A wrecking ball of massM is suspended bya thin cable (of negligible mass). The ball’sposition is recorded by three sequential pic-tures (labeled 1, 2, & 3) with a flash camerain intervals of 1.5 s. The vertical position(in meters) is recorded on the scale on eitherside of the pictures. Throughout the posi-tions illustrated below, the tension remainsconstant.

For each of the pictures below, the verticalposition y of the ball is described as a function


of time t by

y = y0 + v0 t+1

2a t2 .

y0 is the initial vertical height in the firstpicture. v0 is the initial vertical velocity inthe first picture. The positive direction isupward.

1 2 3

5

4

3

2

1

0

[m]

Calculate the acceleration a for the wreck-ing ball.


A ball of mass M is suspended by a thinstring (of negligible mass) from the ceilingof an elevator. The vertical motion of theelevator as it travels up and down is describedin the statements below. Indicate for each ofthe situations described the relation betweenvalue of the tension T in the string and theweight of the ballM g, or whether one cannottell.

M

T

v

Elevatorwith aweightheld bya stringinside it

The elevator is traveling downward and itsdownward velocity is decreasing as it stops ata lower floor.

1. T > M g

2. T < M g

3. T =M g


Pulling 3 Blocks no friction05:12, highSchool, numeric, > 1 min, normal.

Part 1 of 2Consider a force F = 450 N pulling 3 blocks

of masses m1 = 8 kg, m2 = 15 kg, and m3 =22 kg along a frictionless horizontal surface.

m3 m2 m1

T2 T1 F

Find the acceleration a of the blocks.

Part 2 of 2The tension of the strings are T1 and T2 (seesketch).

The equation of motion of m2 is given by

1. T1 − T2 = m2 a .

2. T1 + T2 = m2 a .

3. T1 = m2 a .

4. T1 − T2 = m1 a .

5. T1 + T2 = m1 a .

6. T1 = m1 a .

7. T1 − T2 = (m1 +m3) a .

8. T1 + T2 = (m1 +m3) a .

9. T1 = (m1 +m3) a .

Two Blocks Simple SW05:12, highSchool, multiple choice, < 1 min,fixed.


A block of massm rests on a horizontal fric-tionless surface. This block is connected by astring that passes over a frictionless and mass-less pulley to a suspended block of the samemass m. If the two blocks are initially mov-ing with a velocity v0 (where the suspendedblock is falling) what is the acceleration of thefalling block when it has fallen a distance Dfrom its initial height?

m

m


2.g

2

3. 2g

4. g

5.v20

2D+ g

6.v20

2D+ 2g

7.v20

2D+g

2

8.v20

D+ g

9.v20

D+ 2g

10.v20

D+g

2

Two Tensions 0205:12, highSchool, numeric,> 1min, wording-variable.

Three blocks are on a frictionless horizontalsurface. The bocks are connected by masslessstrings with tensions T` and Tr.

3 kg 5 kg 1 kg

T` Tr67 N 31 N

Calculate the tension T`.

Chapter 5, section 13, Friction 186

Braking a Car 0205:13, highSchool, numeric, < 1 min, normal.

A 1200 kg car moves along a horizontal roadat speed v0 = 20 m/s. The road is wet, sothe static friction coefficient between the tiresand the road is only µs = 0.15 and the kineticfriction coefficient is even lower, µk = 0.105.

The acceleration of gravity is 9.8 m/s2 .What is the shortest possible stopping dis-

tance for the car under such conditions? Useg = 9.8 m/s2 and neglect the reaction time ofthe driver.

Braking a Car 0305:13, highSchool, numeric, < 1 min, normal.

A 1200 kg car moves along a horizontal roadat speed v0 = 20 m/s. The road is wet, sothe static friction coefficient between the tiresand the road is only µs = 0.25 and the kineticfriction coefficient is even lower, µk = 0.175.

The acceleration of gravity is 9.8 m/s2 .Assume: No aerodynamic forces; g =

9.8 m/s2, forward is the positive direction.What is the highest possible deceleration of

the car under such conditions?


If only an external force can change thevelocity of a body, how can the internal forceof the brakes bring a car to rest?

1. Some internal forces can change the ve-locity of a body.

2. It is the driver, not the car itself whocauses the breaking, so it is an externalforce.

3. The engine is stopped, so the car has noforce to run further.

4. It is the force of the road on the tires (anexternal force) that stops the car.


In order to slide a heavy desk across thefloor at constant speed in a straight line, youhave to exert a horizontal force of 500 New-tons.

Compare the 500-Newton horizontal push-ing force F to the frictional force f betweenthe desk and the ground.

1. F > f ; the frictional force is always lessthan any other force acting on the object.

2. F < f ; the frictional force is greater thanthe pushing force since it is such a heavydesk.

3. F = f from Newton’s third law.

4. F = f from Newton’s first law.

5. It depends on the direction the deskmoves.


Part 1 of 2A bicycle rider accelerates from rest up to

full speed on a flat, straight road. The fric-tional force between the road and the tirespushing her forward is f1. The air drag (andother frictional forces) pushing back is f2.

What relationship would f1 and f2 have inthe first few seconds of the ride?

1. f1 = f2

2. f1 > f2

3. f1 < f2


Part 2 of 2


What relationship would f1 and f2 haveafter she has reached full speed?

1. f1 = f2

2. f1 > f2

3. f1 < f2


Conceptual forces 0105:13, highSchool, multiple choice, < 1 min,normal.

Part 1 of 2A string is tied to a book and pulled at an

angle α as shown in the diagram. The bookremains in contact with the table and doesnot move.

m

µs

T α

Which choice best describes the free bodydiagram in the vertical direction for this situ-ation?

1. N = mg

2. N = mg − T cosα

3. N = mg − T sinα

4. N = mg + T cosα

4. N = mg + T sinα

Part 2 of 2Which forces must change in order for thebook to start moving?

1. normal

2. friction

3. tension in the string

4. gravitational

5. normal and gravitational

6. friction and tension in the string

7. normal, friction, and tension in the string

8. friction, tension in the string, and gravi-tational

9. None of these


Part 1 of 3Consider a book that remains at rest on an

incline.

Book



1.

gravitational

frictionnormal


2.

gravitational

normalfriction

3.

gravitational

friction

4.

gravitational

friction

5.

gravitational

normal

6.

gravitational

normal

7.

gravitational

normal

friction

8.

gravitational

normal

friction

Part 2 of 3Compare the normal force exerted on thebook by the inclined plane and the weightforce exerted on the book by the earth.

Are they equal in magnitude?

1. No

2. Yes

3. Their magnitudes cannot be determinedsince the forces are not in the same direction.

Part 3 of 3Are they opposite in direction?

1. No; the normal force acts perpendicularto the surface of the inclined plane.

2.Yes; the normal force always acts oppositethe weight force. Otherwise, the book wouldfall through the inclined plane.

3. Yes; the normal force acts opposite to theweight force because the book is stationary.

4. No; the normal force acts up the inclineto keep the book from sliding down.


Consider a book that remains at rest on anincline.


Book



1.

gravitational

frictionnormal

2.

gravitational

normalfriction

3.

gravitational

friction

4.

gravitational

friction

5.

gravitational

normal

6.

gravitational

normal

7.

gravitational

normal

friction

8.

gravitational

normal

friction


A book is at rest on an incline as shownabove. A constant force vertically downwardis in contact with the book.

F

Book




1.

weightforce

frictionnormal

2.

weightforce

normalfriction

3.

normalfriction weight

force

4.

normal

force

frictionweight

5.

weightfriction

forcenormal

6.

weightfriction

normalforce

7.

weightforce normal

friction

8.

weightnormal

frictionforce


Part 1 of 4A ladder leans against a wall while someone

climbs up, as shown in the figure below.

�

Wp

W`d

`

�

s

A

B

Which way does the normal force point atposition A ?

1.

2.

3.


4.

5.

6.

7.

8.

10. None of these

Part 2 of 4Which way does the normal force point atposition B?

1.

2.

3.

4.

5.

6.

7.

8.

10. None of these

Part 3 of 4Consider the case where both the wall and thefloor are rough.

Which way does the force due to frictionpoint at position A?

1.

2.

3.

4.

5.

6.

7.

8.

10. None of these

Part 4 of 4Which way does the force due to friction pointat position B?

1.

2.

3.

4.

5.

6.

7.


8.


Crate in Truck05:13, highSchool, multiple choice, < 1 min,fixed.

A crate is sitting in the center of a flatbedtruck. As the truck accelerates to the east,the crate moves with it, not sliding on the bedof the truck.

In what direction is the friction force ex-erted by the bed of the truck on the crate?

1. To the west

2. To the east

3. To the north

4. To the south

5. There is no friction force, because thecrate isn’t sliding

Decelerating Car 0205:13, highSchool, multiple choice, < 1 min,fixed.

A car is going up a hill when the driver hitsthe brakes.

car

v

As the car slows to a stop, which vector di-agram below shows the the correct directionsof all of the forces acting on the car?

We know the plane exerts on the car a force

f that acts down the plane as the car slows toa stop.

1.

2.

3.

4.

5.

6.

7.

8.


Dragster05:13, highSchool, multiple choice, > 1 min,fixed.

Yo Big Daddy drives his Team Universaldragster (mass = m) from rest to a final speedv in a distance d.

What is the average coefficient of frictionbetween the pavement and the tires, assumingconstant acceleration and no air friction?


1. µ =mv2

2 d g

2. µ =v2

√d g

3. µ =v2

√2 d g

4. µ =mv2

d g

5. µ =2mv2

d g

6. µ =v2

2 d g

Forces205:13, highSchool, multiple choice, < 1 min,fixed.

You are pushing a wooden crate across thefloor at a constant speed. You decide to turnthe crate on end, reducing by half the area incontact with the floor. In the new orientation,to push the same crate across the same floorwith the same constant speed, the force thatyou apply must be about:

1. 4 times as great

2. 2 times as great

3. equally great

4.1

2as great

5.1

4as great

as the force required before you changedthe crate’s orientation.


Consider a ball at rest in the middle of atoy wagon.

When the wagon is pulled forward, what isthe motion of the ball?

1. The ball will stay at rest on the wagon.

2.The ball will stay where it was; the surfacewould slide beneath the ball.

3. From a point of view outside the wagon,the ball stays in place as the back of the wagonmoves toward it; because of friction, the ballmay roll along the cart surface.

4. The ball will move faster than thewagon.

5. All are wrong.


When you pull horizontally on a crate witha force of 200 N, it slides across the floor indynamic equilibrium.

How much friction acts on the crate?


If it takes 1 N to push horizontally on yourbook to make it slide at constant velocity, howmuch force of friction acts on the book?

1. 0 N

2. 1 N

3. 2 N

4. 4 N

5. All are wrong.

Hewitt CP9 04 E0905:13, highSchool, multiple choice, < 1 min,wording-variable.

A 400 kg bear grasping a vertical tree slidesdown at constant velocity.

The acceleration of gravity is 10 m/s2 .


What is the friction force that acts on thebear?


A race car travels along a raceway at aconstant velocity of 200 km/h.

What is the net force acting on the car?

1. 0 N

2. It depends on the mass of the car.

3. 200 N

4. 100 N

5. All are wrong.


Once a 24 kg crate is in motion on a hori-zontal floor, a horizontal force of 53 N keepsthe crate moving with a constant velocity.

The acceleration of gravity is 9.81 m/s2 .What is µk, the coefficient of kinetic fric-

tion, between the crate and the floor?


Part 1 of 2A 25 kg chair initially at rest on a horizontal

floor requires a 365 N horizontal force to setit in motion. Once the chair is in motion, a327 N horizontal force keeps it moving at aconstant velocity.

The acceleration of gravity is 9.81 m/s2 .a) What is the coefficient of static friction

between the chair and the floor?

Part 2 of 2b) What is the coefficient of kinetic frictionbetween the chair and the floor?


Part 1 of 8A museum curator moves artifacts into

place on many different display surfaces. Con-sider the following table giving approximatevalues for coefficients of friction:


Materials µs µk

steel on steel 0.74 0.57

aluminum on steel 0.61 0.47

rubber on dry concrete 1.0 0.8

rubber on wet concrete – 0.5

wood on wood 0.4 0.2

glass on glass 0.9 0.4

waxed wood on wet snow 0.14 0.1

waxed wood on dry snow – 0.04

metal on metal (lubricated) 0.15 0.06

ice on ice 0.1 0.03

Teflon on Teflon 0.04 0.04

synovial joints in humans 0.01 0.003

a) What is Fs,max for moving a 145 kgaluminum sculpture across a horizontal steelplatform?

Part 2 of 8b) What is Fk for moving the 145 kg alu-minum sculpture across the horizontal steelplatform?

Part 3 of 8c) What is Fs,max for pulling a 15 kg steelsword across a horizontal steel shield?

Part 4 of 8d) What is Fk for pulling the 15 kg steel swordacross the horizontal steel shield?

Part 5 of 8e) What is Fs,max for pushing a 250 kg woodbed on a wood floor?


Part 6 of 8f) What is Fk for pushing the 250 kg woodbed on a wood floor?

Part 7 of 8g) What is Fs,max for sliding a 0.55 kg glassamulet on a glass display case?

Part 8 of 8h) What is Fk for sliding the 0.55 kg glassamulet on a glass display case?

Holt SF 04D 01 0205:13, highSchool, numeric,> 1min, wording-variable.

Part 1 of 2A student moves a box of books down the

hall by pulling on a rope attached to the box.The student pulls with a force of 185 N at anangle of 25.0◦ above the horizontal. The boxhas a mass of 35.0 kg, and µk between the boxand the floor is 0.27.

The acceleration of gravity is 9.81 m/s2 .Find the acceleration of the box.

Part 2 of 2Now the student moves the box up a ramp(with the same coefficient of friction) inclinedat 12◦ with the horizontal.

b) If the box starts from rest at the bottomof the ramp and is pulled at an angle of 25◦

with respect to the incline and with the same185 N force, what is the acceleration up theramp?


Part 1 of 2A 75.0 kg box slides down a 25.0◦ ramp

with an acceleration of 3.60 m/s2.The acceleration of gravity is 9.81 m/s2 .

75kg

µk

3.6m/

s2

25◦

a) Find µk between the box and the ramp.

Part 2 of 2b) What acceleration would a 175 kg masshave down this ramp?


A box of books weighing 325 N moves witha constant velocity across the floor when it ispushed with a force of 425 N exerted down-ward at an angle of 35.2◦ below the horizontal.

Find µk between the box and the floor.


Part 1 of 2A(n) 95 kg clock initially at rest on a hor-

izontal floor requires a(n) 650 N horizontalforce to set it in motion. After the clock is inmotion, a horizontal force of 560 N keeps itmoving with a constant velocity.

The acceleration of gravity is 9.81 m/s2 .a) Find µs between the clock and the floor.

Part 2 of 2b) Find µk between the clock and the floor.


A 30 kg box slides down a 30.0◦ ramp withan acceleration of 1.20 m/s2.



30kg

µ 30◦

Find the coefficient of kinetic friction be-tween the box and the ramp.


A 4.00 kg block is pushed along the ceilingwith a constant applied force of 85.0 N thatacts at an angle of 70.0◦ with the horizontal.The block accelerates to the right at 6.00m/s2.


4 kg

85N70

◦

µ

6 m/s2

What is the coefficient of kinetic frictionbetween the block and the ceiling?


A 5.4 kg bag of groceries is in equilibriumon an incline of 25◦.


5.4kg

µ 25◦

What is the magnitude of the normal forceon the bag?


A clerk moves a box of cans down an aisleby pulling on a strap attached to the box. Theclerk pulls with a force of 185.0 N at an angleof 25.0◦ with the horizontal. The box has amass of 35.0 kg, and the coefficient of kineticfriction between the box and floor is 0.450.

The acceleration of gravity is 9.81 m/s2 .What is the acceleration of the box?


A(n) 925 N crate is being pushed across alevel floor by a force of 325 N at an angleof 25◦ above the horizontal. The coefficientof kinetic friction between the crate and thefloor is 0.25.


925 N

µk = 0.25

325N

25◦

What is the acceleration of the box?


A 35 kg box rests on the back of a truck.The coefficient of static friction between thebox and the truck bed is 0.300.

The acceleration of gravity is 9.81 m/s2 .What maximum acceleration can the truck

have before the box slides backward?



A girl coasts down a hill on a sled, reachinglevel ground at the bottom with a speed of7.0 m/s. The coefficient of kinetic frictionbetween the sled’s runners and the hard, icysnow is 0.050, and the girl and sled togetherweigh 645 N.

The acceleration of gravity is 9.81 m/s2 .How far does the sled travel on the level

ground before coming to a rest?


A box of books weighing 319 N is shovedacross the floor by a force of 485 N exerteddownward at an angle of 35◦ below the hori-zontal.

The acceleration of gravity is 9.81 m/s2 .If µk between the box and the floor is 0.57,

how long does it take to move the box 4.00 m,starting from rest?


Part 1 of 4A 3.00 kg block starts from rest at the top

of a 30.0◦ incline and accelerates uniformlydown the incline, moving 2.00 m in 1.50 s.

The acceleration of gravity is 9.81 m/s2 .a) What is the magnitude of the accelera-

tion of the block?

Part 2 of 4b) What is the coefficient of kinetic frictionbetween the block and the incline?

Part 3 of 4c) What is the magnitude of the frictionalforce acting on the block?

Part 4 of 4d)What is the speed of the block after it slidesthe distance of 2.00?

Holt SF 04Rev 59


The coefficient of static friction between the3 kg crate and the 20◦ incline is 0.3.


3 kg

µk

F

20◦

What minimum force F must be applied tothe crate perpendicular to the incline to pre-vent the crate from sliding down the incline?


The board sandwiched between two otherboards in the figure weighs 95.5 N.

95.5 N

If the coefficient of friction between theboards is 0.663, what must be the magnitudeof the horizontal forces acting on both sidesof the center board to keep it from slippingdownward?


Part 1 of 2A car is traveling at 50.0 km/h on a flat

highway.The acceleration of gravity is 9.81 m/s2 .a) If the coefficient of kinetic friction be-

tween the road and the tires on a rainy day is0.100, what is the minimum distance needed


for the car to stop?

Part 2 of 2b) What is the stopping distance when thesurface is dry and the coefficient of kineticfriction is 0.600?


Part 1 of 3Two blocks with masses of 45.0 kg and 23.5

kg are stacked on a table with the heavierblock on top. The coefficient of static frictionis 0.600 between the two blocks and 0.300between the bottom block and the table. Ahorizontal force is slowly applied to the topblock until one of the blocks moves.

The acceleration of gravity is 9.81 m/s2 .a) What is the friction force between the

blocks?

Part 2 of 3b)What is the friction force between the lowerblock and the table?

Part 3 of 3c) What minimum value for the coefficientof static friction between the masses and thetable would cause the slippage to first happenbetween the blocks?


Part 1 of 2A truck driver slams on the brakes and

skids to a stop through a displacement of ∆x.a) If the truck has twice the mass, by what

factor does the stopping distance change?

1. 1

2. 2

3. 4

4. 0.5

5. 0.25

6. None of these

Part 2 of 2b) If the initial velocity of the truck werehalved, by what factor would the stoppingdistance change?

1. 0.25

2. 1

3. 2

4. 4

5. 0.5

6. None of these


Part 1 of 2A 150 N block rests on a table. The sus-

pended mass has a weight of 75 N.

150 N

75 N

µs

a) What is the magnitude of the minimumforce of static friction required to hold bothblocks at rest?

Part 2 of 2b) What minimum coefficient of static frictionis required to ensure that both blocks remainat rest?

Kopp lect8 prob1



A block is sliding in a straight line alonga rough table. The coefficient of friction be-tween the block and the table is µk while it issliding.

The direction of the frictional force points

1. in the direction of motion.

2. in the direction of the normal force.

3. against the direction of motion.

4. into the table.

5. None of these

Pulling Two Blocks 0105:13, highSchool, multiple choice, > 1 min,normal.

Part 1 of 3Consider a force pulling 2 blocks along a

rough horizontal surface, where the massesare a multiple of a given mass m, as shown inthe figure below. The coefficient of the kineticfriction is µ. The blocks are pulled by a forceof 60µmg.

2m 18mT F

µ

Determine the acceleration.

1. a = 2µ g

2. a = 5µ g

3. a = 11µ g

4. a = 8µ g

5. a = 3µ g

6. a = 6µ g

7. a = 12µ g

8. a = 4µ g

9. a = µ g

Part 2 of 3The equation of motion for the left-hand mass18m is given by

1. T − 18µmg = 18ma

2. T + 18µmg = 18ma

3. 2µmg − T = 18ma

4. 2µmg + T = −18ma

5. T − 2µmg = 18ma

6. T + 2µmg = 18ma

7. T − 18µmg − 2µmg = 18ma

8. T + 18µmg − 2µmg = 18ma

9. T − 18µmg + 2µmg = 18ma

10. T + 18µmg + 2µmg = 18ma

Part 3 of 3Find the tension T in the rope between themasses m1 = 2m and m2 = 18m in terms ofF .

1. T =F

10

2. T =F

3

3. T =F

8

4. T =F

5

5. T =F

6

6. T =F

4


7. T =F

12

8. T =F

7

9. T = F

Static and Kinetic Friction05:13, highSchool, multiple choice, < 1 min,fixed.

An object is held in place by friction on aninclined surface. The angle of inclination isincreased until the object starts moving.

If the surface is kept at this angle, the object

1. slows down.

2. moves at uniform speed.

3. speeds up.

4. none of the other choices

Static Friction and Pulley 0205:13, highSchool, numeric,< 1min, wording-variable.

Block A (60 N) and block B (40 N) areconnected by a massless cord and are at rest.Given µs = 0.8.

The friction on A is :

A

B

µs

Static Friction and Pulley 0305:13, highSchool, multiple choice, > 1 min,fixed.

Block A (60 N) and block B (40 N) areconnected by a massless cord and are ATREST. Given µs = 0.8.

A

B

µs

The friction on A is :

1. 40 N

2. 48 N

3. 60 N

4. 24 N

5. 0 N

6. 20 N

7. 16 N

Three Blocks 01 e105:13, highSchool, multiple choice, > 1 min,fixed.

Given: Each block has masses m1 = m2 =m3 = m and the coefficient of kinetic frictionis µ. The magnitude of F equals twice thetotal frictional force.

Apply a horizontal force F in pushing an ar-ray of three identical blocks in the horizontalplane (see sketch).

m1 m2 m3F

µ

Find the force F23 with which the secondblock is pushing the third block.

1. F23 = mg

2. F23 = 2µmg

3. F23 = 2mg


4. F23 = 3mg

5. F23 = 4mg

6. F23 = µmg

7. F23 = 3µmg

8. F23 = 4µmg

Three Blocks 0205:13, highSchool, numeric, > 1 min, fixed.



m1 m2 m3F

µ

Find the acceleration.

1. a =g

3

2. a =µ g

3

3. a =µ g

2

4. a = 2µ g

5. a =g

2

6. a = 3µ g

7. a = µ g

8. a = g

9. a = 2 g

10. a = 3 g

Three Blocks 03

05:13, highSchool, multiple choice, > 1 min,fixed.



m1 m2 m3F

µ

Find the force F23 with which the secondblock is pushing the third block.

1. F23 = mg

2. F23 = 2µmg

3. F23 = 2mg

4. F23 = 3mg

5. F23 = 4mg

6. F23 = µmg

7. F23 = 3µmg

8. F23 = 4µmg

Two Blocks CPS05:13, highSchool, multiple choice, < 1 min,fixed.

Denote the force exerted on block 2 by theblock 1 to be F21.

m1 m2F

µ1 µ2

If the acceleration is a, the equation ofmotion for block m2 is given by


1. F − µ1m1 g − µ2m2 g = m2 a

2. F21 − µ2m2 g = m2 a

3. F + F21 − µ2m2 g = m2 a

4. F − F21 − µ2m2 g = m2 a

5. F21 − µ1m1 g − µ2m2 g = m2 a

Chapter 5, section 14, Other Resistive Forces (Terminal Velocity) 203


In daily life, will a ball rolling along thefloor keep moving in a straight line at constantspeed?

1. Yes; Newton’s first law predicts this.

2. Yes; Newton’s third law predicts this.

3. No; the ball will curve.

4. No; the ball will slow down.


Part 1 of 2A 28,000 lb jet airliner cruises at 500 mi per

hour at an altitude of 35,000 ft. The forwardthrust of the engines is 10,000 pounds.

Assuming the plane maintains altitude andspeed, what is the total air drag force pushingback on the plane?

1. 50,000 N

2. 140,000 N

3. less than 50,000 N

4. more than 190,000 N

5. 190,000 N

Part 2 of 2What is the total lift force pushing up on

the plane?

1. 50,000 N

2. 140,000 N

3. less than 50,000 N

4. more than 190,000 N

5. 190,000 N

Conceptual 04 Q2105:14, highSchool, multiple choice, < 1 min,wording-variable.

When an object is moving in the air, theair drag force is in the opposite direction tothe velocity. Consider a light foam ball thatis thrown up into the air.

When is the net force on the ball smallest?

1.When the ball moves down

2.When the ball moves up

3. When the ball is at the top of its trajec-tory

4. The net force is constant.

Conceptual 05 Q1905:14, highSchool, multiple choice, > 1 min,fixed.

In StarTrek and other science fiction sagas,you often encounter a fictional device called atractor beam, capable of pulling objects intothe starship. Suppose that an object is fallingunder the influence of gravity and drag. Inaddition, imagine that a tractor beam on theground is pulling the object down.

If there is a limit to the force the tractorbeam can exert, will the object still attain aterminal velocity?

1. No; it will escape from the gravity of theEarth.

2. Yes; the terminal velocity would occurwhen the air drag equals gravity plus the forceof the tractor beam.

3. No; the object will continue to speed upas it falls.

Escape SW01



Aman of mass 80 kg escapes from a burningbuilding by jumping from a window situated30 m above a catching net.

The acceleration of gravity is 9.8 m/s2 .If air friction exerts a constant force of

100 N on him as he falls, what is his speedjust before he hits the net?

1. 24.2487 m/s

2. 8.66025 m/s

3. 16.0156 m/s

4. 22.6495 m/s

5. 6.12372 m/s

6. 17.1464 m/s



1. In free fall, air resistance is more effectivein slowing a feather than a coin.

2. Air resistance is more effective in slowinga feather than a coin.

3. Air resistance is less effective in slowing afeather than a coin.

4. Air resistance is as effective in slowing afeather as a coin.

5. All are wrong.


A parachutist, after opening the chute,finds herself gently floating downward, nolonger gaining speed. She feels the upward

pull of the harness, while gravity pulls herdown.

How much is the pull of the harness?

1. Equal to the gravity

2. Smaller than the gravity

3. Greater than the gravity

4. Half of the gravity

5. All are wrong.


Why will a sheet of paper fall slower thanone that is wadded into a ball?

1. Because the gravitational acceleration ofa sheet is smaller than that for a ball.

2. Because the resistance for the sheet ismuch stronger than that for the ball.

3. Because when the sheet is falling, it hashorizontal velocity, which reduces its verticalvelocity.

4. Because the ball has larger mass densitythan the sheet.

5. None of these


Once terminal speed is reached which sheetof paper has the greatest air resistance? Keepin mind that they fall at different terminalspeeds.

1. A plain sheet

2. A wadded sheet


3. A folded sheet

4. All three forces are the same.

5. More information needed to answer thequestion.


How does the force of gravity on a raindropcompare with the air drag it encounters whenit falls at constant velocity?

1. The force of gravity is larger.

2. The force of air drag is larger.

3. The forces are equal.



When a parachutist opens her parachutewhat is the direction of her acceleration?

1. Upward

2. Downward, but with small accelerationthan before

3. Zero acceleration

4. It depends on the velocity before theparachute opened.



When Galileo dropped two balls from thetop of the Leaning Tower of Pisa, air resis-tance was not really negligible.

Assuming both balls were the same size,one made of wood and one of metal, whichball struck the ground first?

1. The ball of metal, but only by a shorttime span

2. The ball of metal, by half the time as theball of wood

3. They hit the ground at the same time.

4. The ball of wood

5. All are wrong.


In the absence of air drag, why does the hor-izontal component of a projectile’s motion notchange, while the vertical component does?

1. Gravitation acts vertically; there are nohorizontal forces.

2. Gravitation acts horizontally; there areno vertical forces.

3.The force exerted by the projectile is equalto the gravitational force.

4. The force exerted by the projectile isgreater than the gravitational force.

5. The force exerted by the projectile is lessthan the gravitational force.


A 75 kg person escapes from a burningbuilding by jumping from a window 25 mabove a catching net.

The acceleration of gravity is 9.81 m/s2 .Assuming that air resistance is simply a

constant 95 N force on the person during thefall, determine the person’s velocity just be-


fore hitting the net.


The parachute on a race car that weighs8820 N opens at the end of a quarter-mile runwhen the car is traveling 35 m/s.

The acceleration of gravity is 9.81 m/s2 .What net retarding force must be supplied

by the parachute to stop the car in a distanceof 1100 m?

SWCT Escape05:14, highSchool, multiple choice, > 1 min,fixed.

A person of mass 80 kg escapes from aburning building by jumping from a windowsituated 30 m above a catching net.

The acceleration of gravity is 9.8 m/s2 .If air friction exerts a constant force of

100 N on her as she falls, determine her speedjust before she hits the net.

1. 22.6 m/s

2. 21.6 m/s

3. 21.0 m/s

4. 20.6 m/s

5. 20.0 m/s

6. 18.5 m/s

Terminal Speed05:14, highSchool, numeric, > 1 min, normal.

Part 1 of 2Given: g = 9.8 m/s2.

A wooden sphere has radius R = 10 cm,density ρwood = 830 kg/m3, and aerodynami-cal drag coefficient D = 0.5. What is the ter-minal speed vt of this sphere falling throughthe air of density ρair = 1.2 kg/m3?

Part 2 of 2

Now consider the same sphere falling freelywithout any resistance. From which height hshould it fall to reach the same speed?

Chapter 6, section 1, Newton’s Second Law Applied to Uniform Circular Motion 207

Aerobatics06:01, highSchool, numeric, < 1 min, normal.

A fighter plane flying at constant speed400 m/s and constant altitude 5000 mmakes a turn of curvature radius 9400 m.On the ground, the plane’s pilot weighs(70 kg) (9.8 m/s2) = 686 N.

What is his/her apparent weight during theplane’s turn?

Barrel of Fun 0106:01, highSchool, multiple choice, > 1 min,fixed.

As viewed by a bystander, a rider in a“barrel of fun” at a carnival finds herself stuckwith her back to the wall.

ω

Which diagram correctly shows the forcesacting on her?

1.

2.

3.

4.

5.

6. None of the other choices

Barrel of Fun CPS06:01, highSchool, multiple choice, < 1 min,fixed.

A ”Barrel of Fun” consists of a large verticalcylinder that spins about its axis fast enoughso that any person inside will be held againstthe wall.

Assume: At an angular speed ω1, an up-ward frictional force F1 holds a person againstthe wall without slipping.

ω

R

What is the friction force F2, if the angularspeed is doubled, i.e.,ω2 = 2ω1.

1. F2 = 4F1

2. F2 = 2F1

3. F2 = F1

4. F2 =1

2F1

Centripetal Acceleration06:01, highSchool, multiple choice, < 1 min,


fixed.

A car rounds a curve while maintaining aconstant speed.

Is there a net force on the car as it roundsthe curve?

1. No – its speed is constant.

2. Yes.

3. It depends on the sharpness of the curveand speed of the car.

Circle Jerk06:01, highSchool, multiple choice, > 1 min,fixed.

A ball rolls around a circular wall, as shownin the figure below. The wall ends at pointX.

A

B

CD E

X

When the ball gets to X, which path doesthe ball follow?

1. Path A

2. Path B

3. Path C

4. Path D

5. Path E


When you are in the front passenger seat of

a car turning to the left, you may find yourselfpressed against the right-side door.

What concept(s) explain(s) why you pressagainst the door and why the door presses onyou?

1. centrifugal force and Newton’s first law

2. centrifugal force and Newton’s secondlaw

3. Newton’s first and third laws

4. just a centrifugal force


The occupant inside a rotating space habi-tat of the future feels that she is being pulledby artificial gravity against the outer wall ofthe habitat (which becomes the floor).

Which statement is false?

1. At every moment her tendency is to movein a straight-line path.

2. The floor intercepts her path and pressesagainst her feet.

3. The floor provides the centripetal force tokeep her moving in a circular path.

4. Centrifugal force causes her to move in acircular path.


The sketch shows a conical pendulum. Theball swings in a circular path because of thestring attached at the top. The tension Tin the string and weight W of the ball areshown by vectors. A parallelogram createdwith these vectors shows that their resultantF lies in the plane of the circle.


T

WF

What is the name of this resultant force F ?

1. centripetal force

2. centrifugal force

3. frictional force

4. angular force

Concept 08 4106:01, highSchool, multiple choice, < 1 min,normal.

A motorcyclist is able to ride on the verticalwall of a bowl-shaped track as shown. Hisweight is counteracted by the friction of thewall on the tires (vertical arrow).

A drawing of the vectors for the forces thatacts on the cyclist is shown below. The vec-tors are drawn from the center of mass of themotorcyclist.

N

f

mg

r

Which force(s) increase(s) or decrease(s) ifhe rides faster?

1. The frictional and normal forces in-crease.

2. Only the frictional force decreases.

3. Only the frictional force increases.

4. Only the normal force decreases.

5. Only the normal force increases.

6. The frictional and normal forces de-crease.


Consider a ball rolling around in a circularpath on the inner surface of a cone. Theweight of the ball is shown by the vector W.Without friction, only one other force acts onthe ball – a normal force.

W

?

Draw the normal vector; what relationshipdo the vectors have?

1. The normal force is greater than theweight and greater than the centripetalforce.

2. The normal force is less than the weightand greater than the centripetal force.

3. The normal force is greater than theweight and less than the centripetal force.

4. The normal force is less than the weightand less than the centripetal force.


A passenger on a Ferris wheel moves in avertical circle at constant speed.


Are the forces on her balanced?

1. Yes; the speed is constant.

2. Yes; it moves in a vertical circle.

3. No; the direction of net force does notchange.

4. No; there is an inward net force.


A car drives up a straight hill at a constantspeed of 50 kilometers per hour. A truckdrives over the crest of the hill at a constantspeed of 50 miles per hour.

What is the net force on the car and on thetruck?

1. both not zero

2. zero; not zero

3. not zero; zero

4. both zero


Part 1 of 2Calculate the period of a ball tied to a string

of length 0.3 m making 2.5 revolutions everysecond.

Part 2 of 2Calculate the speed of the ball.


Calculate the average speed of the Moonaround the Earth. The Moon has a periodof revolution of 27.3 days and an average dis-tance from the Earth of 3.84× 108 m.

1. 3.68245× 106 m/s

2. 61374.2 m/s

3. 584000 m/s

4. 1022.9 m/s

5. 2045.8 m/s

6. 8.83789× 107 m/s

7. 3688.5 m/s

8. 2054.6 m/s

9. None of these


Calculate the centripetal force exerted onthe Earth by the Sun. Assume that the periodof revolution for the Earth is 365.25 days,the average distance is 1.5 × 108 km and theEarth’s mass is 6× 1024 kg.

1. 7.24562× 1022 N

2. 1.28439× 1026 N

3. 3.56775× 1019 N

4. 4.6238× 1029 N

5. 7.24562× 1020 N

6. 2.66331× 1032 N

7. 1.62932× 1021 N

8. 3.56775× 1022 N

9. None of these

Figuring Physics 1406:01, highSchool, multiple choice, < 1 min,


fixed.

Part 1 of 2(The normal force is perpendicular to the

supporting surface.)

mg

?

The magnitude of the normal force on a blocksliding down to a friction-free inclined plane

1. is equal to mg.

2. is greater than mg, always.

3. may be greater than mg.

4. is less than mg, always.

Part 2 of 2And when the sliding along a horizontal cir-cular path on the inside of a friction-free cone,

mg

?

the magnitude of the normal force

1. is equal to mg.

2. is greater than mg, always.

3. may be greater than mg.

4. is less than mg, always.

5. may be less than mg.


Poke four holes in an aluminum pop canwith a nail; in each hole bend the nail hor-izontally and dent the holes so that whenwater is put in the can it will spurt out with atangential component. Suspend the can withstrings and watch it rotate as water spurtsfrom it, noting its direction of rotation.

Now empty the can and weigh it down atits bottom so that it remains upright whensuspended in water; let water flow into theholes.

What is the direction of rotation now?

1. Same as before.

2. Opposite.

3. Not at all.


Why is the linear speed greater for a horseon the outside of a merry-go-round than for a


horse closer to the center?

1. The tangential speed of the horse is di-rectly proportional to the distance from thecenter.

2. The outside horse moves easier.

3. The horse on the outside is larger.

4. The horse on the outside has longer legs.

5. The horse on the outside feels less forcefrom the merry-go-round.

6. None of these

Holt SF 07H 0306:01, highSchool, numeric,< 1min, wording-variable.

A dog sits 1.50 m from the center of amerry-go-round with an angular speed of 1.20rad/s.

If the magnitude of the force that maintainsthe dog’s circular motion is 40.0 N, what isthe dog’s mass?


Part 1 of 2An airplane is flying in a horizontal circle

at a speed of 105 m/s. The 80.0 kg pilotdoes not want the centripetal acceleration toexceed 7.00 times free-fall acceleration.

a) Find the minimum radius of the plane’spath.

Part 2 of 2b) At this radius, what is the magnitude ofthe net force that maintains circular motionexerted on the pilot by the seat belts, thefriction against the seat, and so forth?


Part 1 of 2An air puck of mass 0.025 kg is tied to

a string and allowed to revolve in a circleof radius 1.0 m on a frictionless horizontalsurface. The other end of the string passesthrough a hole in the center of the surface,and a mass of 1.0 kg is tied to it, as shownin the figure. The suspended mass remainsin equilibrium while the puck revolves on thesurface.


1 m

1 kg

0.025 kg

a) What is the magnitude of the force thatmaintains circular motion acting on the puck?

Part 2 of 2b) What is the linear speed of the puck?


In a popular amusement-park ride, a cylin-der of radius 3.00 m is set in rotation at anangular speed of 5.00 rad/s, as shown in thefigure. The floor then drops away, leaving theriders suspended against the wall in a verticalposition.


3 m

What minimum coefficient of friction be-


tween a rider’s clothing and the wall of thecylinder is needed to keep the rider from slip-ping?


Two identical objects go around circlesof identical diameter, but one object goesaround the circle twice as fast as the other.

The centripetal force required to keep thefaster object on the circular path is

1. the same force required to keep the slowerobject on the path.

2. one fourth as much force as required tokeep the slower object on the path.

3. half as much force as required to keep theslower object on the path.

4. twice as much force as required to keepthe slower object on the path.

5. four times as much force as required tokeep the slower object on the path.

Satellite06:01, highSchool, multiple choice, < 1 min,fixed.

A communication satellite does not fall tothe earthA. only if it is in a geosynchronous orbit.B. because the net force on it is zero.C. because it is beyond the pull of the earth’s

gravity.D. because it is in the earth’s gravitational

field.E. because it is being pulled by the sun and

by other planets as well as the earth.

1. A only

2. B only

3. C only

4. D only

5. E only

6. B and C

7. None of these

SWCT Centrifugal Force06:01, highSchool, multiple choice, < 1 min,fixed.

You are a passenger in a car and not wear-ing your seat belt. Without increasing ordecreasing its speed, the car makes a sharpleft turn, and you find yourself colliding withthe right-hand door.

Which is the correct analysis ofthe situa-tion?

1. Before and after the collision, there isrightward force pushing you into the door.

2. Starting at the time of collision, the doorexerts a leftward force on you.

3. Both of these

4. Neither of these

SWCT Centripetal06:01, highSchool, multiple choice, < 1 min,fixed.

An object moves along a circular path witha constant speed, |~Vo|.

� �AB

~VA

~VBθ θ

North

East

The average acceleration in going from Ato B is


1. zero

2. north

3. south

4. east

5. west

6. none of the others

Chapter 6, section 2, Banked and Unbanked Curves 215

Car on a Banked Curve 0606:02, highSchool, multiple choice, < 1 min,fixed.

A car istraveling very slowly around a banked curve.

What is the free body diagram that describesthe forces acting on the car?

1.

2.

3.

4.

5.

6.

7.

8.


A bicyclist is riding at a tangential speed of13.2 m/s around a circular track with a radiusof 40.0 m.

If the magnitude of the force that maintainsthe bike’s circular motion is 377 N, what is thecombined mass of the bicycle and rider?

Holt SF 07H 0406:02, highSchool, numeric,> 1min, wording-variable.

A 905 kg test car travels around a 3.25 kmcircular track.

If the magnitude of the force that maintainsthe car’s circular motion is 2140 N, what isthe car’s tangential speed?


Part 1 of 3

Chapter 6, section 2, Banked and Unbanked Curves 216

A 13500 N car traveling at 50.0 km/hrounds a curve of radius 2.00× 102 m.

The acceleration of gravity is 9.81 m/s2 .a) Find the centripetal acceleration of the

car.

Part 2 of 3b) Find the force that maintains circular mo-tion.

Part 3 of 3c) Find the minimum coefficient of static fric-tion between the tires and the road that willallow the car to round the curve safely.


A 2 ×103 kg car rounds a circular turn ofradius 20.0 m.

The acceleration of gravity is 9.81 m/s2 .If the road is flat and the coefficient of static

friction between the tires and the road is 0.70,how fast can the car go without skidding?

Chapter 6, section 3, Nonuniform Circular Motion 217

Boy Swinging on a Rope06:03, highSchool, multiple choice, < 1 min,fixed.

A boy is swinging on a rope,starting at a point higher than A.

O

A

Consider the following distinct forces:1. A downward force of gravity,2. A force exerted by the rope pointing

from A to O,3. A force in the direction of the boy’s

motion, and4. A force pointing from O to A.Which of the above forces is (are) acting on

the boy when he is at position A?

1. 1 only.

2. 1 and 2.

3. 1 and 3.

4. 1, 2 and 3.

5. 1, 3 and 4.

Breaking Pendulum06:03, highSchool, multiple choice, < 1 min,fixed.

A long string attached to a mass M formsa simple pendulum. The string, however, isweak enough so that it is likely to break atsome point in the oscillation if you let it swing.You pull the mass back and start it oscillating.

g

m

v 6= 0

r

a r

at

a

φθ

At what point in the cycle is the string mostlikely to break?

1. Just after release.

2. Just when the mass passes through thepoint where the string is vertical.

3. Just after the mass turns around to re-turn.

4. Just after the mass returns to the startingpoint.

5. It is equally likely to break at all posi-tions.


If you partially fill a bucket with water andswing it fast enough in a circle over your head,the water will stay in the bucket even when itis upside down.

Which statement is not true?

1. The acceleration of the water is greaterthan g.

2. The acceleration of the water is less thang.

3. The bucket has a downward force on thewater in it.

Ferris Wheel 0306:03, highSchool, numeric, > 1 min, normal.


The following figure shows a Ferris wheelthat rotates 4 times each minute and has adiameter of 18 m.


R

ω

What is the centripetal acceleration of arider?


A girl sits on a tire that is attached to anoverhanging tree limb by a rope 2.10 m inlength. The girl’s father pushes her with atangential speed of 2.50 m/s. Besides theforce opposing the girl’s weight, the magni-tude of the force that maintains her circularmotion is 88.0 N.

What is the girl’s mass?


Part 1 of 2A roller-coaster car speeds down a hill past

point A and then rolls up a hill past point B,as shown in the figure. The car has a speed of20.0 m/s at point A.


10 m

15 m

A

B

Note: Figure is not drawn to scale.a) If at point A the track exerts a force on

the car that is 2.06 × 104 N greater than thecar’s weight, what is the mass of the car?

Part 2 of 2b) What is the maximum speed the car canhave at point B for the gravitational force tohold it on the track?


Tarzan tries to cross a river by swingingfrom one bank to the other on a vine thatis 10.0 m long. His speed at the bottom ofthe swing, just as he clears the surface of theriver, is 8.0 m/s. Tarzan does not know thatthe vine has a breaking strength of 1.0 × 103

N.The acceleration of gravity is 9.81 m/s2 .What is the largest mass Tarzan can have

and make it safely across the river?

Nonuniform Circular Motion06:03, highSchool, multiple choice, < 1 min,fixed.

A train is moving along a circular trackwith r = 100 m. At A, v = ‖~v‖ = 10 m/s.It is slowing down with a tangential decelera-tion of magnitude atangential = ‖~atangential‖ =1m/s2. Sketch ~atotal at A.


Or

A

v

Quadrants

II I

III IV

Which quadrant should it be in?

1. I

2. II

3. III

4. IV

Pendulum Tension06:03, highSchool, multiple choice, < 1 min,fixed.

A mass m on a massless string of length Lis whirled in a vertical circle. If the stringtension goes to zero just at the top of thecircle, what is the speed at the top?

1.√

gL

2.√

2gL

3. 2√

gL

4. 2√

2gL

5.1

2

√

2gL

6.1

2

√

gL

7. 0

8. not enough information

Whirling a Rock06:03, highSchool, multiple choice, > 1 min,fixed.

A rock of weightW is tied to a massless rodand whirled at constant speed v in a verticalcircle of radius R. The tension in the rod atthe top is TT and the tension at the bottom isTB.

Then

1. TT =M v2

R+W and TB =

M v2

R−W

2. TT =M v2

R−W and TB =

M v2

R+W

3. TT =M v2

Rand TB =

M v2

R

4. TT = +W and TB = −W

5. TT =W−M v2

Rand TB =W+

M v2

R

6. TT =W+M v2

Rand TB =W+

M v2

R

Chapter 6, section 5, Circular Motion in the Presence of Resistive Forces 220


The sketch shows a coin at the edge of aturntable. The weight of the coin is shown bythe vector W. Two other forces act on thecoin, the normal force and a force of frictionthat prevents it from sliding off the edge.

ω

W

Draw force vectors for both of these.

1. fN

2. fN

3. fN

4. fN

5. fN

6. fN

7. fN

8. fN

10. None of these graphs is correct.

Chapter 7, section 2, Kinetic Energy 221


Part 1 of 2If a golf ball and a ping-pong ball both

move with the same kinetic energy, which hasthe greater speed?

1. the golf ball

2. the ping-pong ball

3. The two balls have the same speed.


Part 2 of 2In a gaseous mixture of massive moleculesand light molecules with the same averageKE, which have the greater speed?

1. the massive molecules

2. the light molecules

3. They have the same speed.



Does the KE of a car change more when itaccelerates from 10 km/h to 20 km/h or whenit accelerates from 20 km/h to 30 km/h?

1. No difference

2. From 10 km/h to 20 km/h

3. From 20 km/h to 30 km/h


Conceptual 08 0207:02, highSchool, multiple choice, < 1 min,

normal.

Two objects of same material are travellingnear you. Object A is a 1 kg mass traveling10 m/s; object B is a 2 kg mass traveling5 m/s.

Which object would make you feel worse ifyou are hit by it?

1. A

2. B

3. the same



A car is moving at 60 miles per hour. Thekinetic energy of that car is 500000 J.

How much energy does the same car havewhen it moves at 120 miles per hour?

Conceptual 08 1807:02, highSchool, numeric, > 1 min, fixed.

Part 1 of 3The moon has a mass of 7.4 × 1022 kg and

completes an orbit of radius 3.8×108 m aboutevery 28 days. The Earth has a mass of6 × 1024 kg and completes an orbit of radius1.5× 1011 m every year.

What is the speed of the Moon in its orbit?

Part 2 of 3What is the kinetic energy of the Moon inorbit?

Part 3 of 3What is the kinetic energy of the Earth?


Part 1 of 3The current theory of the structure of the

Earth, called plate tectonics, tells us that the


continents are in constant motion.Assume that the North American continent

can be represented by a slab of rock 5000 kmon a side and 30 km deep and that the rockhas an average mass density of 2800 kg/m3.The continent is moving at the rate of about2 cm/year.

What is the mass of the continent?

Part 2 of 3What is the kinetic energy of the continent?

Part 3 of 3A jogger (of mass 70 kg) has the same kineticenergy as that of the continent.

What would his speed be?


Which of the two object shown below hasthe greatest kinetic energy?

A

m

B

1

2m

v

2v

1. A

2. B

3. Kinetic energies are the same.



A moving car has kinetic energy.If it speeds up until it is going four times

faster than before, how much kinetic energydoes it have in comparison?

1. Four times larger

2. Four times smaller

3. Sixteen times larger

4. Sixteen times smaller

5. The same

6. The mass is needed.


Calculate the speed of an 8.0 × 104 kg air-liner with a kinetic energy of 1.1× 109 J.


What is the speed of a 0.145 kg baseball ifits kinetic energy is 109 J ?


Part 1 of 3Two bullets have masses of 3.0 g and 6.0 g,

respectively. Each is fired with a speed of 40.0m/s.

a) What is the kinetic energy of the firstbullet?

Part 2 of 3b) What is the kinetic energy of the secondbullet?

Part 3 of 3

c) What is the ratioK2

K1of their kinetic ener-

gies?



Part 1 of 3Two 3.0 g bullets are fired with speeds of

40.0 m/s and 80.4 m/s, respectively.a) What is the kinetic energy of the first

bullet?

Part 2 of 3b) What is the kinetic energy of the secondbullet?

Part 3 of 3

c) What is the ratioK2

K1of their kinetic ener-

gies?


A car has a kinetic energy of 4.32 × 105 Jwhen traveling at a speed of 23 m/s.

What is its mass?

Holt SF 05Rev 19 2007:02, highSchool, numeric,> 1min, wording-variable.

Part 1 of 2a) What is the kinetic energy of an auto-

mobile with a mass of 1250 kg traveling at aspeed of 11 m/s?

Part 2 of 2b) What speed would a fly with a mass of0.550 g need in order to have the same kineticenergy as the automobile?

Kinetic Energy Example07:02, highSchool, multiple choice, < 1 min,fixed.

Which of the following is the best exampleof kinetic energy?

1. A calculator battery

2. A tornado

3. A loaded gun

4. Boulder dam

5. A nuclear bomb

6. A tank of gasoline

7. A TV

8. A Jolt cola

9. A strawberry shortcake

10. None of the examples

Chapter 7, section 3, Work 224


The Joule and the kilowatt-hour are bothunits of energy.

1 kW · h is equivalent to how manyJoules?

Work 0107:03, highSchool, multiple choice, < 1 min,fixed.

A force exerted over a distance to move anobject is

1. work.

2. momentum.

3. velocity.

4. measured in Newtons.

Work 0207:03, highSchool, multiple choice, < 1 min,normal.

The amount of work done by two boys whoapply 200 N of force in an unsuccessful at-tempt to move a stalled car is

1. 0.

2. 400 N-m.

3. 400 N.

4. 200 N-m.

5. 200 N.

Work 0407:03, highSchool, numeric, < 1 min, normal.

If you exert a force of 10 N to lift a boxa distance of 0.75 m, how much work do youdo?


A force acting on an object does no work if

1. the force is not in the direction of theobject’s motion.

2. the force is greater than the force of fric-tion.

3. the object accelerates.

4. a machine is used to move the object.

Chapter 7, section 4, Work: a General Constant Force 225

Comparing Work07:04, highSchool, multiple choice, < 1 min,fixed.

A block moves to the right in the positive x-direction through the displacement ∆x whileunder the influence of a force with the samemagnitude F . Which of the following is thecorrect order of the amount of work done byforce F , from most positive to most negative?

(a)

~F

(b)

~F

(c)

~F

(d)

~F

1. d, c, a, b

2. c, a, b, d

3. c, a, d, b

4. a, b, c, d

5. a, c, b, d

6. d, a, b, c

7. a, d, b, c


Part 1 of 2

Zak, helping his mother rearrange the fur-niture in their living room, moves a 50 kg sofa6 m with a constant force of 20 N.

What is the work done by Zak on the sofa?Neglect friction.

Part 2 of 2What is the average acceleration of the sofa?


A 50-pound crate is pushed across the floorby a 20-pound horizontal force F1. Aside fromthe pushing force and gravity F2, there is alsoa 50-pound force F3 exerted upward on thecrate and a 10-pound frictional force F4, asshown in the figure.

F1(20 lb)

F2(50 lb)

F3(50 lb)

F4(10 lb)

What kinds of work do the force F1, F2, F3,F4 do, respectively?

1. +, 0, 0, −

2. +, −, +, −

3. −, +, −, +

4. +, 0, 0, 0

5. +, 0, +, 0

6. +, +, 0, 0

Holt SF 05A 0107:04, highSchool, numeric,> 1min, wording-


variable.

A tugboat pulls a ship with a constant nethorizontal force of 5.00×103 N and causes theship to move through a harbor.

How much work does the tugboat do on theship if each moves a distance of 3.00 km ?


A shopper in a supermarket pushes a cartwith a force of 35 N directed at an angle of25◦ downward from the horizontal.

Find the work done by the shopper on thecart as the shopper moves along a 50.0 mlength of aisle.


A catcher “gives” with a baseball whencatching it.

If the baseball exerts a force of 475 N onthe glove such that the glove is displaced 10.0cm, how much work is done by the ball?


Part 1 of 3A flight attendant pulls her 70.0 N flight

bag a distance of 253 m along a level airportfloor at a constant velocity. The force sheexerts is 40.0 N at an angle of 52.0◦ above thehorizontal.

a) Find the work she does on the flight bag.

Part 2 of 3b) Find the work done by the force of frictionon the flight bag.

Part 3 of 3c) Find the coefficient of kinetic friction be-tween the flight bag and the floor.


Part 1 of 2A horizontal force of 150 N is used to push

a 40.0 kg packing crate a distance of 6.00 mon a rough horizontal surface.

The acceleration of gravity is 9.81 m/s2 .If the crate moves with constant velocity,

calculatea) the work done by the force.

Part 2 of 2b) the coefficient of kinetic friction.


A skier of mass 70.0 kg is pulled up a slopeby a motor-driven cable.

How much work is required to pull the skier60.0 m up a 35.0◦ slope (assumed to be fric-tionless) at a constant speed of 2.0 m/s? Theacceleration of gravity is 9.81 m/s2 .

Work Done by Friction07:04, highSchool, multiple choice, > 1 min,fixed.

A block of mass m is pushed a horizon-tal distance D from position A to position B,along a horizontal plane with friction coeffi-cient µ. Then m is pushed from B to A.

If the force pushing m from A to B is ~P ,and the force pushing m from B to A is −~P ,what is the total work done by friction?

1. −2µmgD

2. 0

3. 2 (µmg − P )D

4. 2 (P − µmg)D

5. +2µmgD


Work On A Train07:04, highSchool, multiple choice, < 1 min,fixed.

A train of mass m and speed v travels adistance L along a frictionless circular trackof radius R.

Neglect air friction.The work done on the train is

1.W = mgL .

2.W = −mgL .

3.W =

(

mv2

R

)

L .

4.W = −(

mv2

R

)

L .

5.W = mgR .

6.W = −mgR .

7.W = 0 .

8. None of the other choices.

Chapter 7, section 5, Work: the Gravitational Force 228


A woman weight lifter can lift a 150 lbweight from the floor to a stand 3.5 ft off theground.

What is the total work done by thewoman?


The stair stepper is a novel exercise ma-chine that attempts to reproduce the workdone against gravity by walking up stairs.With each step, Brad (of mass 60 kg) simu-lates stepping up a distance of 0.2 m with thismachine.

If Brad exercises for 15 min a day witha stair stepper at a frequency of 60 stepsper minute, how much work does he do eachday?


A weight lifter lifts a set of weights a verticaldistance of 2.00 m.

If a constant net force of 350 N is exertedon the weights, how much net work is done onthe weights?


If 2.0 J of work is done in raising a 180 gapple, how far is it lifted?


Part 1 of 2A person lifts a 4.5 kg cement block a ver-

tical distance of 1.2 m and then carries theblock horizontally a distance of 7.3 m.

The acceleration of gravity is 9.81 m/s2 .a) Determine the work done by the person

in the process.

Part 2 of 2b) Determine the work done by the force ofgravity in the process.


A plane designed for vertical takeoff has amass of 8.0× 103 kg.

Find the net work done on the plane asit accelerates upward at 1.0 m/s2 through adistance of 30.0 m after starting from rest.


Part 1 of 3A 5.0 kg block is pushed 3.0 m at a con-

stant velocity up a vertical wall by a constantforce applied at an angle of 30.0◦ with thehorizontal, as shown in the figure.


3 m

30◦

5 kg

F

Drawing not to scale.If the coefficient of kinetic friction between

the block and the wall is 0.30, finda) the work done by the force on the block.

Part 2 of 3b) the work done by gravity on the block.

Part 3 of 3c) the magnitude of the normal force betweenthe block and the wall.


Moving a Refrigerator 0207:05, highSchool, multiple choice, < 1 min,normal.

Part 1 of 2To move a refrigerator of mass m = 150 kg

into a house, the mover puts it on a dolly andcovers the steps leading into the house with awooden plank acting as a ramp. The plankis 8 m long and rises 2 m. The mover pullsthe dolly with constant velocity and with asteady force 740 N up the ramp.

The acceleration of gravity is 9.8 m/s2 .How much work does he perform?

Part 2 of 2What is the minimal work required to lift therefrigerator into the house?

Pushing a Block Upward 0107:05, highSchool, numeric, > 1 min, normal.

Part 1 of 3As shown in the figure, a block of mass

5 kg is pushed up against the vertical wall bya force of 60 N acting at 45◦ to the ceiling.The coefficient of kinetic friction between theblock and the wall is 0.3.


5 kg

F45◦

µk=

0.3

Find the work done by this force in movingthe block upward by a distance 3 m.

Part 2 of 3For a force of F = 60 N, find the magnitudeof the frictional force.

Part 3 of 3

Find the force F needed to keep the blockmoving up with a constant velocity.

Serway CP 05 02 noissues07:05, highSchool, numeric, < 1 min, normal.

A beautiful man with a large nose namedMelvin lifts a 20 kg bucket from a well anddoes 6 kJ of work.

The acceleration of gravity is 9.8 m/s2 .How deep is the well?


Which of the following does not involvework?

1. A golf ball is struck.

2. A child is pushed on a swing.

3. A runner stretches by pushing against awall.

4. A weight lifter does military presses (lift-ing weights over his head.)

5. A professor picks up a piece of chalk fromthe floor.

Work on a Train Car07:05, highSchool, multiple choice, > 1 min,normal.

A train car of mass 3500 kg rolls around acurve along a level frictionless track of length2800 m.

The acceleration of gravity is 9.8 m/s2 .The net work done on the train car is

1.W = 9.604× 107 J .

2.W = −9.604× 107 J .

3.W = 9.8× 106 J .

4.W = −9.8× 106 J .


5.W = 0 J .

6. Not enough information given.

Chapter 7, section 8, Kinetic Energy and the Work-Energy Theorem 231


According to the work-energy theorem, ifwork is done on an object, its potential and/orkinetic energy changes. Consider a car thataccelerates from rest on a flat road.

What force did the work that increased thecar’s kinetic energy?

1. the friction between the road and thetires

2. air resistance

3. the force of the car engine

4. gravity

Conceptual work 0107:08, highSchool, multiple choice, < 1 min,fixed.

Part 1 of 3Two students ride in carts opposite to one

another in a spinning ferris wheel as shownbelow.

��

��

R

B

A

v

Student A is originally at the bottom of theferris wheel while studentB is at the top of theferris wheel. As the wheel turns, student Bcomes to the bottom while student A arrivesat the top, as shown below.

��

�

R

A

B

v

The ferris wheel spins at a constant speed sothat the two students are traveling with con-stant speed. Students A and B have massesm

Aand m

B, respectively. The ferris wheel

has a radius R.What is the magnitude of the TOTAL

work done on student A in moving from thebottom to the top of the ferris wheel? Thetotal work is the sum of the work done byall of the forces on the body; i.e., W total =∑

F ∆s. Neglect air resistance.

1.W totalA

= 0

2.W totalA

= 2mAg R

3.W totalA

= 2mBg R

4.W totalA

= 2 (mA−m

B) g R

5.W totalA

= 2 (mB−m

A) g R

6.W totalA

= 2 (mA+m

B) g R

7.WwheelB

= mBg R

8.WwheelB

= mAg R

9.WwheelB

= (mA+m

B) g R

Part 2 of 3What is the magnitude of the work done onstudent B by the ferris wheel in moving fromthe top to the bottom?


1.WwheelB

= 2mBg R

2.WwheelB

= 2mAg R

3.WwheelB

= 2 (mA−m

B) g R

4.WwheelB

= 2 (mB−m

A) g R

5.WwheelB

= 2 (mA+m

B) g R

6.WwheelB

= 0

7.WwheelB

= mBg R

8.WwheelB

= mAg R

9.WwheelB

= (mA+m

B) g R

Part 3 of 3What is the sign of the work done on studentB by the ferris wheel in moving from the topto the bottom?

1. negative (WwheelB

< 0)

2. positive (WwheelB

> 0)

3. undetermined, sinceWwheelB

= 0

Conceptual work 0207:08, highSchool, multiple choice, > 1 min,fixed.

Two students ride in carts opposite to oneanother in a spinning ferris wheel as shownbelow.

��

��

R

B

A

v

Student A is originally at the bottom of theferris wheel while studentB is at the top of theferris wheel. As the wheel turns, student Bcomes to the bottom while student A arrivesat the top, as shown below.

��

�

R

A

B

v

The ferris wheel spins at a constant speed sothat the two students are traveling with con-stant speed. Students A and B have massesm

Aand m

B, respectively. The ferris wheel

has a radius R.What is the magnitude of the TOTAL

work done on student A in moving from thebottom to the top of the ferris wheel? Thetotal work is the sum of the work done byall of the forces on the body; i.e., W total =∑

F ∆s. Neglect air resistance.

1.W totalA

= 0


2.W totalA

= 2mAg R

3.W totalA

= 2mBg R

4.W totalA

= 2 (mA−m

B) g R

5.W totalA

= 2 (mB−m

A) g R

6.W totalA

= 2 (mA+m

B) g R

7.WwheelB

= mBg R

8.WwheelB

= mAg R

9.WwheelB

= (mA+m

B) g R

Elevator Work Energy07:08, highSchool, multiple choice, < 1 min,fixed.

An elevator of mass m is initially at rest onthe first floor of a building. It moves upward,and passes the second and third floors witha constant velocity, and finally stops at thefourth floor. The distance between adjacentfloors is h.

What is the net work done on the elevatorduring the entire trip, from the first floor tothe fourth floor?

1.W = 3mg h

2.W = −3mg h

3.W = 0

4.W = 4mg h

5.W = −4mg h

6. None of these.

Five Ramps07:08, highSchool, multiple choice, < 1 min,fixed.

Five ramps lead from the ground to thesecond floor of a workshop, as sketched below.All five ramps have the same height; ramps B,

C, D and E have the same length; ramp A islonger than the other four. You need to pusha heavy cart up to the second floor and youmay choose any one of the five ramps.

A

B

C

D

E

Assuming no frictional forces on the cart,which ramp would require you to do the leastwork?

1. Ramp A.

2. Ramp B.

3. Ramp C.

4. Ramp D.

5. Ramp E.

6. Same work for all five ramps.

7. Same work for ramps B, C, D or E; morework for ramp A.

8. Same work for the straight ramps A andB; less work for ramps C, D, and E.

9. Unable to determine without knowing theexact profiles of ramps C, D or E.

Friction and Kinetic Energy07:08, highSchool, multiple choice, < 1 min,fixed.

Can frictional forces ever increase the ki-netic energy of an object?

1. Yes.


2. No.


A student wearing frictionless in-line skateson a horizontal surface is pushed by a friendwith a constant force of 45 N.

How far must the student be pushed, start-ing from rest, so that her final kinetic energyis 352 J ?


A 2.0 × 103 kg car accelerates from restunder the action of two forces. One is aforward force of 1140 N provided by tractionbetween the wheels and the road. The other isa 950 N resistive force due to various frictionalforces.

How far must the car travel for its speed toreach 2.0 m/s?


A 2.1 × 103 kg car accelerates from restat the top of a driveway that is sloped at anangle of 20.0◦ with the horizontal. An averagefrictional force of 4.0×103 N impedes the car’smotion so that the car’s speed at the bottomof the driveway is 3.8 m/s.

The acceleration of gravity is 9.81 m/s2 .What is the length of the driveway?


A 75 kg bobsled is pushed along a horizon-tal surface by two athletes. After the bobsledis pushed a distance of 4.5 starting from rest,its speed is 6.0 m/s.

Find the magnitude of the net force on thebobsled.


Part 1 of 5A 10.0 kg crate is pulled up a rough incline

with an initial speed of 1.5 m/s. The pullingforce is 100.0 N parallel to the incline, whichmakes an angle of 15.0◦ with the horizontal.The coefficient of kinetic friction is 0.40 andthe crate is pulled a distance of 7.5 m.

The acceleration of gravity is 9.81 m/s2 .a) Find the work done by Earth’s gravity

on the crate.

Part 2 of 5b) Find the work done by the force of frictionon the crate.

Part 3 of 5c) Find the work done by the puller on thecrate.

Part 4 of 5d) Find the change in kinetic energy of thecrate.

Part 5 of 5e) Find the speed of the crate after it is pulled7.5 m.


A 50 kg diver steps off a diving board anddrops straight down into the water. The waterprovides an average net force of resistance of1500 N to the diver’s fall.

The acceleration of gravity is 9.81 m/s2 .If the diver comes to rest 5 m below the

water’s surface, what is the total distance be-tween the diving board and the diver’s stop-ping point underwater?


In a circus performance, a monkey on a sled


is given an initial speed of 4.0 m/s up a 25◦

incline. The combined mass of the monkeyand the sled is 20.0 kg, and the coefficientof kinetic friction between the sled and theincline is 0.20.

The acceleration of gravity is 9.81 m/s2 .How far up the incline does the sled move?


A person doing a chin-up weighs 700.0 N,disregarding the weight of the arms. Duringthe first 25.0 cm of the lift, each arm exertsan upward force of 355 N on the torso.

The acceleration of gravity if 9.81 m/s2 .If the upward movement starts from rest,

what is the person’s speed at this point?


A 98.0 N grocery cart is pushed 12.0 malong an aisle by a shopper who exerts aconstant horizontal force of 40.0 N.

The acceleration of gravity is 9.81 m/s2 .If all frictional forces are neglected and the

cart starts from rest, what is the grocery cart’sfinal speed?


Part 1 of 3A 0.60 kg rubber ball has a speed of 2.0 m/s

at point A and kinetic energy 7.5 J at pointB. Find

a) the ball’s kinetic energy at A.

Part 2 of 3b) the ball’s speed at B.

Part 3 of 3c) the total work done on the ball as it movesfrom A to B.


Part 1 of 2A 5.00 g bullet moving at 600.0 m/s pene-

trates a tree trunk to a depth of 4.00 cm.a) Use work and energy considerations to

find the magnitude of the force that stops thebullet.

Part 2 of 2b) Assuming that the frictional force is con-stant, determine how much time elapses be-tween the moment the bullet enters the treeand the moment the bullets stops moving.


Part 1 of 2A 2.50× 103 kg car requires 5.0 kJ of work

to move from rest to some final speed. Duringthis time, the car moves 25.0 m.

Neglecting friction, finda) the final speed.

Part 2 of 2b) the net horizontal force exerted on thecar.

Inclined plane consv energy07:08, highSchool, multiple choice, < 1 min,fixed.

A block is released from rest, at a height h,and allowed to slide down an inclined plane.There is friction on the plane. At the bottomof the plane, there is a spring that the blockwill compress. After compressing the spring,the block will slide up the plane to some maxi-mum height, hA, after which it will again slideback down.

How much work is done on the block be-tween its release at height h and its ascent toits next maximum height?

1. mA g (h − hA)


2. 2µmA g hA

3. 0

4. mA g (h− hA) + 2µmA g hA


5. None of these

Sliding a Box 020407:08, highSchool, numeric, > 1 min, normal.

Part 1 of 2A 40 kg box initially at rest is pushed 5 m

along a rough, horizontal floor with a constantapplied horizontal force of 130 N.

The acceleration of gravity is 9.8 m/s2 .If the coefficient of friction between box and

floor is 0.3, find the work done by the friction.

Part 2 of 2Find the the final speed of the box.

Sliding Block07:08, highSchool, multiple choice, > 1 min,normal.

A block of mass 4.2 kg, sliding on a hor-izontal plane, is released with a velocity of2.3 m/s. The block slides and stops at a dis-tance of 1.5 m beyond the point where it wasreleased.

How far would the block have slid if itsinitial velocity were increased by a factor of2.1?

SWCTWork and Energy07:08, highSchool, multiple choice, < 1 min,fixed.

A cart on an air track is moving 0.5 m/swhen the air is turned off. The cart comes toa rest after traveling 1 m.

How far would the cart travel if it weremoving at 1 m/s when the air was turned off?

1. 1m

2. 2m

3. 3m

4. 4m

5. impossible to determine

Work Done by Friction 0207:08, highSchool, multiple choice, < 1 min,fixed.

A block sliding on a horizontal surface hasan initial speed of 0.5 m/s. The block travelsa distance of 1 m as it slows to a stop.

What distance would the block have trav-eled if its initial speed had been 1 m/s?

1. 0.5 m

2. 1 m

3. 2 m

4. 3 m

5. 4 m

6. more information is needed to answer thequestion

Chapter 7, section 10, Kinetic Friction 237

Falling Paper07:10, highSchool, multiple choice, < 1 min,fixed.

A piece of paper of massm is dropped froma height H, to the floor (height = 0). Theforce of air friction has magnitude f .

The net workWnet done on the paper is

1.Wnet = mgH .

2.Wnet = −mgH .

3.Wnet = f H .

4.Wnet = −f H .

5.Wnet = (mg − f)H .

6.Wnet = (f −mg)H .

Chapter 7, section 11, Power 238

Climbing a Rope 0207:11, highSchool, numeric, < 1 min, normal.

A student weighing 700 N climbs at con-stant speed to the top of an 8 m vertical ropein 10 s.

What is the average power expended by thestudent to overcome gravity?


Part 1 of 2Assume your mass is 80 kg. The accelera-

tion due to gravity is 9.8 m/s2.How much work against gravity do you do

when you climb a flight of stairs 3 m high?

Part 2 of 2Consider the energy consumed by a 60 Wlight bulb in an hour.

How many flights of stairs would you haveto climb to equal the work of the lightbulb?


Part 1 of 2A small air compressor operates on a 1.5 hp

(horsepower) electric motor for 8 hours a day.Howmuch energy is consumed by the motor

daily? 1 hp equals about 750 watts.

Part 2 of 2If electricity costs 20 cents per kilowatt-hour,how much does it cost to run the compressoreach day?


Part 1 of 2Georgie was pulling her brother (of mass

20 kg) in a 10 kg sled with a constant force of25 N for one block (100 m).

How much work did Georgie do?

Part 2 of 2

How long would a 100 W lightbulb have toglow to produce the same amount of energyexpended by Georgie?


What energy is produced by a 100 W light-bulb lit for 2.5 hours?

Conceptual 08 1107:11, highSchool, numeric, < 1 min, fixed.

Normally the rate at which you expendenergy during a brisk walk is 3.5 calories perminute. (A calorie is the common unit of foodenergy, equal to 0.239 Joules.)

How long do you have to walk in order toproduce the same amount of energy as in acandy bar (approximately 280 cal)?

Conceptual 08 1207:11, highSchool, numeric,> 1min, wording-variable.

Normally the rate at which you expendenergy during a brisk walk is 3.5 calories perminute. (A calorie is the common unit of foodenergy, equal to 0.239 J.)

How long do you have to walk to producethe same amount of energy as a 100 W light-bulb that is lit for 1 hour?


Sleeping consumes 1.3 calories of energy perminute for your friend Ben.

How many calories are expended during anight’s sleep of 8 hours?


You leave your 75 W portable color TVon for 6 hours during the day and evening,and you do not pay attention to the cost ofelectricity.

If the dorm (or your parents) charged you


for your electricity use and the cost was$0.1 /kW · h, what would be your monthly(30 day) bill?


Two construction cranes are each able tolift a maximum load of 20000 N to a height of100 m. However, one crane can lift that load

in1

3the time it takes the other.

Howmuch more power does the faster cranehave?

1. 3

2.1

3

3. 9

3.1

9

3. 1



As a freely falling object picks up downwardspeed, what happens to the power supplied bythe gravitational force?

1. The power increases.

2. The power decreases.

3. The power stays the same.



In order to lose 1 pound per week, you needto reduce your daily intake by 500 Calories

per day.How long would you have to run in order

to burn 500 Calories if you burn 7 cal/min?The Calories burned vary with the weight andintensity of the runner.


Energy-efficient appliances are importantin today’s economy. Suppose that a lightbulbgives as much light as a 100-watt bulb, butconsumes only 20 W while costing $2 more.

If electricity costs 8 cents per kilowatt-hour,how long will the bulb would have to operateto make up the difference in price?

Energy 5007:11, highSchool, multiple choice, < 1 min,normal.

How much energy will a stock tank heaterrated at 1500 Watts use in a 24 hour period?

1. 1500 Joules

2. 1500 × 24 × 60 Joules

3. 1500 × 3600 Joules

4. 1500 × 24 × 3600 Joules

Energy AndWork207:11, highSchool, multiple choice, > 1 min,fixed.

A sports car accelerates from zero to30mph in 1.5 s.

How long does it take for it to acceleratefrom zero to 60mph, assuming the power ofthe engine to be independent of velocity andneglecting friction.

1. 2 s

2. 3 s

3. 4.5 s


4. 6 s

5. 9 s

6. 12 s


A 1.0× 103 kg elevator carries a maximumload of 800.0 kg. A constant frictional forceof 4.0 × 103 N retards the elevator’s motionupward.

The acceleration of gravity is 9.81 m/s2 .What minimum power must the motor de-

liver to lift the fully loaded elevator at a con-stant speed 3.00 m/s?


A car with a mass of 1.50 × 103 kg startsfrom rest and accelerates to a speed of 18.0m/s in 12.0 s. Assume that the force ofresistance remains constant at 400.0 N duringthis time.

What is the average power developed bythe car’s engine?


A rain cloud contains 2.66× 107 kg of watervapor.

The acceleration of gravity is 9.81 m/s2 .How long would it take for a 2.00 kW pump

to raise the same amount of water to thecloud’s altitude of 2.00 km?


How long does it take a 19 kW steam engineto do 6.8× 107 J of work?


Part 1 of 2A 1.50 × 103 kg car accelerates uniformly

from rest to 10.0 m/s in 3.00 s.a) What is the work done on the car in this

time interval?

Part 2 of 2b) What is the power delivered by the enginein this time interval?


Note: One horsepower is equal to 746 watts.An automobile engine delivers 50.0 hp.How much time will it take for the engine

to do 6.40× 105 J of work?


Water flows over a section of Niagara Fallsat the rate of 1.2× 106 kg/s and falls 50.0 m.

The acceleration of gravity if 9.81 m/s2 .How much power is generated by the falling

water?

Kilowatt hours07:11, highSchool, multiple choice, < 1 min,fixed.

A kilowatt-hour is a unit of

1. current

2. voltage

3. torque

4. work

5. force


6. power

7. None of these

Output Power07:11, highSchool, multiple choice, > 1 min,normal.

A hot rod of mass 1200 kg, starting fromrest reaches a speed of 180 m/s in only 17.2 s.What is the average output power?

1. 1.13023 MW

2. 2.26047 MW

3. 0.0125581 MW

4. 0.0657112 MW

5. 0.000365062 MW

Power 0107:11, highSchool, multiple choice, < 1 min,fixed.

Power equals work

1. divided by time.

2. divided by weight.

3. divided by distance.

4. times distance.


The unit of power is the

1.Watt.

2. Joule.

3. Coulomb.

4. Newton.


The rate at which work is done is called

1. power.

2. force.

3. resistance.

4. energy.

Power 0407:11, highSchool, numeric, < 1 min, normal.

If you exert a force of 50 N to walk 4 m up aflight of stairs in 4 seconds, how much powerdo you use?

Power Output07:11, highSchool, numeric, > 1 min, normal.

Rosie (mass 47 kg) pushes a box with ahorizontal force of 140 N (31.472 lb) at a speed15 m/min. What is Rosie’s power output?

Woman Push Lawn Mower 0207:11, highSchool, numeric, > 1 min, normal.

A woman pushes a lawn mower with a con-stant force of 112 N at an angle of 37◦ withrespect to the horizontal. The lawn mowermoves at a speed of 20 cm/sec (1/2mph).What is her power output? (1 hp = 746Watts)

Woman Push Lawn Mower07:11, highSchool, multiple choice, > 1 min,fixed.

A woman pushes a lawn mower with a con-stant force of 112 Newtons at an angle of 37degrees with respect to the horizontal. Thelawn mower moves at a speed of 20 cm/sec.What is her power output? (1 hp = 746Watts)


1. 0.020 hp

2. 0.024 hp

3. 0.030 hp

4. 0.034 hp

5. 0.040 hp

6. 0.044 hp

Chapter 7, section 13, Energy and the Automobile 243


How many kilometers per liter will a carreach if its engine is 35% efficient and it en-counters an average retarding force of 500 Nat highway speed? (Assume that the energycontent of gasoline is 50 MJ/L.)

Chapter 7, section 14, Kinetic Energy at High Speeds 244


Consider three wires connected at a junc-tion, as shown in the figure. You measure200 electrons per second flowing in wire A to-ward the junction and 300 electrons per sec-ond flowing in wire B away from the junction.

A

C

B

What is the electron flow in wire C?

1. 100 electrons/s in wire C toward the junc-tion.

2. 100 electrons/s in wire C away from thejunction.

3. 500 electrons/s in wire C away from thejunction.

4. 500 electrons/s in wire C toward the junc-tion.


A water tank empties itelf by draining wa-ter out of the bottom through a pipe network.The figure shows two possible configurationsof pipes leading out of the bottom. In eachcase the pipe has the same diameter and thereare two identical constrictions in the pipe. (Aconstriction is simply a location where thepipe diameter is smaller.)

A B

Which tank will drain faster?

1. A

2. B

3. Both drain at the same rate.


The figure represents two possible ways toconnect two lighbulbs to a battery. All of thebulbs are identical.

A

Chapter 7, section 14, Kinetic Energy at High Speeds 245

B

In which case will the total current runningthrough the battery be greater?

1. A

2. B

3. The same current runs through the bat-tery in both cases.


The figure represents two possible ways toconnect two lighbulbs X and Y to a battery.Bulb X has less resistance than bulb Y .

Y

X

A

X Y

B

Which bulb has the most current runningthrough it?

1. Bulb X in A

2. Bulb Y in A

3. Bulb X in B

4. Bulb Y in B

Chapter 7, section 15, Simple and Compound Machines 246


Part 1 of 3Consider the following devices:I) a toothbrush;II) a pizza cutter with a circular disk;III) a saw;IV) a chisel;V) a pencil sharpener.In which of the devices is a lever present?

1. I

2. I, II and III

3. II and V

4. I, III and IV

5. II, III, IV and V

Part 2 of 3In which of the devices is an inclined planepresent?

1. I

2. I, II and III

3. II and V

4. II, III, IV and V

5. I, II, III and V

6. I and II

Part 3 of 3In which of the devices is a wheel and axlepresent?

1. I

2. I, II and III

3. II and V

4. III and VI


6. I and II


Part 1 of 2A 500-N crate needs to be lifted 1 meter

vertically in order to get it into the back of apickup truck.

What gives the crate a greater potentialenergy?

1. lift it straight up into the truck

2. slide it up a frictionless inclined plane

3. Either


Part 2 of 2What is the advantage of using the inclinedplane?

1. less force

2. less distance

3. less total energy

4. more power


Part 1 of 4Many everyday devices incorporate some of

the following simple machines:I) the lever;II) the inclined plane; andIII) the wheel and axle.What kind(s) of simple machine compo-


nents can be found in a crowbar?

1. I only

2. I and II only

3. II and III only

4. I and III only

5. I, II and III

Part 2 of 4What kind(s) of simple machine componentscan be found in a pair of scissors?

1. I only

2. I and II only

3. II and III only

4. I and III only

5. I, II and III

Part 3 of 4What kind(s) of simple machine componentscan be found in a stapler?

1. I only

2. I and II only

3. II and III only

4. I and III only

5. I, II and III

Part 4 of 4What kind(s) of simple machine componentscan be found in corkscrew?

1. I only

2. I and II only

3. II and III only

4. I and III only

5. I, II and III


The efficiency of a pulley system is 64 per-cent. The pulleys are used to raise a mass of78 kg to a height of 4.0 m.

The acceleration of gravity is 9.81 m/s2 .What force is exerted on the rope of the

pulley system if the rope is pulled for 24 min order to raise the mass to the requiredheight?


A crate is pulled 2.0 m at constant velocityalong a 15◦ incline. The coefficient of kineticfriction between the crate and the plane is0.160.

Calculate the efficiency of this procedure.


A pulley system has an efficiency of 87.5percent.

The acceleration of gravity is 9.81 m/s2 .How much of the rope must be pulled in if

a force of 648 N is needed to lift a 150 kg desk2.46 m?


A pulley system is used to lift a piano 3.0m.

The acceleration of gravity is 9.81 m/s2 .If a force of 2200 N is applied to the rope

as the rope is pulled in 14 m, what is theefficiency of the machine? Assume the mass


of the piano is 750 kg.

Levers 0107:15, highSchool, multiple choice, < 1 min,fixed.

A fulcrum is

1. the place where a lever is supported.

2. measured in Newton-meters.

3. measured in Joules.

4. a support for an inclined plane.


Which of the following is not a third-classlever?

1. scissors

2. broom

3. baseball bat

4. shovel


The advantage of using a third-class leveris that it

1. multiplies distance.

2. decreases distance.

3. multiplies effort force.

4. makes the resistance force smaller.


The fulcrum of which class lever is alwaysbetween the effort force and the resistanceforce?

1. first

2. second

3. third

4. None of these

Lifting Weights With Pulleys07:15, highSchool, numeric, > 1 min, normal.

Part 1 of 3A pulley system lifts a 1345 N weight a

distance of 0.975 m. Paul pulls the rope adistance of 3.9 m, exerting a force of 375 N.

The acceleration of gravity is 9.8 m/s2 .What is the ideal mechanical advantage of

the system?

Part 2 of 3What is the mechanical advantage?

Part 3 of 3How efficient is this system?

Machines 0107:15, highSchool, multiple choice, < 1 min,fixed.

An example of a compound machine is a

1. typewriter.

2. pair of scissors.

3. pair of pliers.

4. hammer.


A simple machine that is a straight slanted


surface is

1. an inclined plane.

2. a lever.

3. a pulley.

4. a wedge.

5. a screw.

6. a wheel and axle.


A doorknob is a simple machine called

1. a wheel and axle.

2. a lever.

3. a pulley.

4. a wedge.

5. a screw.

6. an inclined plane.


Which property of a machine compares itswork output with its work input?

1. mechanical efficiency

2. mechanical advantage

3. ideal mechanical advantage

4. energy

Machines 0507:15, highSchool, multiple choice, < 1 min,

fixed.

A machine with a(n) of two doublesthe force applied to the machine.

1. mechanical advantage

2. mechanical efficiency

3. ideal mechanical advantage

4. energy


Consider the following statements.A. A third-class lever requires a larger effort

force for a given resistance force.B. If the effort force is less than the resis-

tance force, the mechanical advantage is lessthan 1.

C. The mechanical efficiency of a machineis decreased by reducing friction within themachine.

Which statement(s) is/are true?

1. Only A is true.

2. A, B, and C are true.

3. Only B is true.

4. Only C is true.

5. Only A and B are true.

5. Only A and C are true.

5. Only B and C are true.


Consider the following statements.A. Windmills can be used to change me-

chanical energy into electric energy.


B. Work relates force and simple machines.C. Power is the rate at which work is done.Which statement(s) is/are true?


2. Only A is true.


4. Only B is true.

5. Only C is true.




Consider the following statements.A. The mechanical efficiency of a machine

is always less than 100 percent.B. A machine that works with one move-

ment is a simple machine.C. A combination of complex machines is a

compound machine.Which statement(s) is/are true?


2. Only A is true.


4. Only B is true.

5. Only C is true.




A screwdriver being used to pry open a canof paint is an example of which type of simplemachine?

1. lever

2. wheel and axle

3. pulley

4. inclined plane

5. wedge

6. screw


If you have to apply 30 N of force on a crow-bar to lift an object that weighs 330 N, whatis the mechanical advantage of the crowbar?

1. 11

2. 0.09

3. 9900

4. 0.36


An inclined plane reduces the effort forceby

1. applying the force over a greater dis-tance.

2. reducing the work.

3. increasing the work.

4. applying the force over a shorter dis-tance.



How does an inclined plane differ from othersimple machines?

1. It has no moving parts.

2. It is not a lever.

3. It uses gears.

4. It is free of friction.

Mechanical Advantage 0107:15, highSchool, multiple choice, < 1 min,fixed.

The mechanical advantage of a machine isthe number of times it

1. multiplies the effort force.

2. changes the direction of the effort force.

3. changes the direction of the resistanceforce.

4. multiplies the resistance force.

Pulley 0107:15, highSchool, multiple choice, < 1 min,fixed.

The mechanical advantage of a pulley sys-tem is equal to the

1. number of rope segments pulling up onthe load.

2. distance the load has to be moved.

3. weight of the object being lifted.

4. length of the rope.

Pulley 0207:15, highSchool, multiple choice, < 1 min,

fixed.

Pulleys can

1. All of these

2. multiply force.

3. multiply distance.

4. have a mechanical advantage of less thanone.

5. change the direction of the force.

Chapter 8, section 1, Potential Energy 252


Part 1 of 2Consider the following systems:I) water behind a dam;II) a swinging pendulum;III) an apple on an apple tree;IV) the space shuttle in orbit.In which of the systems is potential energy

present?

1. I and II

2. I, II and III

3. II and IV

4. II, III and IV


Part 2 of 2In which of the systems is kinetic energy

present?

1. I and II

2. I, II and III

3. II and IV

4. II, III and IV



What does the International Space Stationpossess?

1. Neither

2. kinetic energy

3. gravitational potential energy

4. Both


A car is lifted a vertical distance in a servicestation and therefore has potential energy rel-ative to the floor.

If it were lifted twice as high, how muchpotential energy would it have?

1. The same

2. Twice as much

3. One half as much



Two cars are lifted to the same elevation ina service station.

If one car is twice as massive as the other,how do their potential energies compare?

1. They have the same potential energiessince they are lifted to the same elevation.

2. The car which is twice as massive as theother will have twice potential energy.

3. The car which is twice as massive as theother will have one half potential energy thanthe other car.



Part 1 of 3A 40.0 kg child is in a swing that is attached

Chapter 8, section 1, Potential Energy 253

to ropes 2.00 m long.The acceleration of gravity is 9.81 m/s2 .Find the gravitational potential energy as-

sociated with the child relative to the child’slowest position under the following condi-tions:

a) when the ropes are horizontal.

Part 2 of 3b) when the ropes make a 30.0◦ angle withthe vertical.

Part 3 of 3c) at the bottom of the circular arc.


Part 1 of 3A 55 kg skier is at the top of a slope, as in

the figure. At the initial point A, the skier is10.0 m vertically above the final point B.


10 m

a) Find the difference in gravitational po-tential energy associated with the skier at thepoints A and B if the zero level for gravita-tional potential energy is at point B.

Part 2 of 3b) Find the difference in potential energy ifthe zero level is at point A.

Part 3 of 3c) Find the difference in potential energy ifthe zero level is midway down the slope, at aheight of 5.00 m.


Part 1 of 3A 2.00 kg ball is attached to a ceiling by a

1.00 m long string. The height of the room is3.00 m.

The acceleration of gravity is 9.81 m/s2 .What is the gravitational potential energy

associated with the ball relative toa) the ceiling?

Part 2 of 3b) the floor?

Part 3 of 3c) a point at the same elevation as the ball?

Chapter 8, section 2, Spring Potential Energy 254


A spring with a force constant of 5.2 N/mhas a relaxed length of 2.45 m. When amass is attached to the end of the spring andallowed to come to rest, the vertical length ofthe spring is 3.57 m.

Calculate the elastic potential energystored in the spring.


The staples inside a stapler are kept in placeby a spring with a relaxed length of 0.115 m.

If the spring constant is 51.0 N/m, howmuch elastic potential energy is stored in thespring when its length is 0.150 m?


Part 1 of 3A spring has a force constant of 500.0 N/m.Find the potential energy stored in the

spring when the spring isa) stretched 4.00 cm from equilibrium.

Part 2 of 3b) compressed 3.00 cm from equilibrium.

Part 3 of 3c) unstretched.

Chapter 8, section 4, Conservative Forces and Potential Energy 255


From a rooftop, one ball is dropped fromrest while another identical ball is throwndownward.

What will be the same for both balls?I) change of KE in the first second of fall;II) change of PE in the first second of fall;III) change of KE in the first meter of fall;IV) change of PE in the first meter of fall.

1. I only

2. II only

3. III only

4. IV only

5. III and IV only

6. I and II only

7. None of these

Pushing a Cart08:04, highSchool, multiple choice, < 1 min,fixed.

Part 1 of 2Consider pushing a cart up each of the four

frictionless ramps shown below. The cartbegins at rest to the left of each ramp andthen ends at rest at the top. Let WA, WB,WC andWD be the amount of work needed topush the cart up each ramp.

A B DC

Which of the following describes the rela-tionship between the work required in eachcase?

1.WA < WB < WC < WD

2.WA > WB > WC > WD

3.WA =WB =WC =WD

4.WA > WB =WC =WD

5.WA < WB =WC =WD

6.WA =WB =WC < WD

Part 2 of 2Just as each cart reaches the top of each ramp,it is released and rolls back down to the left.Just as it reaches the floor, its velocity on eachramp is vA, vB, vC and vD.

Which of the following describes the rela-tionship between the final velocities in eachcase?

1. vA < vB < vC < vD

2. vA > vB > vC > vD

3. vA = vB = vC = vD

4. vA > vB = vC = vD

5. vA < vB = vC = vD

6. vA = vB = vC < vD

Chapter 8, section 5, Conservation of Mechanical Energy 256

Bungee Jumping 0108:05, highSchool, numeric, > 1 min, normal.

Consider a bungee cord of unstretchedlength L0 = 35 m. When the cord isstretched to L > L0 it behaves like a springand obeys Hooke’s law with the spring con-stant k = 24 N/m. However, unlike a spring,the cord folds instead of becoming compressed

when the distance between its ends is lessthan the unstretched length: For L < L0 thecord has zero tension and zero elastic energy.

To test the cord’s reliability, one end is tiedto a high bridge (height H = 168 m above thesurface of a river) and the other end is tied toa steel ball of weightmg = 100 kg× 9.8 m/s2.The ball is dropped off the bridge with zeroinitial speed. Fortunately, the cord works andthe ball stops in the air before it hits the water— and then the cord pulls it back up.

Calculate the ball’s height hbot at the lowestpoint of its trajectory. For simplicity, neglectsthe cord’s own weight and inertia as well asthe air drag on the ball and the cord.

Bungee Jumping 0208:05, highSchool, numeric, > 1 min, normal.

Part 1 of 2Consider a bungee cord of unstretched

length L0 = 35 m. When the cord isstretched to L > L0 it behaves like a springand obeys Hooke’s law with the spring con-stant k = 24 N/m. However, unlike a spring,the cord folds instead of becoming compressed

when the distance between its ends is lessthan the unstretched length: For L < L0 thecord has zero tension and zero elastic energy.

To test the cord’s reliability, one end is tiedto a high bridge (height H = 168 m above thesurface of a river) and the other end is tied toa steel ball of weightmg = 100 kg× 9.8 m/s2.The ball is dropped off the bridge with zeroinitial speed. Fortunately, the cord works andthe ball stops in the air before it hits the water— and then the cord pulls it back up.

Calculate the ball’s height hbot at the lowestpoint of its trajectory. For simplicity, neglects

the cord’s own weight and inertia as well asthe air drag on the ball and the cord.

Part 2 of 2What is the upward acceleration of the ball atthe lowest point?

Bungee Jumping 0308:05, highSchool, numeric, < 1 min, normal.

Consider a bungee cord of unstretchedlength L0 = 35 m. When the cord is stretchedto L > L0 it behaves like a spring and its ten-sion follows the Hooke’s law T = k(L − L0).But unlike a spring, the cord folds instead ofbecoming compressed when the distance be-tween its ends is less than the unstretchedlength: For L < L0 the cord has zero tensionand zero elastic energy.

To test the cord’s reliability, one end is tiedto a high bridge (height H = 103 m above thesurface of a river) and the other end is tied toa steel ball of weightmg = 100 kg× 9.8 m/s2.The ball is dropped off the bridge with zeroinitial speed. Fortunately, the cord works andthe ball stops in the air 18 m above the water— and then the cord pulls it back up.

Calculate the cord’s ‘spring’ constant k.For simplicity, neglects the cord’s own weightand inertia as well as the air drag on the balland the cord.


Part 1 of 3At what point in its motion is the KE of a

pendulum bob a maximum?

1. at the lowest point

2. at the highest point

3. midway between the highest and lowestpoints

4. The KE does not change.


Part 2 of 3At what point is its PE a maximum?

1. at the lowest point

2. at the highest point

3. midway between the highest and lowestpoints

4. The PE does not change.

Part 3 of 3When its KE is half of its maximum value,how much PE does it have?

1. its minimum value

2. its maximum value

3. half of its maximum value

4. the same as its PE at any other point.


Part 1 of 2Consider a ball thrown straight up in the

air.At what position is its kinetic energy a

maximum?

1. the lowest point

2. the highest point

3. midway between the the lowest point andthe highest point

4. KE is constant at all points.

Part 2 of 2Where is its gravitational potential energy amaximum?

1. the lowest point

2. the highest point

3. midway between the the lowest point andthe highest point

4. Potential energy is constant every-where.


You are on a rooftop and you throw one ballstraight down and another straight up. Thesecond ball, after rising, falls and also strikesthe ground below.

If air resistance can be neglected and if yourdownward and upward initial speeds are thesame, how will the speed of the balls compareupon striking the ground?

1. They have same speed.

2. The speed of the second ball is larger thanthat of the first one.

3. The speed of the second ball is smallerthan that of the first one.

4. More information is needed


Part 1 of 4You throw a softball (of mass 250 g)

straight up into the air. It reaches a max-imum altitude of 15 m and then returns toyou.

What is the gravitational potential energyof the softball at its highest position? Assumethe ball departed from and returned to groundlevel.

Part 2 of 4Assume no energy is lost by the softball whileit is in the air.

What is the kinetic energy of the softball assoon as it leaves your hand?


Part 3 of 4What is the kinetic energy of the softball whenit returns to your hand?

Part 4 of 4What is the speed of the ball?


Part 1 of 2While skiing in Jackson, Wyoming, your

friend Ben (of mass 65 kg) started his descentdown the bunny run, 25 m above the bottomof the run.

If he started at rest and converted all ofhis gravitational potential energy into kineticenergy, what is Ben’s kinetic energy at thebottom of the bunny run?

Part 2 of 2What is his final velocity?


Part 1 of 2Lora (of mass 50 kg) is an expert skier. She

starts at 3 m/s at the top of the lynx run,which is 85 m above the bottom.

What is her final kinetic energy at the bot-tom of the ski run?

Part 2 of 2What is her speed at the bottom?


Part 1 of 3A pendulum swings left to right in the fig-

ure.

�

�

�

AB C

What kinds of work does the gravitationalforce do at the positions A, B, C?

1. +, +, +

2. −, −, −

3. +, 0, −

4. +, +, 0

4. +, 0, +

Part 2 of 3What is happening to the speed of the pendu-lum at the positions A, B, C?

1. increasing, increasing, decreasing

2. increasing, constant, decreasing

3. decreasing, constant, increasing

4. constant, increasing, decreasing

Part 3 of 3Where does the pendulum have the greatestkinetic energy?

1. A

2. B

3. C

4. Same kinetic energy at all points.

Conceptual 08 Q0508:05, highSchool, multiple choice, < 1 min,


fixed.

Part 1 of 2Consider the following figure.

A

B

CD

E

Where is the gravitational force doing pos-itive work?

1. A

2. B

3. C

4. D

5. E

Part 2 of 2Where does the ball have the greatest gravi-tational potential energy?

1. A

2. B

3. C

4. D

5. E


Is the total amount of gravitational andkinetic energy conserved in an open system?

1. Yes; it is conserved in any system.

2. No; it is conserved only in a closed sys-tem.

3. No; it will increase in an open system.

4. No; it will decrease in an open system.

Falls on a Spring08:05, highSchool, numeric, > 1 min, normal.

A(n) 100 g ball is dropped from a heightof 60 cm above a spring of negligible mass.The ball compresses the spring to a maximumdisplacement of 4 cm.


x

h

Calculate the spring force constant k.


Suppose a cannon is propped against a mas-sive tree to reduce recoil when it fires.

The range of the cannonball will be

1. increased.


2. decreased.

3. unchanged.

Frictionless Ramp08:05, highSchool, multiple choice, < 1 min,normal.

A block initially at rest is allowed to slidedown a frictionless ramp and attains a speedv at the bottom.

To achieve a speed 2 v at the bottom, how

many times as highh2

h1must a new ramp be?

Girl on Swing 0308:05, highSchool, numeric, > 1 min, normal.

A girl swings on a playground swing in sucha way that at her highest point she is 3.5 mfrom the ground, while at her lowest point sheis 0.5 m from the ground.


9.5 m

3.5 m0.5 m

What is her maximum speed?


A bird is flying with a speed of 18.0 m/sover water when it accidentally drops a 2.00kg fish.

The acceleration of gravity is 9.81 m/s2 .If the altitude of the bird is 5.40 m and air

resistance is disregarded, what is the speed ofthe fish when it hits the water?

Holt SF 05E 02 0308:05, highSchool, numeric,> 1min, wording-variable.

Part 1 of 3A 755 N diver drops from a board 10.0 m

above the water’s surface.The acceleration of gravity is 9.81 m/s2 .a) Find the diver’s speed 5.00 m above the

water’s surface.

Part 2 of 3b) Find the diver’s speed just before strikingthe water.

Part 3 of 3c) If the diver leaves the board with an initialupward speed of 2.00 m/s, find the diver’sspeed when striking the water.


An Olympic runner leaps over a hurdle.The acceleration of gravity is 9.81 m/s2 .If the runner’s initial vertical speed is 2.2

m/s, how much will the runner’s center ofmass be raised during the jump?


A pendulum bob is released from some ini-tial height such that the speed of the bob atthe bottom of the swing is 1.9 m/s.

The acceleration of gravity is 9.81 m/s2 .What is the initial height of the bob?


A child and sled with a combined massof 50.0 kg slide down a frictionless hill that is7.34 m high at an angle of 30◦ from horizontal.

The acceleration of gravity is 9.81 m/s2 .If the sled starts from rest, what is its speed

at the bottom of the hill?

Holt SF 05Rev 34



Part 1 of 2Tarzan swings on a 30.0 m long vine ini-

tially inclined at an angle of 37.0 ◦ with thevertical.

The acceleration of gravity if 9.81 m/s2 .What is his speed at the bottom of the

swing if hea) starts from rest?

Part 2 of 2b) pushes off with a speed of 4.00 m/s?


Part 1 of 5A 215 g particle is released from rest at

point A inside a smooth hemispherical bowlof radius 30.0 cm, as shown in the figure

The acceleration of gravity if 9.81 m/s2 .

2

3RR

A C

B

Calculatea) the gravitational potential energy at A

relative to B.

Part 2 of 5b) the particle’s kinetic energy at B.

Part 3 of 5c) the particle’s speed at B.

Part 4 of 5d) the potential energy at C.

Part 5 of 5

e) the kinetic energy at C.


A 50.0 kg pole vaulter running at 10.0 m/svaults over the bar.

The acceleration of gravity is 9.81 m/s2 .If the vaulter’s horizontal component of ve-

locity over the bar is 1.0 m/s and air resistanceis disregarded, how high is the jump?


Tarzan and Jane, whose total mass is 130.0kg, start their swing on a 5.0 m long vinewhen the vine is at an angle 30.0◦ with thehorizontal. At the bottom of the arc, Jane,whose mass is 50.0 kg, releases the vine.

The acceleration of gravity is 9.81 m/s2 .What is the maximum height at which

Tarzan can land on a branch after his swingcontinues? (Hint: Treat Tarzan’s and Jane’senergies as separate quantities.)


A 0.250 kg block on a vertical spring with aspring constant of 5.00 × 103 N/m is pusheddownward, compressing the spring 0.100 m.When released, the block leaves the springand travels upward vertically.

The acceleration of gravity is 9.81 m/s2 .How high does it rise above the point of

release?


Part 1 of 2An acrobat on skis starts from rest 50.0

m above the ground on a frictionless trackand flies off the track at a 45.0◦ angle above


the horizontal and at a height of 10.0 m.Disregard air resistance.

The acceleration of gravity is 9.81 m/s2 .a) What is the skier’s speed when leaving

the track?

Part 2 of 2b) What is the maximum height attained?


Part 1 of 3A projectile of mass 5 kg kg is shot hori-

zontally with an initial speed of 17 m/s froma height of 25 m above a flat desert surface.

The acceleration of gravity is 9.81 m/s2 .a) For the instant before the projectile hits

the surface, find the work done on the projec-tile by gravity.

Part 2 of 3b) Find the change in kinetic energy since theprojectile was fired.

Part 3 of 3c) Find the final kinetic energy of the projec-tile.


A light horizontal spring has a spring con-stant of 105 N/m. A 2.00 kg block is pressedagainst one end of the spring, compressing thespring 0.100 m. After the block is released,the block moves 0.250 m to the right beforecoming to rest.

The acceleration of gravity is 9.81 m/s2 .What is the coefficient of kinetic friction be-

tween the horizontal surface and the block?


Part 1 of 4A 25 kg child on a 2.0 m long swing is

released from rest when the swing supportsmake an angle of 30.0◦ with the vertical.

The acceleration of gravity is 9.81 m/s2 .a) What is the maximum potential energy

associated with the child?

Part 2 of 4b) Disregarding friction, find the child’s speedat the lowest position.

Part 3 of 4c) What is the child’s total mechanical en-ergy?

Part 4 of 4d) If the speed of the child at the lowestposition is 2.00 m/s, what is the change inmechanical energy due to friction?


Part 1 of 3A block starts at rest and slides down a

frictionless track.The acceleration of gravity is 9.81 m/s2 .It leaves the track horizontally, striking the

ground (as shown in the figure above).

� � ��

��

�

�

�

�

�

�

522 g

h

2.5m

4.6 m9.81

m/s

2

a) At what height h above the ground is theblock released?

Part 2 of 3b) What is the speed of the block when itleaves the track?

Part 3 of 3c) What is the speed of the block when it hitsthe ground?



Part 1 of 2A mass-spring system oscillates with an

amplitude of 3.5 cm. The spring constantis 250 N/m and the mass is 0.500 kg.

a) Calculate the mechanical energy of themass-spring system.

Part 2 of 2b) Calculate the maximum acceleration of themass-spring system.

Loop a Loop 0308:05, highSchool, multiple choice, > 1 min,wording-variable.

Neglect: Friction between the block andthe track is negligible.

Consider a loop-the-loop system where theradius of the loop is R. A small block (of massm and negligible size) is released from rest at

the point P , which is at a height of 37

8R.

31

8R

RB

P

m

The kinetic energy KB at B is given by

1. KB =23

8mgR

2. KB =21

8mgR

3. KB =12

5mgR

4. KB =5

3mgR

5. KB =15

8mgR

6. KB =12

7mgR

7. KB =8

3mgR

8. KB =13

3mgR

9. KB =15

7mgR

10. KB =19

7mgR





8R.

31

8R

R

A

P

m

The force NAwith which the track is push-

ing up on the block at the point A, which isat the bottom of the loop, is given by


1. NA=

35

4mg

2. NA=

35

3mg

3. NA=

21

2mg

4. NA=

27

4mg

5. NA=

79

7mg

6. NA=

83

7mg

7. NA=

19

2mg

8. NA=

55

7mg

9. NA=

29

4mg

10. NA=

57

5mg





8R.

31

8R

R

C

P

m

The tangential speed vCat C is given by

1. vC=

√

15

4g R

2. vC=

√

4

3g R

3. vC=

√

16

5g R

4. vC=

√

7

4g R

5. vC=

√

5

4g R

6. vC=

√

44

7g R

7. vC=

√

31

4g R

8. vC=

√

32

5g R

9. vC=

√

9

4g R

10. vC=

√

11

2g R


Part 1 of 2Neglect: Friction between the block and

the track is negligible.Consider a loop-the-loop system where the

radius of the loop is R. A small block (of massm and negligible size) is released from rest atthe point P , which is at a height of h.

hR

CP

m

What is the minimum speed vmin of the


block at C so that the block can pass by thispoint without falling off from the track?

1. vmin =√

g R

2. vmin =√

2 g R

3. vmin = 2√

g R

4. vmin =√

g R+mg

5. vmin =√

g R−mg

6. vmin =√

g R+ 2mg

7. vmin =√

g R− 2mg

8. vmin = g R

9. vmin = 4 g R

10. vmin =√

3 g R

Part 2 of 2What is the minimum height hmin of the blockat P so that the block can pass by point Cwithout falling off from the track?

1. hmin =5

2R

2. hmin =3

2R

3. hmin =1

2R

4. hmin = 2R

5. hmin = 4R

6. hmin = 6R

7. hmin =√2R

8. hmin =

√2

3R

9. hmin =√3R

10. hmin =

√3

2R



Consider a loop-the-loop system where theradius of the loop is R. A small block (of massm and negligible size) is released from rest atthe point P , which is at a height of h.

hR

CP

m

Given that the mass presses on the track at

C with a force of magnitude3

4mg , find the

initial height of the block, h .

1. h =23

8R

2. h =11

2R

3. h =13

5R

4. h =43

8R

5. h =36

7R

6. h =33

7R

7. h =13

4R

8. h =24

7R


9. h =39

8R

10. h =27

8R



Consider a loop-the-loop system where theradius of the loop is R. A small block (ofnegligible size) is released from rest at thepoint P , which is at a height of h.

h

R

C

P

m

Given that the mass’s velocity at C is√

15

4g R , find the initial height h of the

block.

1. h =31

8R

2. h =16

5R

3. h =25

8R

4. h =47

8R

5. h =14

5R

6. h =17

8R

7. h =35

8R

8. h =27

8R

9. h =19

4R

10. h =40

7R

Playground Swing 0208:05, highSchool, numeric,> 1min, wording-variable.

Betty weighs 420 N . She is sitting on aplayground swing seat that hangs 0.4 m abovethe ground in its rest position. Her initialspeed is zero and her initial height above theground is 1.4 m . At some later time her speedis 1 m/s and her height above the ground is0.8 m .

The acceleration of gravity is 9.8 m/s2 .Assume: There is friction.What is the magnitude of the work done by

friction durning this time?

Potential Energy Sums08:05, highSchool, multiple choice, < 1 min,fixed.

An object hangs motionless from a spring.When the object is pulled down, the sum ofelastic potential energy of the spring and thegravitational potential energy of the objectand Earth

1. increases.

2. stays the same.

3. decreases.

Three Identical Balls08:05, highSchool, multiple choice, < 1 min,fixed.

Three identical balls are thrown from thetop of a building, all with the same initialspeed. The first ball is thrown horizontally,the second at some angle above the horizon-


tal, and the third at some angle below thehorizontal.

Neglecting air resistance, rank the speedsof the balls as they reach the ground, fromthe slowest to the fastest.

1. 3, 2, 1

2. 1, 3, 2

3. 2, 1, 3

4. 2, 3, 1

5. 3, 1, 2

6. All three balls strike the ground with thesame speed

Toy Dart Gun08:05, highSchool, multiple choice, > 1 min,fixed.

A spring-loaded toy dart gun is used toshoot a dart straight up in the air, and thedart reaches a maximum height of 24 m. Thesame dart is shot up a second time from thesame gun, but this time the spring is com-pressed only half as far before firing.

How far up does the dart go this time, ne-glecting friction and assuming an ideal spring?

1. 96 m

2. 48 m

3. 24 m

4. 12 m

5. 6 m

6. 3 m

7. Impossible to determine.

Chapter 8, section 6, Changes in Mechanical Energy 268


In the absence of air resistance, a ballthrown vertically upward with a certain ini-tial KE will return to its original level withthe same KE.

When air resistance is a factor affecting theball, compare its KE to its original KE whenit returns to its original level.

1. less than its original KE

2. the same as its original KE

3. more than its original KE


Concept 07 3908:06, highSchool, multiple choice, < 1 min,wording-variable.

A stone is dropped from a certain heightand penetrates into mud.

All else being equal, if it is dropped fromthrice the height, how much farther should itpenetrate mud?

1. Approximately as far

2. Thrice as far

3. Farther than before, but less than thriceas far

4. More than thrice as far

Concepts of Energy08:06, highSchool, multiple choice, < 1 min,fixed.

A block is placed on the top of a rampas shown in the figure below. The blockis released from rest on the frictionless in-cline. When the block reaches the flatportion of the table it begins to feel a

frictional force with the table character-ized by a coefficient of kinetic friction µk.

µkh

Which of the following statements about theenergy and work of the system couldNOT becorrect?

1. Along the incline, gravity does work onthe block causing it to speed up.

2. The block’s gravitational potential en-ergy loss is equal to kinetic energy gain as itdescends.

3. When the block reaches the bottom ofthe incline, its kinetic energy reaches a maxi-mum.

4. On the table, friction does work on theblock causing it to slow down.

5. Along the incline, the potential energy ofthe system decreases from its initial value.

6. The normal force from the incline does nowork on the block.

7. The sum of the potential energy and thekinetic energy of the block at any point alongthe entire path of travel is conserved.


In the absence of air resistance, a fallingrock gains kinetic energy and loses potentialenergy, while the total energy of the rockremains constant. In the presence of air re-sistance, however, the rock eventually reachesterminal velocity. Now the kinetic energyis constant, but the potential energy contin-ues to decrease as the rock falls toward theground.

Why is some energy missing?


1. The energy isn’t conserved in this sys-tem.

2. The “missing” energy is transferred to theair molecules because of the air resistance.

3. No energy is “missing” because the massof the rock changes.

Energy And Work308:06, highSchool, multiple choice, > 1 min,fixed.

Suppose you drop a 1 kg rock from a heightof 5m above the ground.

When it hits, how much force does the rockexert on the ground?

1. 0.2N

2. 5N

3. 50N

4. 100N

5. Can’t be determined.


An 80.0 N box of clothes is pulled 20.0 m upa 30.0◦ ramp by a force of 115 N that pointsalong the ramp.

The acceleration of gravity is 9.81 m/s2 .If the coefficient of kinetic friction between

the box and ramp is 0.22, calculate the changein the box’s kinetic energy.


Part 1 of 3Starting from rest, a 5.0 kg block slides 2.5

m down a rough 30.0◦ incline in 2.0 s.The acceleration of gravity is 9.81 m/s2 .Find

a) the work done by the force of gravity.

Part 2 of 3b) the change in mechanical energy due tofriction.

Part 3 of 3c) the work done by the normal force betweenthe block and the incline.


Part 1 of 2A 70.0 kg base runner begins his slide into

second base while moving at a speed of 4.0m/s. The coefficient of friction between hisclothes and Earth is 0.70. He slides so thathis speed is zero just as he reaches the base.

The acceleration of gravity is 9.81 m/s2 .a) How much mechanical energy is lost due

to friction acting on the runner?

Part 2 of 2b) How far does he slide?


A skier starts from rest at the top of a hillthat is inclined at 10.5◦ with the horizontal.The hillside is 200.0 m long, and the coef-ficient of friction between the snow and theskis is 0.075. At the bottom of the hill, thesnow is level and the coefficient of friction isunchanged.

The acceleration of gravity is 9.81 m/s2 .How far does the skier move along the hor-

izontal portion of the snow before coming torest?


Part 1 of 3Starting from rest, a 10.0 kg suitcase slides


3.00 m down a frictionless ramp inclined at30.0◦ from the floor. The suitcase then slidesan additional 5.00 m along the floor beforecoming to a stop.

The acceleration of gravity is 9.81 m/s2 .a) Find the speed of the suitcase at the

bottom of the ramp.

Part 2 of 3b) Find the coefficient of kinetic friction be-tween the suitcase and the floor.

Part 3 of 3c) Find the change in mechanical energy dueto friction.


An egg is dropped from a third-floor win-dow and lands on a foam-rubber pad withoutbreaking.

The acceleration of gravity is 9.81 m/s2 .If a 56.0 g egg falls 12.0 m from rest and the

5.00 cm thick foam pad stops it in 6.25 ms,by how much is the pad compressed? Assumeconstant upward acceleration as the egg com-presses the foam-rubber pad. (Assume thatthe potential energy that the egg gains whilethe pad is being compressed is negligible.)


Part 1 of 2A 75 kg man jumps from a window 1.0 m

above a sidewalk.The acceleration of gravity is 9.81 m/s2 .a) What is his speed just before his feet

strike the pavement?

Part 2 of 2b) If the man jumps with his knees and an-kles locked, the only cushion for his fall isapproximately 0.50 cm in the pads of his feet.

Calculate the magnitude of the averageforce exerted on him by the ground in this

situation.

Chapter 8, section 8, Energy Diagrams and the Equilibrium of a System 271

Cart and Spring 0108:08, highSchool, multiple choice, > 1 min,fixed.

In part (a) of the figure, an air track cartattached to a spring rests on the track at theposition xeq and the spring is relaxed.

xstxeq

m

v

(a)

m

xv⊃= 0

µ = 0

(b)

In (b), the cart is pulled to the position xst

and released. It then oscillates about xeq.Which graph correctly represents the po-

tential energy of the spring as a function ofthe position of the cart?

1. U

xst xst

xeq

2. U

xst xst

xeq

3. U

xst

xst

xeq

4. U

xst

xstxeq

5. U

xst

xst

xeq

6. U

xst

xstxeq

7. U

xst xst

xeq

8. U

xst xst

xeq

Complicated Potential 0108:08, highSchool, multiple choice, < 1 min,wording-variable.

Use the potential energy vs. position plotshown below to answer the following question.

A particle is released from point A andmoves in the potential U(x). Suppose themechanical energy of the system is conserved.


x

U(x)

T

V

Z

A

At which position(s) will the kinetic energyof the particle have its maximum value?

1. Point T .

2. Point Z.

3. Point V .

4. Points T and Z.

5. The particle remains stationary at pointA.

Complicated Potential 0208:08, highSchool, numeric,> 1min, wording-variable.

Use the potential energy vs. position plotshown below to answer the following question.

A particle is released from point A andmoves in the potential U(x). Suppose themechanical energy of the system is conserved.

x

U(x)

T

V

Z

A

At which position(s) will the kinetic energyof the particle have its maximum value?

1. Point Z.

2. Point T .

3. Point V .

4. Points T and Z.

5. The particle remains stationary at pointA.

Energy of Ball on Track08:08, highSchool, multiple choice, > 1 min,fixed.

Part 1 of 2A bead slides without friction around a

loop-the-loop. The bead is released from aheight h from the bottom of the loop-the-loopwhich has a radius r.

h

r

Which of the following diagrams best rep-resents the kinetic energy of the bead versustime?

1.

t

K

2.

t

K

3.


t

K

4.

t

K

5.

t

K

6.

t

K

Part 2 of 2Which of the following could represent thegravitational potential energy of the bead ver-sus time?

1.

t

U

2.

t

U

3.

t

U

4.

t

U

5.

t

U

6.

t

U


Part 1 of 3The figure is a graph of the gravitational

potential energy and kinetic energy of a 75 gyo-yo as it moves up and down on its string.


0 1 2 3 4 5 6 7 80

200

400

600

Energy(m

J)

Time (s)

Mechanical energy

Kinetic energy

Potential energy


a) By what amount does the mechanicalenergy of the yo-yo change after 6.0 s?

Part 2 of 3b) What is the speed of the yo-yo after 1.5 s?

Part 3 of 3c) What is the maximum height of the yo-yo?

Tree Stops a Bullet 0208:08, highSchool, numeric, > 1 min, normal.

A bullet with a mass of 5 g and a speedof 600 m/s penetrates a tree horizontally toa depth of 4 cm. Assume that a constantfrictional force stops the bullet.

Hint: Try energy considerations.Calculate the magnitude of this frictional

force.

Chapter 8, section 9, Work Done on a System by an External Force 275

Conceptual work 0308:09, highSchool, multiple choice, < 1 min,fixed.

Suppose you observe the circular motion ofthe “hurricane” carnival ride. In this ride, theoccupants of a spinning cylinder are pinnedagainst the wall and the floor is removedfrom beneath them, yet they do not fall.

ω

R

You observe that the cylinder speeds up andthen slows back down to its original speed.

What is the sign of the net work done on theoccupants? Neglect nonconservative forces.

1. zero

2. positive

3. negative

Chapter 8, section 10, Conservation of Energy in General 276

Energy 0108:10, highSchool, multiple choice, < 1 min,fixed.

Mechanical energy is associated with

1. motion.

2. chemical reactions.

3. the nuclei of atoms.

4. the motion of electric charges.


Electromagnetic energy is associated with

1. the motion of electric charges.

2. the nuclei of atoms.

3. motion.

4. chemical reactions.


Heat energy is associated with

1. the internal motion of particles of mat-ter.

2. motion.

3. position or shape.

4. holding together the nuclei of atoms.


Chemical energy is

1. energy that bonds atoms or ions to-gether.

2. contained in the nuclei of atoms.

3. a result of the motion of electric charges.

4. a result of the internal motion of particlesof matter.


Nuclear energy is

1. contained in the nuclei of atoms.

2. a result of the motion of electric charges.

3. a result of the internal motion of particlesof matter.

4. energy that bonds atoms or ions to-gether.


An example of stored chemical energy is

1. gasoline in an automobile.

2. an electric motor.

3. the sun’s energy.

4. light.


Potential energy and kinetic energy areforms of what kind of energy?

1. mechanical

Chapter 8, section 10, Conservation of Energy in General 277

2. chemical

3. heat

4. electromagnetic

5. nuclear


Note: Coal and oil are non-renewable re-sources.

A friend says the energy of oil and coal isactually a form of solar energy.

Is your friend correct, or mistaken?

1. Correct; these materials are the resultof photosynthesis, a physical-chemical pro-cess that incorporates the sun’s radiant en-ergy into plant tissue.

2.Mistaken; the energy is actually nuclear.

3. Mistaken; the energy is actually geother-mal.


What is the ultimate source of energies forthe burning of fossil fuels, dams, and wind-mills?

1. The Sun

2. Nuclear energy

3. Geothermal power

4.Water

5. Rain

6. None of these

Chapter 9, section 1, Linear Momentum 278


A lunar vehicle is tested on Earth at a speedof 10 km/h.

When it travels this fast on the moon, howdoes its momentum compare to the momen-tum on Earth?

1. greater than on Earth

2. less than on Earth

3. the same as on Earth

4. None of these


A stone is dropped from the top of a highcliff with zero initial velocity.

In which system is the net momentum zeroas the stone falls freely?

1. the stone and the person who drops it

2. the stone and the Earth

3. the stone itself

4. None of these


When an apple falls from a tree and strikesthe ground without bouncing, what happensto its momentum?

1. The momentum of the falling apple istransferred to the Earth.

2. The momentum of the apple while fallingis increasingly smaller.

3. The momentum of the apple after strikingthe ground is reversed.

4. The speed of the apple is equal and oppo-site to the speed of the Earth.


Part 1 of 2When the velocity of an object is doubled,

by what factor is its momentum changed?

1. 1

2. 2

3.1

2

4.1

4

5.1

8

6. 4

7. 8

Part 2 of 2When the velocity of an object is doubled, bywhat factor is its kinetic energy changed?

1. 1

2. 2

3. 4

4. 8

5.1

2

6.1

4

7.1

8

Conceptual 06 01



Part 1 of 4Calculate the momentum for a 0.2 kg rifle

bullet traveling 300 m/s.

Part 2 of 4What momentum does a 1000 kg automobiletraveling 0.1 m/s (a few miles per hour) have?

Part 3 of 4What momentum does a 70 kg person running10 m/s (a fast sprint) have?

Part 4 of 4What momentum does a 10000 kg truck trav-eling 0.01 m/s (a slow roll) have?


Part 1 of 2Two 1 kg balls move away from each other,

one traveling 5 m/s to the right, the other5 m/s to the left.

What is the magnitude of the total momen-tum of the system?

Part 2 of 2Two 1000 kg cars drive east; the first movingat 20 m/s, the second at 40 m/s.

What is the magnitude of the total momen-tum of the system?


Part 1 of 3A 20 metric ton train moves toward the

south at 50 m/s.At what speed must it travel to have two

times its original momentum?

Part 2 of 3At what speed must it travel to have a

momentum of 500000 kg ·m/s?

Part 3 of 3

If there were a speed limit for this train asit traveled through a city, but not a weightlimit, what mass in kilograms must be addedto the train to slow it down to 20 m/s whileat the same time keeping the momentum thesame as in the second part?

Conceptual 06 0909:01, highSchool, multiple choice, < 1 min,wording-variable.

Which object has a greater momentum?


2. A 3000 kg truck moving at 0.01 m/s.

3. A 0.1 kg bullet traveling at 300 m/s.


What is the momentum of a two-particlesystem composed of a 1000 kg car moving eastat 50 m/s and a second 1000 kg car movingwest at 25 m/s? Let east be the positivedirection.


Which of the following undergoes the great-est change in momentum if the baseballs havethe same speed just before being caught andjust before being thrown?

1. A baseball that is caught

2. A baseball that is thrown

3.A baseball that is caught and then thrownback


Can momenta cancel? Can kinetic energies


cancel?

1. They both can cancel.

2.Momenta can cancel; kinetic energies can-not cancel.

3. Neither can cancel.

4. Momenta cannot cancel; kinetic energiescan.


If a moving object doubles its speed, howmuch more momentum does it have? Howmuch more kinetic energy?

1. Both will double.

2. Momentum won’t change; kinetic energydoubles.

3. Momentum doubles; kinetic energy willincrease by four times.

4.Momentum doubles; kinetic energy won’tchange.

5. Both will remain the same.



An ostrich with a mass of 146 kg is runningto the right with a velocity of 17 m/s.

Find the momentum of the ostrich.


Part 1 of 3A 21 kg child is riding a 5.9 kg bike with a

velocity of 4.5 m/s to the northwest.

a) What is the total momentum of the childand the bike together?

Part 2 of 3b) What is the momentum of the child?

Part 3 of 3c) What is the momentum of the bike?


What velocity must a car with a mass of1210 kg have in order to have the same mo-mentum as a 2250 kg pickup truck travelingat 25 m/s to the east?


Part 1 of 4Calculate the magnitude of the linear mo-

mentum for each of the following casesa) a proton with mass 1.67× 10−27 kg mov-

ing with a velocity of 5× 106 m/s.

Part 2 of 4b) a 1.5 g bullet moving with a speed of300 m/s to the right.

Part 3 of 4c) a 7.5 kg sprinter running with a velocity of10 m/s.

Part 4 of 4d) Earth (m = 5.98× 1024 kg) moving withan orbital speed equal to 29800 m/s.


What is the momentum of a 0.148 kg base-ball thrown with a velocity of 35 m/s towardhome plate?

Holt SF 06Rev 4109:01, highSchool, numeric,< 1min, wording-


variable.

If a 0.147 kg baseball has a momentum of6.17 kg·m/s as it is thrown from home tosecond base, what is its velocity?


Part 1 of 2A moving object has a kinetic energy of 150

J and a momentum of 30.0 kg·m/s.a) Find the speed of the object.

Part 2 of 2b) Find the mass of the object.


Part 1 of 2A 0.10 kg ball of dough is thrown straight

up into the air with an initial speed of 15 m/s.The acceleration of gravity is 9.81 m/s2 .a) What is its momentum at its maximum

height?

Part 2 of 2b) What is its momentum halfway to its max-imum height on the way up?

Chapter 9, section 2, Impulse and Momentum 282

Bouncing Rubber Ball09:02, highSchool, multiple choice, > 1 min,fixed.

A rubber ball strikes a sidewalk at an angleθ with respect to the horizontal and bouncesoff the sidewalk, again making an angle θ withrespect to the horizontal.

The direction of the impulse vector on theball is

1. vertically downward.

2. horizontal.

3. at an angle θ with respect to the horizon-tal.

4. at an angle θ with respect to the vertical.

5. vertically upward.


If you throw a raw egg against a wall, you’llbreak it, but if you throw it with the samespeed into a sagging sheet it won’t break.Why?

1. The impact time when the egg strikes asagging sheet is long, so the impact force issmall.

2. The sheet is much slicker than the wall.

3. The velocity of the egg decreases faster inthe sheet than on the wall.

4. The breaking egg causes a larger impacttime, decreasing the force.


Why do 6-ounce boxing gloves hit harder

than 16-ounce gloves?

1. The lighter gloves have less padding, thusless ability to extend the time of impact.

2.With lighter gloves, one can attack muchquicker.

3. The lighter gloves have more momen-tum.

4. The heavier gloves are difficult to use.


What is the impulse needed to stop a 10 kgbowling ball moving at 6 m/s?


Part 1 of 3A 0.5 kg hockey puck moving at 35 m/s hits

a straw bale, stopping in 1 s.What impulse was imparted to the hockey

puck?

Part 2 of 3

What is the average net force exerted bythe puck on the straw bale?

Part 3 of 3What is more important in determining the

amount of damage an object sustains in acollision?

1. the total momentum change

2. the total momentum change per unittime

3. None of these

4. Both of these

Hewitt CP9 06 R02



How does impulse differ from force?

1. Force produces acceleration; impulse pro-duces change in momentum.

2. Force produces acceleration; impulse pro-duces momentum.

3. Force produces momentum; impulse pro-duces acceleration.

4. Force is usually larger than momentum.

5. Momentum is larger than force.

6. None of these


Why might a wine glass survive a fall ontoa carpeted floor but not onto a concrete floor?

1. Since the carpet is softer than the concreteand the force of impact is reduced by theextended time of impact.

2. The decrease of momentum of the wineglass in the carpet is less than that in theconcrete.

3. The decrease of momentum of the wineglass in the carpet is more than that in theconcrete.

4. The decrease of velocity of the wine glassin the carpet is less than that in the concrete.

5. The decrease of velocity of the wine in thecarpet is more than that in the concrete.

6. None of these

Holt SF 06B 0109:02, highSchool, numeric,< 1min, wording-

variable.

A 0.50 kg football is thrown with a velocityof 15 m/s to the right. A stationary receivercatches the ball and brings it to rest in 0.020s.

What is the force exerted on the receiver?


An 82 kg man drops from rest on a divingboard 3.0 m above the surface of the waterand comes to rest 0.55 s after reaching thewater.

The acceleration due to gravity is9.81 m/s2.

What force does the water exert on theman?


A 0.40 kg soccer ball approaches a playerhorizontally with a velocity of 18 m/s to thenorth. The player strikes the ball and causesit to move in the opposite direction with avelocity of 22 m/s.

What impulse was delivered to the ball bythe player?


Part 1 of 2A 0.50 kg object is at rest. A 3.00 N force

to the right acts on the object during a timeinterval of 1.50 s.

a) What is the velocity of the object at theend of this time interval?

Part 2 of 2At the end of this interval, a constant force of4.00 N to the left is applied for 3.00 s.

b) What is the velocity at the end of the3.00 s?



Part 1 of 2A 2250 kg car traveling to the west at 20.0

m/s slows down uniformly.a) How long would it take the car to come

to a stop if the force on the car is 8450 N tothe east?

Part 2 of 2b) What is the car’s displacement during thetime it takes to stop?


Part 1 of 3A 2500 kg car traveling to the north is

slowed down uniformly from an initial velocityof 20.0 m/s by a 6250 N braking force actingopposite the car’s motion.

a) What is the car’s velocity after 2.50 s?

Part 2 of 3b) How far does the car move during the 2.5 ss?

Part 3 of 3c) How long does it take the car to come to acomplete stop?


Part 1 of 2A 2250 kg car traveling to the west at 20.0

m/s slows down uniformly under a force of8450 N to the east.

a) How much force would be required tocause the same acceleration on a car of mass3250 kg?

Part 2 of 2b) How far would the car move before stop-

ping?


A 2.5 kg ball strikes a wall with a velocityof 8.5 m/s to the left. The ball bounces offwith a velocity of 7.5 m/s to the right.

If the ball is in contact with the wall for0.25 s, what is the constant force exerted onthe ball by the wall?


A football punter accelerates a 0.55 kg foot-ball from rest to a speed of 8.0 m/s in 0.25s.

What constant force does the punter exerton the ball?


Part 1 of 2A 0.15 kg baseball moving at +26 m/s is

slowed to a stop by a catcher who exerts aconstant force of −390 N.

a) How long does it take this force to stopthe ball?

Part 2 of 2b) How far does the ball travel before stop-ping?


A 0.025 kg golf ball moving at 18.0 m/scrashes through the window of a house in 5.0×10−4 s. After the crash, the ball continues inthe same direction with a speed of 10.0 m/s.

Assuming the force exerted on the ball bythe window was constant, what was the mag-nitude of this force?



Part 1 of 2A constant force of 2.5 N to the right acts

on a 1.5 kg mass for 0.50 s.a) Find the final velocity of the mass if it is

initially at rest.

Part 2 of 2b) Find the final velocity of the mass if itis initially moving along the x-axis with avelocity of 2.0 m/s to the left.


Part 1 of 2A 55 kg pole vaulter falls from rest from a

height of 5.0 m onto a foam rubber pad. Thepole vaulter comes to rest 0.30 s after landingon the pad.

a) Calculate the athlete’s velocity just be-fore reaching the pad.

Part 2 of 2b) Calculate the constant force exerted on thepole vaulter due to the collision.

Chapter 9, section 3, Conservation of Linear Momentum 286

Blocks and Spring09:03, highSchool, multiple choice, > 1 min,fixed.

Part 1 of 2Two blocks, A and B, are connected by

a compressed spring. The mass of block Ais twice that of block B. Immediately afterrelease, compare the net force on block Ato the net force on block B. The table isfrictionless and the mass of the spring is zero.

1. FA,net will be in the opposite directionand half as large as FB,net.

2. FB,net will be in the opposite directionand half as large as FA,net.

3. FA,net is equal in magnitude and directionto FB,net, and not zero.

4. There is no net force on block A or blockB.

5. FA,net and FA,net are both directed towardthe left with FA,net larger than FA,net, but nottwice as large. Block A is pulling block B.

6. FA,net is equal in magnitude and oppositein direction to FB,net, and not zero.

Part 2 of 2Which of the following best describes the sit-uation after the blocks are released?

1. The total momentum of the system ofblocks is not conserved because there is anexternal velocity acting on the system.

2. The momentum of block A is conservedand the momentum of block B is conserved.It follows that the total momentum of thesystem of blocks is also conserved.

3. The total momentum of the system ofblocks is conserved because there is no netexternal force.

4. The total momentum of the system is notconserved because there are external forces;e.g., gravity.

5. The momentum of block A is conservedand the momentum of block B is conserved.However, the total momentum of the systemof blocks is not conserved.

6. Momentum for any body is always con-served.


Part 1 of 4Allison (of mass 30 kg) is coasting in her

wagon (of mass 10 kg) at a constant velocityof 5 m/s . She passes her mother, who dropsa bag of toys (of mass 5 kg) into the wagon.

What will happen to the speed of thewagon?

1. slow down

2. speed up

3. remain the same


Part 2 of 4What is the initial momentum of Allison andthe wagon before her mother drops the toysin?

Part 3 of 4What is the final momentum of Allison, thewagon, and the toys?

Part 4 of 4What is the speed of the wagon after Allison’smother drops the toys in?


Part 1 of 3Tony (of mass 60 kg) coasts on his bicycle


(of mass 10 kg) at a constant speed of 5 m/s,carrying a 5 kg pack. Tony throws his packforward, in the direction of his motion, at5 m/s relative to the speed of bicycle justbefore the throw.

What is the initial momentum of the system(Tony, the bicycle, and the pack)?

Part 2 of 3What is the momentum of the system im-

mediately after the pack is thrown?

Part 3 of 3What is the bicycle speed immediately after

the throw?


Suppose two carts, one twice as massiveas the other, fly apart when the compressedspring that joins them is released.

How fast does the heavier cart roll com-pared with the lighter cart?

1. vheavy =1

2vlight

2. vheavy = 2 vlight

3. vheavy = vlight

4. vheavy =1

3vlight

5. All are wrong.


A 63.0 kg astronaut is on a space walk whenthe tether line to the shuttle breaks. Theastronaut is able to throw a 10.0 kg oxygentank in a direction away from the shuttle witha speed of 12.0 m/s, propelling the astronautback to the shuttle.

Assuming that the astronaut starts fromrest, find the final speed of the astronaut after

throwing the tank.

Holt SF 06D 0209:03, highSchool, numeric, > 1 min, normal.

Note: Take East as the positive direction.A(n) 85 kg fisherman jumps from a dock

into a 135 kg rowboat at rest on the West sideof the dock.

If the velocity of the fisherman is 4.3 m/sto the West as he leaves the dock, what is thefinal velocity of the fisherman and the boat?


A boy on a 2.0 kg skateboard initially atrest tosses a(n) 8.0 kg jug of water in theforward direction.

If the jug has a speed of 3.0 m/s relative tothe ground and the boy and skateboard movein the opposite direction at 0.60 m/s, find theboy’s mass.


Part 1 of 2A 65.0 kg ice skater moving to the right

with a velocity of 2.50 m/s throws a 0.150 kgsnowball to the right with a velocity of 32.0m/s relative to the ground.

What is the velocity of the ice skater afterthrowing the snowball? Disregard the frictionbetween the skates and the ice.

Part 2 of 2A second skater initially at rest with a massof 60.0 kg catches the snowball.

What is the velocity of the second skaterafter catching the snowball in a perfectly in-elastic collision?



A tennis player places a 55 kg ball machineon a frictionless surface. The machine fires a0.057 kg tennis ball horizontally with a veloc-ity of 36 m/s toward the north.

What is the final velocity of the machine?


A 85.0 kg astronaut is working on the en-gines of a spaceship that is drifting throughspace with a constant velocity. The astronautturns away to look at Earth and several sec-onds later is 30.0 m behind the ship, at restrelative to the spaceship. The only way to re-turn to the ship without a thruster is to throwa wrench directly away from the ship. Thewrench has a mass of 0.500 kg, and the astro-naut throws the wrench with a speed of 20.0m/s.

How long does it take the astronaut to reachthe ship?


A 7.50 kg laundry bag is dropped from restat an initial height of 3.00 m.

The acceleration of gravity is −9.81 m/s2 .Use the value 5.98× 1024 kg as the mass ofEarth.

What is the speed of Earth toward the bagjust before the bag hits the ground?

Jump Up09:03, highSchool, multiple choice, < 1 min,fixed.

Bill (mass m) plants both feet solidly onthe ground and then jumps straight up with

velocity→v .

The earth (massM) then has velocity

1. VEarth

= +

√

m

M

→v

man.

2. VEarth

= −√

m

M

→v

man.

3. VEarth

= − →v

man.

4. VEarth

= +→v

man.

5. VEarth

= −(

M

m

)

→v

man.

6. VEarth

= +

(

M

m

)

→v

man.

7. VEarth

= −(m

M

)

→v

man.

8. VEarth

= +(m

M

)

→v

man.

Row Boat09:03, highSchool, multiple choice, < 1 min,fixed.

A fisherman is out at sea in his row boatwhen it starts raining. At this point his boatstarts to fill up with water.

Providing that he is always applying thesame force to move his boat, the speed of theboat will then

1. decrease.

2. increase.

3. stay the same.

Spring Between Blocks 0209:03, highSchool, numeric, > 1 min, normal.

Two blocks of massesM and 3M are placedon a horizontal, frictionless surface. A lightspring is attached to one of them, and theblocks are pushed together with the springbetween them.


M 3M

M 3M

Before

After

(a)

(b)

v

A cord holding them together is burned,after which the block of mass 3M moves tothe right with a speed of 8 m/s. What is thespeed of the block of mass M?

Spring Between Blocks 0309:03, highSchool, numeric, > 1 min, normal.

Two blocks of massesM and 3M are placedon a horizontal, frictionless surface. A lightspring is attached to one of them, and theblocks are pushed together with the springbetween them.

M 3M

M 3M

Before

After

(a)

(b)

v

A cord holding them together is burned,after which the block of mass 3M moves tothe right with a speed of 2 m/s. What is thespeed of the block of mass M?

Spring Between Blocks 0409:03, highSchool, multiple choice, < 1 min,fixed.

Two blocks of massesM and 3M are placedon a horizontal, frictionless surface. A light

spring is attached to one of them, and theblocks are pushed together with the springbetween them.

M 3M

M 3M

Before

After

(a)

(b)

v

The two blocks are at rest first. Then thecord holding them together is burned, afterwhich the block of mass 3M moves to theright with a speed of 2 m/s. What is thespeed of the block of mass M?

1. 6 m/s

2. 2 m/s

3. 4 m/s

4. 1.5 m/s

5. 0 m/s

6. 0.67 m/s


SWCTMomentum09:03, highSchool, multiple choice, < 1 min,fixed.

Particle 1 with momentum ~P1 strikes par-ticle 2 which is at rest. Let ~P ′

1 and ~P ′2 be the

momenta after collision.If the collision is elastic, then

1. ~P ′1 = ~P ′

2

2. P1x = P ′1x + P ′

2x

3. P ′1y = P ′

2y


4. P1x = P ′1x − P ′

2x

5. P1y = P ′1y − P ′

2y

Two Blocks and a Spring09:03, highSchool, multiple choice, < 1 min,fixed.

Two Blocks of masses M and 4M areplaced in a horizontal frictionless table andconnected by a massless spring.

If the blocks are pushed together and thenreleased after the spring has been compressed,what will be the magnitude of the velocity ofmassM if mass 4M moves with velocity v?

1.v

M

v4M

= 4

2.v

M

v4M

= 2

3.v

M

v4M

= 1

4.v

M

v4M

= 16

5.v

M

v4M

= 8

6.v

M

v4M

=1

2

7.v

M

v4M

=1

4

8.v

M

v4M

=1

8

9.v

M

v4M

=1

16

Two Head on Collisions09:03, highSchool, multiple choice, < 1 min,fixed.

Think fast! You’ve just driven around acurve in a narrow one-way street at 25 mphwhen you notice a car identical to yours com-ing straight toward you at 25 mph. You haveonly two options: hitting the other car headon or swerving into a massive concrete wall,also head on.

Which course will cause the least damageto you?

1. hit the other car

2. hit the wall

3. hit either one - it makes no difference

4. consult your lecture notes

Chapter 9, section 4, Elastic Collisions 291

Colliding particles09:04, highSchool, multiple choice, < 1 min,fixed.

Particle 1 with momentum→p 1 strikes Par-

ticle 2, which is at rest. The particles movein different directions after the collision. The

momenta after the collision are→p 1

′and

→p 2

′.

What relationship is true?

1.→p 1

′=

→p 2

′

2. p1x = p′1x + p′2x

3. p1y = p′2y

4. p1x = p′1x − p′2x

5. p1y = p′1y − p′2y

6. p21 = (p′1)

2 + (p′2)2

7. (p′1)2 = p2

1 + (p′2)2

Elastic Head On Collision 0409:04, highSchool, multiple choice, > 1 min,normal.

Consider the elastic head-on collision be-tween a sledge hammer with 7000 g mass anda golf ball with a 4 g mass.

The initial velocity of the sledge hammer is18 m/s , and the golf ball is initially at rest.

7000 g 4 g

18 m/s

Estimate the approximate final speed v′2 ofthe golf ball.

1. v′2 ≈ 18 m/s

2. v′2 ≈ 36 m/s

3. v′2 ≈ 56.5487 m/s

4. v′2 ≈ 72 m/s

5. v′2 ≈ 90 m/s

6. v′2 ≈ 5.72958 m/s

7. v′2 ≈ 9 m/s

8. v′2 ≈ 144 m/s

9. v′2 ≈ 180 m/s

10. v′2 À 180 m/s

Head On Collision 0209:04, highSchool, numeric, > 1 min, fixed.

Two particles of masses m and 3m aremoving toward each other along the x-axiswith the same speed v. They undergo a head-on elastic collision and rebound along the x-axis.

m

v

3m

v

Determine the final speed of the heavierobject.

1. v′3m

= 0

2. v′3m

= 2 v

3. v′3m

= v

4. v′3m

= 3 v

5. v′3m

=1

2v

6. v′3m

=3

2v

7. v′3m

=2

3v


8. v′3m

=1

3v

9. v′3m

= 4 v

10. v′3m

=∞


Railroad car A rolls at a certain speed andmakes a perfectly elastic collision with car Bof the same mass. After the collision, car A isobserved to be at rest.

How does the speed of car B compare withthe initial speed of car A?

1. The speed of car B is more than the initialspeed of car A.

2. The speed of car B is less than the initialspeed of car A.

3. The speed of car B is the same as theinitial speed of car A.

4. Cannot compare since energy is not con-served.


Part 1 of 3Each croquet ball in a set has a mass of

0.50 kg. The green ball, traveling at 12.0 m/s,strikes the blue ball, which is at rest.

Assuming that the balls slide on a friction-less surface and all collisions are head-on, findthe final speed of the blue ball in each of thefollowing situations:

a) The green ball stops moving after itstrikes the blue ball.

Part 2 of 3b) The green ball continues moving after thecollision at 2.4 m/s in the same direction.

Part 3 of 3c) The green ball continues moving after thecollision at 0.3 m/s in the same direction.


Part 1 of 2After being struck by a bowling ball, a 1.5

kg bowling pin sliding to the right at 3.0 m/scollides head-on with another 1.5 kg bowlingpin initially at rest.

Find the final velocity of the second pin inthe following situations:

a) The first pin moves to the right after thecollision at 0.5 m/s.

Part 2 of 2b) The first pin stops moving when it hits thesecond pin.

Inertial Mass 0109:04, highSchool, multiple choice, > 1 min,fixed.

You are given two carts, A and B. Theylook identical, and you are told that they aremade of the same material. You place Aat rest on an air track and give B a constantvelocity directed to the right so that it collideselastically with A. After the collision, bothcarts move to the right, the velocity of Bbeing smaller than what it was before thecollision.

What do you conclude?

1. Cart A is hollow

2. The two carts are identical

3. Cart B is hollow

4. need more information

Inertial Mass 0209:04, highSchool, multiple choice, < 1 min,fixed.


You are given two carts, A and B. Theylook identical, and you are told that they aremade of the same material. You place Bat rest on an air track and give A a constantvelocity directed to the right so that it collideselastically with B. After the collision, bothcarts move to the right, the velocity of Abeing smaller than what it was before thecollision.

What do you conclude?

1. Cart B is hollow

2. The two carts are identical

3. Cart A is hollow


People Jumping09:04, highSchool, multiple choice, > 1 min,fixed.

Suppose the entire population of the worldgathers in one spot and, at the sounding of aprearranged signal, everyone jumps up.

While all the people jump up, does theEarth gain momentum in the opposite direc-tion?

1. No.

2. Yes; because of its much larger inertialmass, however, the change in momentum ofEarth is much less than that of all the jumpingpeople.

3. Yes, the Earth recoils, like a rifle firing abullet, with a change in momentum equal toand opposite that of the people.

4. It depends.

Silly Putty and Bowling Ball09:04, highSchool, multiple choice, > 1 min,fixed.

A ball of silly putty hits and sticks to abowling ball that was initially at rest. After

the collision, the total kinetic energy of thebowling ball and silly putty is

1. the same as the kinetic energy of the sillyputty before the collision

2. more than the kinetic energy of the sillyputty before the collision

3. less than the kinetic energy of the sillyputty before the collision

Two Balls and a Pin09:04, highSchool, multiple choice, < 1 min,fixed.

A person attempts to knock down a largewooden bowling pin by throwing a ball at it.The person has two balls of equal size andmass, one made of rubber and the other ofputty. The rubber ball bounces back, whilethe ball of putty sticks to the pin.

Which ball is most likely to topple the bowl-ing pin?

1. the rubber ball

2. the putty ball

3. makes no difference


Chapter 9, section 5, Inelastic Collisions 294

Car and Truck09:05, highSchool, multiple choice, > 1 min,fixed.

A compact car and a large truck collidehead on and stick together.

Which undergoes the larger momentumchange?

1. car

2. truck

3. The momentum change is the same forboth vehicles.

4. Can’t tell without knowing the final ve-locity of the combined mass.

Car Truck Collision09:05, highSchool, multiple choice, < 1 min,fixed.

A car and a large truck traveling at thesame speed collide head-on and stick together.Which vehicle experiences the larger changein the magnitude of its momentum? (Ignorethe friction)

1. the car

2. the truck

3. the change in the magnitude of momen-tum is the same for both


Chapter 9, section 6, One-Dimensional Collisions 295

Elastic Head On Collision 0209:06, highSchool, multiple choice, > 1 min,fixed.

Consider the collision of two identical par-ticles, with m1 = m2 = 10 g.

The initial velocity of particle 1 is v1 andparticle 2 is initially at rest, v2 = 0 m/s..

1 2

v1

After an elastic head-on collision, the finalvelocity of particle 2 is v′2 and given by

1. v′2 = v1

2. v′2 = 0

3. v′2 =v1

4

4. v′2 =v1

3

5. v′2 =v1

2

6. v′2 =2 v1

3

7. v′2 =3 v1

4

8. v′2 =4 v1

3

9. v′2 =5 v1

3

10. v′2 = 2 v1

Elastic Head On Collision 0309:06, highSchool, multiple choice, > 1 min,fixed.

Particle 1 is a sledge hammer with massm1 = 10 kg, particle 2 by a golf ball with amassm2 = 10 g. Consider the elastic head-oncollision between the hammer and the ball.

The initial velocity of the sledge hammer isv1, the golf ball is initially at rest, v2 = 0 m/s.

1 2v1

Estimate the approximate final speed v′2 ofthe golf ball.

1. v′2 ≈ 2 v1

2. v′2 ≈ v1

3. v′2 ≈ 5 v1

4. v′2 ≈ 10 v1

5. v′2 ≈ 20 v1

6. v′2 ≈ 50 v1

7. v′2 ≈ 100 v1

8. v′2 ≈ 200 v1

9. v′2 ≈ 500 v1

10. v′2 ≈ 1000 v1


Whenever an interaction occurs in a sys-tem, forces occur in equal and opposite pairs.

V

Before

After

Which of the following do not always occur


in equal and opposite pairs?

1. Impulses

2. Accelerations

3. Momentum Changes

4. But all of these occur in equal and oppo-site pairs.

3. None of these

Head On Collision 0309:06, highSchool, multiple choice, > 1 min,fixed.

Part 1 of 2Two particles of masses m and 4m are

moving toward each other along the x-axiswith the same speed v. They undergo a head-on elastic collision and rebound along the x-axis.

m

v

4m

v

Determine the magnitude of the total mo-mentum of the system ‖~ptotal‖ at the instantwhen the two particles are touching eachother; i.e., at the moment of collision.

1. ‖~ptotal‖ = 3mv

2. ‖~ptotal‖ = mv







9. ‖~ptotal‖ = 0

10. ‖~ptotal‖ =∞

Part 2 of 2Determine the final speed v4m of the heavierobject.

1. v4m =1

5v

2. v4m = 2 v

3. v4m = v

4. v4m = 3 v

5. v4m =3

2v

6. v4m =2

3v

7. v4m =1

3v

8. v4m = 4 v

9. v4m = 0

10. v4m =∞

Head On Collision 0409:06, highSchool, multiple choice, > 1 min,fixed.

Part 1 of 2Two particles of masses m and 3m are

moving toward each other along the x-axiswith the same speed v. They undergo a head-on elastic collision and rebound along the x-axis.

m

v

3m

v

Determine the magnitude of the momen-tum of the center of mass at the instant whenthe two particles are touching each other; i.e.,


at the moment of collision.

1. ‖~pcm‖ = 2mv

2. ‖~pcm‖ = mv

3. ‖~pcm‖ = 3mv

4. ‖~pcm‖ = 4mv

5. ‖~pcm‖ = 5mv

6. ‖~pcm‖ = 6mv

7. ‖~pcm‖ = 7mv

8. ‖~pcm‖ = 8mv

9. ‖~pcm‖ = 0

10. ‖~pcm‖ =∞

Part 2 of 2Determine the final speed of the heavier ob-ject.

1. v′3m = 0

2. v′3m = 2 v

3. v′3m = v

4. v′3m = 3 v

5. v′3m =1

2v

6. v′3m =3

2v

7. v′3m =2

3v

8. v′3m =1

3v

9. v′3m = 4 v

10. v′3m =∞

Head on Collision09:06, highSchool, multiple choice, < 1 min,

fixed.

An object of massmmoves to the right witha speed v. It collide head-on with an objectof mass 3m moving with speed v/3 in theOPPOSITE direction. If the two objects sticktogether, what is the speed of the combinedobject, of mass 4m, after the collision?

1. 0

2. v/2

3. v

4. 2 v

5. 3 v

6. v/3

7. v/4


A 1500 kg car traveling at 15.0 m/s to thesouth collides with a 4500 kg truck that isinitially at rest at a stoplight. The car andtruck stick together and move together afterthe collision.

What is the final velocity of the two-vehiclemass?


A grocery shopper tosses a(n) 9.0 kg bagof rice into a stationary 18.0 kg grocery cart.The bag hits the cart with a horizontal speedof 5.5 m/s toward the front of the cart.

What is the final speed of the cart andbag?



A 1.50× 104 kg railroad car moving at 7.00m/s to the north collides with and sticks toanother railroad car of the same mass that ismoving in the same direction at 1.50 m/s.

What is the velocity of the joined cars afterthe collision?


A dry cleaner throws a 22 kg bag of laundryonto a stationary 9.0 kg cart. The cart andlaundry bag begin moving at 3.0 m/s to theright.

Find the velocity of the laundry bag beforethe collision.


Part 1 of 2A 47.4 kg student runs down the sidewalk

and jumps with a horizontal speed of 4.20 m/sonto a stationary skateboard. The studentand skateboard move down the sidewalk witha speed of 3.95 m/s.

a) Find the mass of the skateboard.

Part 2 of 2b) How fast would the student have to jumpto have a final speed of 5.00 m/s?


Two carts with masses of 4.0 kg and 3.0kg move toward each other on a frictionlesstrack with speeds of 5.0 m/s and 4.0 m/s,respectively. The carts stick together aftercolliding head-on.

Find their final speed.


A 1.20 kg skateboard is coasting along thepavement at a speed of 5.00 m/s when a 0.800kg cat drops from a tree vertically downwardonto the skateboard.

What is the speed of the skateboard-catcombination?


Two carts with masses of 10.0 kg and 2.5 kgmove in opposite directions on a frictionlesshorizontal track with speeds of 6.0 m/s and3.0 m/s, respectively. The carts stick togetherafter colliding head-on.

Find their final speed.


A billiard ball traveling at 4.0 m/s has anelastic head-on collision with a billiard ball ofequal mass that is initially at rest. The firstball is at rest after the collision.

What is the speed of the second ball afterthe collision?


A 25.0 g marble sliding to the right at 20.0cm/s overtakes and collides elastically with a10.0 g marble moving in the same directionat 15.0 cm/s. After the collision, the 10.0 gmarble moves to the right at 22.1 cm/s.

Find the velocity of the 25.0 g marble afterthe collision.


A 15 g toy car moving to the right at20 cm/s has a head-on nearly elastic collisionwith a 20 g toy car moving in the opposite di-rection at 30 cm/s. After colliding, the 15 g


car moves with a velocity of 37 cm/s to theleft.

Find the speed of the second car after thecollision.


Two shuffleboard disks of equal mass, oneorange and the other yellow, are involved inan elastic collision. The yellow disk is initiallyat rest and is struck by the orange disk movinginitially to the right at 5.00 m/s. After thecollision, the orange disk is at rest.

What is the velocity of the yellow disk afterthe collision?


A 3.00 kg mud ball has a perfectly inelasticcollision with a second mud ball that is ini-tially at rest. The composite system moveswith a speed equal to one-third the originalspeed of the 3.00 kg mud ball.

What is the mass of the second mud ball?


A 5.5 g experimental dart is fired into ablock of wood with a mass of 22.6 g. Thewood block is initially at rest on a 1.5 m tallpost. After the collision, the wood block anddart land 2.5 m from the base of the post.

Find the initial speed of the dart.


A 730 N student stands in the middle of afrozen pond having a radius of 5.0 m. He isunable to get to the other side because of alack of friction between his shoes and the ice.To overcome this difficulty, he throws his 2.6

kg physics textbook horizontally toward thenorth shore at a speed of 5.0 m/s.

The acceleration of gravity is 9.81 m/s2 .How long does it take him to reach the

south shore?


A 1550 kg car moving south at 10.0 m/scollides with a 2550 kg car moving north. Thecars stick together and move as a unit afterthe collision at a velocity of 5.22 m/s to thenorth.

Find the velocity of the 2550 kg car beforethe collision.


Part 1 of 2A 2150 kg car moving east at 10.0 m/s

collides with a 3250 kg car moving east. Thecars stick together and move east as a unitafter the collision at a velocity of 5.22 m/s.

a) What is the velocity of the 3250 kg carbefore the collision?

Part 2 of 2b) What is the decrease in kinetic energyduring the collision?


A 0.400 kg bead slides on a straight fric-tionless wire with a velocity of 3.50 cm/s tothe right, as shown. The bead collides elas-tically with a larger 0.600 kg bead initiallyat rest. After the collision, the smaller beadmoves to the left with a velocity of 0.70 cm/s.

0.4 kg

3.5 cm/s

0.6 kg

Find the distance the larger bead moves


along the wire in the first 5.0 s following thecollision.

Chapter 9, section 8, The Center of Mass 301

Abstract Sculpture09:08, highSchool, numeric, < 1 min, normal.

An abstract sculpture consists of a ball (ra-dius R = 75 cm) resting on top of a cube(each side L = 120 cm long). The ball andthe cube are made of the same material ofuniform density; there are no hollow spacesinside them. The bottom face of the cuberests on a horizontal floor.

How high is the sculpture’s center of massabove the floor?


Rest two vertical sticks on the floor, withone against a wall, and the other in the middleof a perfectly smooth floor.

How do the paths taken by their centers ofmass compare when you allow them to fall?

1. a quarter-circle arc and a elliptical curve,respectively

2. a vertical straight line and an ellipticalcurve, respectively

3. a quarter-circle arc and a vertical straightline, respectively

4. an elliptical curve and a quarter-circlearc, respectively


Why is the wobbly motion of a single staran indication that the star has one or moreplanets orbiting around it?

1. Planets near the star distorted the time-space, which affects the star.

2. The light emitted from the star is scat-tered by planets.

3. The motion of a star is affected by thegravity of planets.

4. The star is revolving about the center ofmass of planets.


Sometimes a kicked football sails throughthe air without rotating, and at other times ittumbles end over end as it travels.

With respect to the center of mass of theball, how is it kicked in both cases?

1. in the middle; below the middle

2. in the middle; to the side of the middle

3. below the middle; in the middle

4. below the middle; to the side of the mid-dle


How can the three bricks

�

�

�

be stacked so that the top brick has max-imum horizontal displacement from the bot-tom brick? (Start with the top brick and workdown. At every interface the center of gravityof the bricks above must not extend beyondthe end of the supporting brick.)

1. Both bricks overhang half of theirlengths.

2. Top brick overhangs are one-fourth of itslength; middle brick half of its length.


3. Top brick overhangs half of its length;middle brick one-fourth of its length.

4. Top brick overhangs half of its length;middle brick one-third of its length.

5. Both bricks overhang one-third of theirlengths.


Where is the center of mass of the Earth’satmosphere?

1. at the center of the Earth

2. at the surface of the Earth

3. at points halfway between the surface ofthe Earth and the outer limits of the atmo-sphere

4. at the center of the Sun


Which location is most likely to be thecenter of mass of the dumbbell?

� � �

2m m

A B C

1. Point A

2. Point B

3. Point C

4. None of the points, because the center ofmass is not on the dumbbell.

Conceptual centerofmass09:08, highSchool, multiple choice, > 1 min,fixed.

You are standing on a swing set as shownbelow. Neither you nor the swing is in motion.Your hands do not touch the ropes which holdthe seat.

The weight of the swing is negligible com-pared to your own weight, so consider it to bezero.

You prepare to jump towards the leftfrom the seat of the swing as shown above.

There is anX marking the location directlybeneath the location of the seat.

Where will you land?

1. on the X; conservation of momentum

2. to the left of the X; conservation of mo-mentum

3. to the left of the X; conservation of en-ergy

4. to the left of the X; the horizontal forceyou exert on the center of mass

5. to the right of the X; conservation ofmomentum

6. to the right of the X; conservation ofenergy

7. to the right of the X; the horizontal forceyou exert on the center of mass

8. on the X; energy conservation

9. on the X; momentum isn’t conserved.

Rigid System Rotating 0209:08, highSchool, multiple choice, > 1 min,normal.


The figure below shows a rigid 3-mass sys-tem which can rotate about an axis perpen-dicular to the system. The mass of eachconnecting rod is negligible. Treat the massesas particles. The x-axis is along the horizon-tal direction with the origin at the left-mostmass 2M .

2M 4M 5M

L Lx

Each mass is an integer multiple of massM .The masses are separated by rods of length L,so that the entire length is 2L.

Determine the x-coordinate of the center ofmass for the three-mass system with respectto the origin.

1. xcm =14

11L

2. xcm =15

15L

3. xcm =9

15L

4. xcm =7

12L

5. xcm =15

14L

6. xcm =16

14L

7. xcm =21

21L

8. xcm =9

11L

9. xcm =17

17L

10. xcm =11

10L

Rigid System Rotating 0409:08, highSchool, numeric, > 1 min, normal.

The figure below shows a rigid 3-mass sys-tem which can rotate about an axis perpen-dicular to the system. The mass of each

connecting rod is negligible. Treat the massesas particles.

The x-axis is along the horizontal directionwith the origin at the left-most mass 2 kg.

2 kg 4 kg 5 kg

3 m 3 mx

The masses are separated by rods of length3 m, so that the entire length is 2 (3 m).

Determine the x-coordinate of the center ofmass for the three-mass system with respectto the origin.

Three Masses 0109:08, highSchool, numeric, > 1 min, normal.

Part 1 of 2Three spherical masses are located in a

plane at the positions shown in the figure be-low. A has mass 9.26 kg, B has mass 59.3 kg,and C has mass 27 kg.

0 1 2 3 4 5 6 7 8 9 100

1

2

3

4

5

6

7

8

9

10

A

B

C

yDistance

(m)

x Distance (m)

Three Masses in a Plane

Figure: Drawn to scale.Calculate the x-coordinate of the center of

mass.

Part 2 of 2Calculate the y-coordinate of the center of


mass.

Three Particle 109:08, highSchool, numeric, > 1 min, normal.

Three particles are placed in the xy plane.A m1 = 40 g particle is located at (x1, y1),where x1 = 3 m and y1 = 4 m and a m2 =50 g particle is located at (x2, y2), wherex2 = −2 m and y2 = −6 m.

What must be the x coordinate of them3 =20 g particle so that the center of mass of thethree-particle system is at the origin?

Volleyball Hit09:08, highSchool, multiple choice, < 1 min,fixed.

Part 1 of 2Henry serves a volleyball, striking

the initially motionless ball a bitabove the centerline with the horizon-tal FORCE shown in the diagram.

y

xWhich of the following describes the motionof the center of the volleyball?

1.y

x

2.

y

x

3.y

x

4.y

x

5.y

x

6.y

x

7.


y

x

8.y

x

Part 2 of 2Henry had paint on his hand when he hit theball. Which of the following describes themotion of the paint mark Henry left on theball’s surface?

1.y

x

2.y

x

3.y

x

4.y

x

5.y

x

6.y

x

7.y

x

8.y

x

Chapter 9, section 10, Motion of a System of Particles (Explosions) 306


Part 1 of 2An unstable nucleus with a mass of 17.0 ×

10−27 kg initially at rest disintegrates intothree particles. One of the particles, of mass5.0 × 10−27 kg, moves along the positive y-axis with a speed of 6.0 × 106 m/s. Anotherparticle, of mass 8.4 × 10−27 kg, moves alongthe positive x-axis with a speed of 4.0 × 106

m/s.a) Find the speed of the third particle.

Part 2 of 2b) At what angle does the third particle move?

1. 41.7603◦ below the negative x-axis

2. 41.7603◦ above the negative x-axis

3. 41.7603◦ below the positive x-axis

4. 41.7603◦ above the positive x-axis

5. 20.8801◦ below the negative x-axis

6. 20.8801◦ above the negative x-axis

7. 20.8801◦ below the positive x-axis

8. 20.8801◦ above the positive x-axis

9. None of these

Projectile Explosion09:10, highSchool, multiple choice, > 1 min,fixed.

A projectile fired into the air suddenly ex-plodes into several fragments.

What can be said about the motion of thecenter of mass of the system made up of allthe fragments after the explosion?

1. Center of mass of the system follows thesame parabolic path the projectile would have

followed if there had been no explosion,

2. Center of mass of the system moves in thedirection of the biggest fragment,

3. Center of mass of the system moves inthe direction opposite to the direction of thebiggest fragment,

4. Center of mass of the system moves inthe direction of a fragment with the biggestmass,

5. Center of mass of the system moves inthe direction opposite to the direction of afragment with the biggest mass,

6. Center of mass of the system moves inthe direction opposite to the direction of aprojectile just before it exploded,

7. Center of mass does not move,

8.There is not enough information given.

Three Balls09:10, highSchool, multiple choice, < 1 min,fixed.

Three balls are thrown into the air simulta-neously.

What is the magnitude of the accelerationof their center of mass while they are in mo-tion?

1. g

2. 3g

3.g3

4. not enough information given

5. 0

Chapter 9, section 11, Energy of a System of Particles 307

Collision of Masses 0309:11, highSchool, numeric, > 1 min, normal.

Two masses undergo a front-to-back col-lision. The masses are m1 = m, with ini-tial velocity 2v0, and m2 = 3m, with ini-tial velocity v0. Due to the collision, theystick together, forming a compound system.

m 1

02v

m 2

0v

If m = 1.5 kg and v0 = 6 m/s, find the mag-nitude of the loss in kinetic energy after thecollision.

Conservation of What09:11, highSchool, multiple choice, > 1 min,fixed.

Part 1 of 3Given: Two masses (M1 and M2) are a

system. Let E = K +U be the total mechan-ical energy of the system and ~p be the totalmomentum of this system.

Amassm1 slides on a frictionless horizontalplane and collides and sticks to a massm2 thatis at the bottom of a frictionless ramp.

m1 m2v1

What is conserved in the collision?

1. E is conserved in the collision.

2. ~p is conserved in the collision.

3. Both E and ~p are conserved in the colli-sion.

4. Neither E nor ~p is conserved in the colli-sion.

Part 2 of 3After the collision, masses m1 and m2 slidetogether up the curved ramp and come to arest.

m12 v′

What is conserved during this motion?

1. E is conserved during this motion.

2. ~p is conserved during this motion.

3. Both E and ~p are conserved during thismotion.

4. Neither E nor ~p is conserved during thismotion.

Part 3 of 3Now suppose there is friction between themasses and the curved ramp. Again, themassesm1 andm2 slide together up the rampand come to a rest.

What is conserved during this motion?

1. E is conserved during this motion.

2. ~p is conserved during this motion.

3. Both E and ~p are conserved during thismotion.

4. Neither E nor ~p is conserved during thismotion.

Conservation on the Track SW 0109:11, highSchool, multiple choice, < 1 min,fixed.

Part 1 of 2The coefficient of friction is µ from A to

B, and B to E is frictionless. Block m1 ispushed down the ramp and released at A withvelocity v1 and is accelerating down. Let

E = K + U = mechanical energy

~P = momentum


�

�

� �

�

A

BC D

E

m1

m2

What is conserved asm1 goes from A to B?

1. E

2. ~P

3. Both E and ~P

4. Neither E nor ~P

Part 2 of 2What is conserved as the massesm1+m2 slidetogether from D to E?

1. E

2. ~P

3. Both E and ~P

4. Neither E nor ~P

Conservation on the Track SW09:11, highSchool, multiple choice, > 1 min,fixed.

Part 1 of 3The coefficient of friction is µ from A to

B, and B to E is frictionless. Block m1 ispushed down the ramp and released at A withvelocity v1 and is accelerating down. Let

E = K + U = mechanical energy

~P = momentum

�

�

� �

�

A

BC D

E

m1

m2

What is conserved asm1 goes from A to B?

1. E

2. ~P

3. Both E and ~P

4. Neither E nor ~P

Part 2 of 3What is conserved in a completely inelasticcollision of m1 with m2?

1. E

2. ~P

3. Both E and ~P

4. Neither E nor ~P

Part 3 of 3What is conserved as the massesm1+m2 slidetogether from D to E?

1. E

2. ~P

3. Both E and ~P

4. Neither E nor ~P

Football Hitting a Cart09:11, highSchool, multiple choice, < 1 min,fixed.

Part 1 of 2


A football is thrown hard horizontallyand it hits and sticks in a cart thatis on a track at position A in the di-agram. The cart with the football init then moves along the hilly frictionlesstrack to position B, where the cart stops.

B

A

football

What is conserved in the collision of the foot-ball with the cart at position A?

1. mechanical energy and momentum

2. mechanical energy only

3. momentum only

4. neither mechanical energy nor momen-tum

5. more information is needed to answer

Part 2 of 2What is conserved as the cart with the foot-ball in it moves from position A to positionB?

1. mechanical energy and momentum

2. mechanical energy only

3. momentum only

4. neither mechanical energy nor momen-tum

5. more information is needed to answer


Part 1 of 2A 0.25 kg arrow with a velocity of 12 m/s

to the west strikes and pierces the center of a6.8 kg target.

a)What is the final velocity of the combined

mass?



Part 1 of 2During practice, a student kicks a 0.40 kg

soccer ball with a velocity of 8.5 m/s to thesouth into a 0.15 kg bucket lying on its side.The bucket travels with the ball after thecollision.

a)What is the final velocity of the combinedmass?



Part 1 of 2A 56 kg ice skater traveling at 4.0 m/s to

the north suddenly grabs the hand of a 65 kgskater traveling at 12.0 m/s in the oppositedirection as they pass. Without rotating, thetwo skaters continue skating together withjoined hands.

a) What is the final velocity of the twoskaters?



Part 1 of 2A railroad car with a mass of 2.00 × 104

kg moving at 3.00 m/s collides and joins withtwo railroad cars already joined together, each


with the same mass as the single car andinitially moving in the same direction at 1.20m/s.

a)What is the final speed of the three joinedcars after the collision?



Part 1 of 2An 88 kg fullback moving east with a speed

of 5.0 m/s is tackled by a 97 kg opponentrunning west at 3.0 m/s, and the collision isperfectly inelastic.

a) What is the velocity of the players im-mediately after the tackle?



Part 1 of 2A 5.0 g coin sliding to the right at 25.0

cm/s makes an elastic head-on collision witha 15.0 g coin that is initially at rest. After thecollision, the 5.0 g coin moves to the left at12.5 cm/s.

a) Find the final velocity of the other coin.

Part 2 of 2b) How much kinetic energy is transferred tothe 15.0 g coin?


A 2250 kg car traveling at 10.0 m/s collideswith a 2750 kg car that is initially at restat a stoplight. The cars stick together and

move 2.50 m before friction causes them tostop. Assume that the negative accelerationis constant and that all wheels on both carslock at the time of impact.

The acceleration of gravity is 9.81 m/s2 .Determine the coefficient of kinetic friction

between the cars and the road.

Chapter 9, section 12, Energy and Momentum Conservation in Collisions 311

Ballistic Block09:12, highSchool, numeric, > 1 min, normal.

Part 1 of 3Assume: The bullet penetrates into the

block and stops due to its friction with theblock. The compound system of the blockplus the bullet rises to a height of 5 cm alonga circular arc with a 9 cm radius.

Assume: The entire track is frictionless.A bullet with a m1 = 30 g mass is fired

horizontally into a block of wood with m2 =5.4 kg mass.


9 cm

5.4 kg30 g

vbullet5 cm

Calculate the total energy of the compositesystem at any time after the collision.

Part 2 of 3Taking the same parameter values as those inPart 1, determine the initial velocity of thebullet.

Part 3 of 3Denote vbullet to be the initial velocity, findthe momentum of the compound system im-mediately after the collision.

1. pf = mbullet vbullet

2. pf = mblock vbullet

3. pf = (mbullet +mblock) vbullet

4. pf =1

2(mbullet +mblock) vbullet

5. pf =√mbullet +mblock vbullet

6. pf = mbullet

√

g h

7. pf = (mbullet +mblock)√

g h

8. pf = mblock

√

g h

9. pf =1

2(mbullet +mblock)

√

g h

10. pf =√mbullet +mblock g h

Conceptual momentum09:12, highSchool, multiple choice, > 1 min,fixed.

A flying bird is trapped in an airtight con-tainer sitting on the ground, as shown above.

The bird attempts to escape by flying intothe ceiling of the container, as shown.

Will the bird be able to make the containerleave the ground and sustain it in flight?

1. No; conservation of momentum

2. No; conservation of energy

3. No; conservation of angular momentum

4. Yes; the bird exerts a net force up on thecontainer.

5. Yes; the impulse provided by the birdshould lift the container.

6. Yes; the bird exerts a torque which willcause the container to rotate.

Conservation of Momentum09:12, highSchool, multiple choice, > 1 min,fixed.


Block m1 of mass 2m and velocity v0 istraveling to the right (+x) and makes an elas-tic head-on collision with block m2 of mass mand velocity −2 v0 (i.e., traveling to the left).

What is the velocity v1′ of block m1 after

the collision?

1. v1′ = −v0

2. v1′ = v0

3. v1′ = 2 v0

4. v1′ = −2 v0

5. v1′ = 3 v0

6. v1′ = −3 v0

7. v1′ =

3

2v0

8. v1′ = −3

2v0


Part 1 of 3A 0.015 kg marble sliding to the right at

22.5 cm/s on a frictionless surface makes anelastic head-on collision with a 0.015 kg mar-ble moving to the left at 18.0 cm/s. After thecollision, the first marble moves to the left at18.0 cm/s.

a) Find the velocity of the second marbleafter the collision.

Part 2 of 3b) What is the total kinetic energy before thecollision?

Part 3 of 3c) What is the total kinetic energy after thecollision?


Part 1 of 3A 16.0 kg canoe moving to the left at 12 m/s

makes an elastic head-on collision with a 4.0kg raft moving to the right at 6.0 m/s. Afterthe collision, the raft moves to the left at 22.7m/s. Disregard any effects of the water.

a) Find the velocity of the canoe after thecollision.




Part 1 of 3A 4.0 kg bowling ball sliding to the right at

8.00 m/s has an elastic head-on collision withanother 4.0 kg bowling ball initially at rest.The first ball stops after the collision.

a) Find the velocity of the second ball afterthe collision.




Part 1 of 3A 25.0 kg bumper car moving to the right

at 5.00 m/s overtakes and collides elasticallywith a 35.0 kg bumper car moving to theright. After the collision, the 25.0 kg bumpercar slows to 1.50 m/s to the right, and the35.0 kg car moves at 4.50 m/s to the right.


a) Find the velocity of the 35.0 kg bumpercar before the collision.




A(n) 8.0 g bullet is fired into a 2.5 kg pen-dulum bob initially at rest and becomes em-bedded in it. The pendulum rises a verticaldistance of 6.0 cm.

The acceleration of gravity is 9.81 m/s2 .What was the initial speed of the bullet?


A bird perched on a swing like the onebelow has a mass of 52.0 g, and the base ofthe swing has a mass of 153 g.


8 cm

The swing and bird are originally at rest,then the bird takes off horizontally at 2.00m/s.

How high will the base of the swing riseabove its original level? Disregard friction.


Part 1 of 2Two billiard balls with identical masses and

sliding in opposite directions have an elastichead-on collision. Before the collision, eachball had a speed of 22 cm/s.

a) Find the velocity of the billiard ball ini-tially moving to the right immediately afterthe collision.

Part 2 of 2b) Find the velocity of the billiard ball ini-tially moving to the left immediately after thecollision.

Inelastic Collision 1109:12, highSchool, numeric, > 1 min, normal.

Part 1 of 2Given two identical 3.1 kg masses. The first

mass is moving with a velocity v1 immediatelybefore colliding with the second mass, whichis suspended by a string of length 0.9 m .

The two masses are stuck together as a re-sult of the collision. The compound systemthen swings to the right and rises to the hori-zontal level.


O

0.9m

3.1 kg6.2kg

3.1 kg

v1

90◦

Find the kinetic energy of the compoundsystem immediately after the collision.

Part 2 of 2What is v1, the speed of m1 immediately be-fore the collision?

Linear Collision 0109:12, highSchool, multiple choice, > 1 min,fixed.


Part 1 of 6Two balls have masses m1 and m2. Ball

m1 has an initial velocity v1 > 0 (left-to-rightis the positive direction, along a line joiningthe two balls), as shown in the figure below.Ball m2 is at rest. Balls m1 and m2 make ahead-on elastic collision with each other.

m1

v1

m2

If m1 = m2, what is the final velocity v′1 ofthe ball m1?

1. v′1 = 0

2. v′1 = +v1

3. v′1 = −v1

4. v′1 = +2 v1

5. +2 v1 < v′1 ≤ +∞

6. −∞ ≤ v′1 < −v1

7. −v1 < v′1 < 0

8. 0 < v′1 < +v1

9. +v1 < v′1 < +2 v1

Part 2 of 6If m1 = m2, what is the final velocity v′2 ofthe ball m2?

1. v′2 = +v1

2. v′2 = 0

3. v′2 = +2 v1

4. v′2 = −v1

5. +2 v1 < v′1 ≤ +∞

6. −∞ ≤ v′1 < −v1

7. −v1 < v′1 < 0

8. 0 < v′1 < +v1

9. +v1 < v′1 < +2 v1

Part 3 of 6In the limit, when m1 ¿ m2, what is the finalvelocity v′1 of the ball m1?

1. v′1 = −v1

2. v′1 = 0

3. v′1 = +v1

4. v′1 = +2 v1

5. +2 v1 < v′1 ≤ +∞

6. −∞ ≤ v′1 < −v1

7. −v1 < v′1 < 0

8. 0 < v′1 < +v1

9. +v1 < v′1 < +2 v1


1. v′2 = 0

2. v′2 = +2 v1

3. v′2 = +v1

4. v′2 = −v1

5. +2 v1 < v′1 ≤ +∞

6. −∞ ≤ v′1 < −v1

7. −v1 < v′1 < 0

8. 0 < v′1 < +v1


9. +v1 < v′1 < +2 v1

Part 5 of 6In the limit, whenm1 À m2, what is the finalvelocity v′1 of the ball m1?

1. v′1 = +v1

2. v′1 = −v1

3. v′1 = +2 v1

4. −v1 < v′1 < +v1

5. +2 v1 < v′1 ≤ +∞

6. −∞ ≤ v′1 < −v1

7. −v1 < v′1 < 0

8. 0 < v′1 < +v1

9. +v1 < v′1 < +2 v1

Part 6 of 6In the limit, whenm1 À m2, what is the finalvelocity v′2 of the ball m2?

1. v′2 = +2 v1

2. −v1 < v′2 < +v1

3. v′2 = +v1

4. v′2 = −v1

5. +2 v1 < v′2 ≤ ∞

6. −∞ ≤ v′1 < −v1

7. −v1 < v′1 < 0

8. 0 < v′1 < +v1

9. +v1 < v′1 < +2 v1

Linear Collision 0209:12, highSchool, multiple choice, > 1 min,

fixed.



m1

v1

m2


1. v′1 = 0

2. v′1 = +v1

3. v′1 = −v1

4. v′1 = +2 v1

5. +2 v1 < v′1 ≤ +∞

6. −∞ ≤ v′1 < −v1

7. −v1 < v′1 < 0

8. 0 < v′1 < +v1

9. +v1 < v′1 < +2 v1


1. v′2 = +v1

2. v′2 = 0

3. v′2 = +2 v1

4. v′2 = −v1

5. +2 v1 < v′1 <≤ ∞


6. −∞ ≤ v′1 < −v1

7. −v1 < v′1 < 0

8. 0 < v′1 < +v1

9. +v1 < v′1 < +2 v1

Part 3 of 4In the limit, whenm1 ¿ m2, what is the finalvelocity v′1 of the ball m1?

1. v′1 = −v1

2. v′1 = 0

3. v′1 = +v1

4. v′1 = +2 v1

5. +2 v1 < v′1 <≤ ∞

6. −∞ ≤ v′1 < −v1

7. −v1 < v′1 < 0

8. 0 < v′1 < +v1

9. +v1 < v′1 < +2 v1

Part 4 of 4In the limit, whenm1 ¿ m2, what is the finalvelocity v′2 of the ball m2?

1. v′2 = 0

2. v′2 = +2 v1

3. v′2 = +v1

4. v′2 = −v1

5. +2 v1 < v′1 ≤ +∞

6. −∞ ≤ v′1 < −v1

7. −v1 < v′1 < 0

8. 0 < v′1 < +v1

9. +v1 < v′1 < +2 v1




m1

v1

m2


1. v′1 = 0

2. v′1 = +v1

3. v′1 = −v1

4. v′1 = +2 v1

5. +2 v1 < v′1 ≤ +∞

6. −∞ ≤ v′1 < −v1

7. −v1 < v′1 < 0

8. 0 < v′1 < +v1

9. +v1 < v′1 < +2 v1


1. v′2 = +v1

2. v′2 = 0


3. v′2 = +2 v1

4. v′2 = −v1

5. +2 v1 < v′1 ≤ +∞

6. −∞ ≤ v′1 < −v1

7. −v1 < v′1 < 0

8. 0 < v′1 < +v1

9. +v1 < v′1 < +2 v1




m1

v1

m2

In the limit, when m1 ¿ m2, what is thefinal velocity v′1 of the ball m1?

1. v′1 = −v1

2. v′1 = 0

3. v′1 = +v1

4. v′1 = +2 v1

5. +2 v1 < v′1 ≤ +∞

6. −∞ ≤ v′1 < −v1

7. −v1 < v′1 < 0

8. 0 < v′1 < +v1

9. +v1 < v′1 < +2 v1


1. v′2 = 0

2. v′2 = +2 v1

3. v′2 = +v1

4. v′2 = −v1

5. +2 v1 < v′1 ≤ +∞

6. −∞ ≤ v′1 < −v1

7. −v1 < v′1 < 0

8. 0 < v′1 < +v1

9. +v1 < v′1 < +2 v1

Part 3 of 4In the limit, when m1 À m2, what is the finalvelocity v′1 of the ball m1?

1. v′1 = +v1

2. v′1 = −v1

3. v′1 = +2 v1

4. −v1 < v′1 < +v1

5. +2 v1 < v′1 ≤ +∞

6. −∞ ≤ v′1 < −v1

7. −v1 < v′1 < 0

8. 0 < v′1 < +v1

9. +v1 < v′1 < +2 v1

Part 4 of 4


In the limit, whenm1 À m2, what is the finalvelocity v′2 of the ball m2?

1. v′2 = +2 v1

2. −v1 < v′2 < +v1

3. v′2 = +v1

4. v′2 = −v1

5. +2 v1 < v′2 ≤ ∞

6. −∞ ≤ v′1 < −v1

7. −v1 < v′1 < 0

8. 0 < v′1 < +v1

9. +v1 < v′1 < +2 v1

Linear Collision 0609:12, highSchool, numeric,> 1min, wording-variable.

Part 1 of 2Two balls have masses of 41 kg and 29 kg.

The 41 kg ball has an initial velocity 66 m/s >0 (left-to-right is the positive direction, alonga line joining the two balls), as shown in thefigure below. The 29 kg ball is at rest. Thetwo balls make a head-on elastic collision witheach other.

41 kg

66 m/s

29 kg

0 m/s

What is the final velocity of the 41 kg ball?

Part 2 of 2What is the final velocity of the 29 kg ball?

Chapter 9, section 13, Center of Mass Reference Frame 319

Air Cars With Springs 0109:13, highSchool, numeric, > 1 min, normal.

Two air blocks with masses 200 g and200 g are equipped with identical springs(k = 3000 N/m) . The blocks move towardeach other with identical speeds of 3 m/s on ahorizontal air track and collide, compressingthe springs.

200 g

3 m/s3000 N/m

200 g

3 m/s3000 N/m

Find the maximum compression of thespring attached to the 200 g mass.

Air Cars With Springs 0209:13, highSchool, numeric, > 1 min, normal.

Two air blocks with masses 300 g and200 g are equipped with identical springs(k = 3000 N/m) . The blocks move towardeach other with identical speeds of 3 m/s on ahorizontal air track and collide, compressingthe springs.

300 g

3 m/s3000 N/m

200 g

3 m/s3000 N/m

Find the maximum compression of thespring attached to the 300 g mass.

Center of Mass SW09:13, highSchool, multiple choice, < 1 min,fixed.

Two balls of masses m1 and m2 are movingalong a line on frictionless surface with veloc-ities v1 and v2. Mass m1 collides elasticallywith m2.

What is the center of mass velocity V cm ofthis system of two balls after collision?

1. V cm ≡ m2 v2 −m1 v1

m2 −m1

2. V cm ≡ m1 v1 −m2 v2

m1 +m2

3. V cm ≡ m2 v2 −m1 v1

m1 +m2

4. V cm ≡ m1 v1 +m2 v2

m1 −m2

5. V cm ≡ m1 v1 −m2 v2

m1 −m2

6. V cm ≡ m2 v2 −m1 v1

m1 −m2

7. V cm ≡ m1 v1 +m2 v2

m2 −m1

8. V cm ≡ m1 v1 −m2 v2

m2 −m1

9. V cm ≡ m1 v1 +m2 v2

m1 +m2

10. V cm ≡ m2 v1 +m1 v2

m1 +m2

Man in a Boat 0209:13, highSchool, numeric, < 1 min, normal.

A 80 kg man sits on the stern of a 5 m longboat. The prow of the boat touches the pier,but the boat isn’t tied. The man notices hismistake, stands up and walks to the boat’sprow, but by the time he reaches the prow,it’s moved 2.5 m away from the pier.

Assuming no water resistance to the boat’smotion, calculate the boat’s mass (not count-ing the man).

Chapter 10, section 1, Angular Position, Velocity and Acceleration 320


The value of g at the Earth’s surface isabout 10 m/s2.

How would this value change if the Earthrotated faster about its axis?

1. increase

2. decrease

3. no change

4. It depends on the latitude.


A car tire rotates with an average angularspeed of 29 rad/s.

In what time interval will the tire rotate 3.5times?


A girl ties a toy airplane to the end of astring and swings it around her head. Theplane’s average angular speed is 2.2 rad/s.

In what time interval will the plane movethrough an angular displacement of 3.3 rad?


The average angular speed of a fly movingin a circle is 7.0 rad/s.

How long does the fly take to move through2.3 rad?


Part 1 of 4Consider the following values

ωavg ∆θ ∆ta +2.3 rad 10.0 s

+0.75 rev/s b 0.050 sc −1.2 turns 1.2 s

+2.0π rad/s +1.5π rad d

What is the value of a?

Part 2 of 4What is the value of b?

Part 3 of 4What is the value of c?

Part 4 of 4What is the value of d?


A figure skater begins spinning counter-clockwise at an angular speed of 4.0π rad/s.During a 3.0 s interval, she slowly pulls herarms inward and finally spins at 8.0π rad/s.

What is her average angular accelerationduring this time interval?


What angular acceleration is necessary toincrease the angular speed of a fan blade from8.5 rad/s to 15.4 rad/s in 5.2 s?


Part 1 of 3Consider the following values

Chapter 10, section 1, Angular Position, Velocity and Acceleration 321

αavg ∆ω ∆ta +121.5 rad/s 7.0 s

+0.75 rad/s2 b 0.050 sc −1.2 turns/s 1.2 s

What is the value of a?

Part 2 of 3What is the value of b?

Part 3 of 3What is the value of c?


How long does it take the second hand of aclock to move through 4.00 rad?


A phonograph record has an initial angularspeed of 33 rev/min. The record slows to 11rev/min in 2.0 s.

What is the record’s average angular accel-eration during this time interval?


If a flywheel increases its average angularspeed by 2.7 rad/s in 1.9 s, what is its averageangular acceleration?

Holt SF 07Rev 4110:01, highSchool, numeric, < 1 min, fixed.

Earth orbits the sun once every 365.25 days.Find the average angular speed of Earth

about the sun.

Merry Go Round 0210:01, highSchool, multiple choice, < 1 min,fixed.

Feng and Isaac are riding on a merry-go-round. Feng rides on a horse at the outer rimof the circular platform, twice as far from thecenter of the circular platform as Isaac, whorides on an inner horse.

When the merry-go-round is rotating at aconstant angular speed, what is Feng’s angu-lar speed?

1. twice Isaac’s

2. the same as Isaac’s

3. half of Isaac’s


Chapter 10, section 2, Kinematic Equations for Uniformly Accelerated Rotational 322


When a rolling yo-yo falls to the bottom ofits cord, what is its rotation as it climbs backup the cord?

1. reversed rotation due to inertia

2. same rotation due to inertia

3. reversed rotation due to the rebound

4. same rotation due to the rebound


The wheel on an upside-down bicycle movesthrough 18.0 rad in 5.00 s.

What is the wheel’s angular acceleration ifits initial angular speed is 2.0 rad/s?

Holt SF 07D 0210:02, highSchool, numeric,< 1min, wording-variable.

A diver performing a double somersaultspins at an angular speed of 4.0π rad/s pre-cisely 0.50 s after leaving the platform.

Assuming the diver begins with zero initialangular speed and accelerates at a constantrate, what is the diver’s angular accelerationduring the double somersault?

Holt SF 07D 0310:02, highSchool, numeric,< 1min, wording-variable.

A fish swimming behind an oil tanker getscaught in a whirlpool created by the ship’spropellers. The fish has an initial angularspeed of 1.0 rad/s. After 4.5 s, the fish’sangular speed is 14.5 rad/s.

If the water in the whirlpool accelerates ata constant rate, what is the angular accelera-

tion?

Holt SF 07D 04 0510:02, highSchool, numeric,> 1min, wording-variable.

Part 1 of 2A remote-controlled car’s wheel accelerates

at 22.4 rad/s2.If the wheel begins with an angular speed of

10.8 rad/s, what is the wheel’s angular speedafter exactly four full turns?

Part 2 of 2How long does the wheel take to make thefour turns?


A potter’s wheel moves from rest to anangular speed of 0.20 rev/s in 30.0 s.

Assuming constant angular acceleration,what is its angular acceleration in rad/s2?


Part 1 of 2A drill starts from rest. After 3.20 s of

constant angular acceleration, the drill turnsat a rate of 2628 rad/s.

Find the drill’s angular acceleration.

Part 2 of 2Find the angle through which the drill rotatesduring this period.


A tire placed on a balancing machine ina service station starts from rest and turnsthrough 4.7 rev in 1.2 s before reaching itsfinal angular speed.

Assuming that the angular acceleration of

Chapter 10, section 2, Kinematic Equations for Uniformly Accelerated Rotational 323

the wheel is constant, calculate the wheel’sangular acceleration.


The tub within a washer goes into its spincycle, starting from rest and reaching an an-gular speed of 11 π rad/s in 8.0 s. At thispoint, the lid is opened, and a safety switchturns off the washer. The tub slows to rest in12.0 s.

Through how many revolutions does thetub turn? Assume constant angular acceler-ation while the machine is starting and stop-ping.


A car traveling at 30.0 m/s undergoes aconstant deceleration of 2.00 m/s2 when thebrakes are applied.

How many revolutions does each tire makebefore the car comes to a stop? Assume thatthe car does not skid and that each tire has aradius of 0.300 m.


A coin with a diameter of 2.40 cm isdropped onto a horizontal surface. The coinstarts out with an initial angular speed of18.0 rad/s and rolls in a straight line withoutslipping.

If the rotation slows with an angular decel-eration of 1.90 rad/s2, how far does the coinroll before coming to rest?


A mass attached to a 50.0 cm string startsfrom rest and is rotated in a circular path

exactly 40 times in 1.00 min before reaching afinal angular speed.

What is the angular speed of the mass after1.00 min?


A copper block rests 30.0 cm from the cen-ter of a steel turntable. The coefficient ofstatic friction between the block and the sur-face is 0.53. The turntable starts from restand rotates with a constant angular accelera-tion of 0.50 rad/s2.

After what time interval will the block startto slip on the turntable? The acceleration ofgravity is 9.81 m/s2 .

Chapter 10, section 4, Relationships Between Angular and Linear Quantities 324


A ladybug traveling with tangential veloc-ity v sits halfway between the axis and theedge of a phonograph record.

What will happen to its tangential speed ifthe RPM rate is doubled? At this doubledrate, what will happen to its tangential speedif it crawls out to the edge?

1.v

2,v

2

2. v , 2v

3. 2v , 2v

4. 2v , 4v


A large wheel is coupled to a wheel withhalf the diameter as shown.

r 2r

How does the rotational speed of thesmaller wheel compare with that of the largerwheel? How do the tangential speeds atthe rims compare (assuming the belt doesn’tslip)?

1.The smaller wheel has twice the rotationalspeed and the same tangential speed as thelarger wheel.

2. The smaller wheel has half the rotationalspeed and half the tangential speed as thelarger wheel.

3. The smaller wheel has four times the ro-

tational speed and the same tangential speedas the larger wheel.

4.The smaller wheel has twice the rotationalspeed and twice the tangential speed as thelarger wheel.


An automobile speedometer is configuredto read speed proportional to the rotationalspeed of its wheels.

If larger wheels, such as those of snowtires, are used, what will be the effect onthe speedometer reading?

1. Lower

2. Higher

3. No different

4. It depends on the speed.


Harry and Sue cycle at the same speed. Thetires on Harry’s bike have a larger diameterthan those on Sue’s bike.

Which tires have the greater rotationalspeed?

1. Harry’s tires

2. Sue’s tires

3. The rotational speeds are the same.

4. It depends on the speed.


Unlike a phonograph record that has a con-


stant angular speed, a CD scans informationat a constant linear speed (130 cm/s).

Does the CD rotate at a constant or varyingangular speed?

1. constant angular speed

2. varying angular speed


A woman passes through a revolving doorwith a tangential speed of 1.8 m/s.

If she is 0.80 m from the center of the door,what is the door’s angular speed?


A softball pitcher throws a ball with a tan-gential speed of 6.93 m/s.

If the pitcher’s arm is 0.660 m long, whatis the angular speed of the ball before thepitcher releases it?


An athlete spins in a circle before releasinga discus with a tangential speed of 9.0 m/s.

What is the angular speed of the spinningathlete? Assume the discus is 0.75 m from theathlete’s axis of rotation.


Part 1 of 4Consider the following table:

vt ω ra 121.5 rad/s 0.0300 m

0.75 m/s b 0.050 mc 1.2 turns/s 3.8 m

2.0π m/s 1.5π rad/s d

a) What is the value of a?

Part 2 of 4b) What is the value of b?

Part 3 of 4c) What is the value of c?

Part 4 of 4d) What is the value of d?

Holt SF 07F 0110:04, highSchool, numeric,< 1min, wording-variable.

A dog on a merry-go-round undergoes a 1.5m/s2 linear acceleration.

If the merry-go-round’s angular accelera-tion is 1.0 rad/s2, how far is the dog from theaxis of rotation?


A young boy swings a yo-yo horizontallyabove his head at an angular acceleration of0.35 rad/s2.

If the tangential acceleration of the yo-yoat the end of the string is 0.18 m/s2, how longis the string?


What is a tire’s angular acceleration if thetangential acceleration at a radius of 0.15 mis 9.4× 10−2 m/s2?



A small pebble breaks loose from the treadsof a tire with a radius of 32 cm.

If the pebble’s tangential speed is 49 m/s,what is the tire’s angular speed?


The Emerald Suite is a revolving restaurantat the top of the Space Needle in Seattle,Washington.

If a customer sitting 12 m from therestaurant’s center has a tangential speed of2.18× 10−2 m/s, what is the angular speed ofthe restaurant?


A bicycle wheel has an angular accelerationof 1.5 rad/s2.

If a point on its rim has a tangential accel-eration of 48 cm/s2, what is the radius of thewheel?


When a string is pulled in the correct di-rection on a window shade, a lever is releasedand the shaft that the shade is wound aroundspins.

If the shaft’s angular acceleration is 3.8rad/s2 and the shade accelerates upward at0.086 m/s2, what is the radius of the shaft?

Chapter 10, section 5, Rotational Kinetic Energy 327

Figuring Physics 3410:05, highSchool, multiple choice, > 1 min,fixed.

Two balls of equal mass at the bottom ofan incline are rolled upward without slippingat the same initial velocity.

One ball is solid and the other is a thin-walled hollow ball.

Which rolls higher up the incline beforecoming to a stop?

1. The hollow ball.

2. The solid ball.

3. Both will roll to the same height.

4. Depends on the relative diameters of theballs.


A solid cylinder with a mass of 4.10 kgand a radius of 0.050 m starts from rest at aheight of 2.00 m and rolls down a 30.0◦ slope,as shown.

The acceleration of gravity is 9.81 m/s2 .What is the translational speed of the cylin-

der when it leaves the incline?

Holt SF 08E 01ball10:05, highSchool, numeric,> 1min, wording-variable.

A solid ball with a mass of 4.10 kg and aradius of 0.050 m starts from rest at a heightof 2.00 m and rolls down a 30.0◦ slope, asshown.

The acceleration of gravity is 9.81 m/s2 .What is the translational speed of the ball

when it leaves the incline?


A 1.5 kg bicycle tire of radius 0.33 m startsfrom rest and rolls down from the top of a hillthat is 14.8 m high.

The acceleration of gravity is 9.81 m/s2 .What is the translational speed of the tire

when it reaches the bottom of the hill? (As-sume that the tire is a hoop with I = mr2.)


A regulation basketball has a 25 cm di-ameter and may be approximated as a thinspherical shell.

The acceleration of gravity is 9.81 m/s2 .How long will it take a basketball starting

from rest to roll without slipping 4.0 m downan incline that makes an angle of 30.0◦ withthe horizontal?


The net work done in accelerating a pro-peller from rest to an angular speed of 220rad/s is 3000.0 J.

What is the moment of inertia of the pro-peller?


A 0.0200 m diameter coin rolls up a 15.0◦

inclined plane. The coin starts with an initialangular speed of 45.0 rad/s and rolls in astraight line without slipping.

The acceleration of gravity is 9.81 m/s2 .How much vertical distance does it gain

before it stops rolling?


In a circus performance, a large 4.0 kg hoop

Chapter 10, section 5, Rotational Kinetic Energy 328

with a radius of 2.0 m rolls without slipping.The acceleration of gravity is 9.81 m/s2 .If the hoop is given an angular speed of

6.0 rad/s while rolling on the horizontal andis allowed to roll up a ramp inclined at 15◦

with the horizontal, how far (measured alongthe incline) does the hoop roll?


As part of a kinetic sculpture, a 5.0 kg hoopwith a radius of 3.0 m rolls without slipping.

The acceleration of gravity is 9.81 m/s2 .If the hoop is given an angular speed of

3.0 rad/s while rolling on the horizontal andthen rolls up a ramp inclined at 20.0◦ with thehorizontal, how far does the hoop roll alongthe incline?


A coin with a diameter of 4.37 cm rolls up a30.0◦ inclined plane. The coin starts with aninitial angular speed of 60.0 rad/s and rolls ina straight line without slipping.

The acceleration of gravity is 9.81 m/s2 .How far does it roll up the inclined plane?


A solid sphere rolls along a horizontal,smooth surface at a constant linear speedwithout slipping.

What is the ratio between the rotationalkinetic energy about the center of the sphereand the sphere’s total kinetic energy?

1.2

5

2.3

5

3.2

7

4.3

7

5.5

3

6.7

2

7. None of these

SWCT Rotational KE10:05, highSchool, multiple choice, < 1 min,fixed.

A flywheel with inertia I1, rotating at800 rpm, is brought into contact coaxiallywith a flywheel with inertia I2 = 2 I1. Whatis the ratio of final to initial kinetic energy?

1.1

4

2.1

3

3.1

2

4.2

3

5. 1

6. 3

Chapter 10, section 6, Calculation of Moments of Inertia 329


Moving the front wheels far out in front ofa racing vehicle helps to keep the vehicle fromnosing upward when it accelerates.

What physics concept plays a role here?

1. linear momentum

2. rotational inertia

3. kinetic energy

4. conservation of energy


Why is a long pole more beneficial to atightrope walker if the pole droops?

1. The pole contributes more momemtum.

2. The pole makes the walker heavier.

3. The pole lowers the center of gravity.

4. The pole allows the walker not to rotate.


A girl sitting on a merry-go-round movescounterclockwise through an arc length of2.50 m.

If the girl’s angular displacement is 1.67rad, how far is she from the center of themerry-go-round?


A beetle sits at the top of a bicycle

wheel and flies away just before it would besquashed. Assuming that the wheel turnsclockwise, the beetle’s angular displacementis π rad, which corresponds to an arc lengthof 1.2 m.

What is the wheel’s radius?


A car on a Ferris wheel has an angulardisplacement of π4 rad, which corresponds toan arc length of 29.8 m.

What is the Ferris wheel’s radius?


Part 1 of 4Consider the following table:

∆θ ∆s ra +0.25 m 0.10 m

+0.75 rad b 8.5 mc −4.2 m 0.75 m

+135◦ +2.6 m d

a) What is the value of a?

Part 2 of 4b) What is the value of b?

Part 3 of 4c) What is the value of c?

Part 4 of 4d) What is the value of d?


A car on a Ferris wheel has an angulardisplacement of 0.34 rad.

If the car moves through an arc length of 12m, what is the radius of the Ferris wheel?

Chapter 10, section 6, Calculation of Moments of Inertia 330


When a wheel is rotated through an angleof 35◦, a point on the circumference travelsthrough an arc length of 2.5 m. When thewheel is rotated through angles of 35 rad and35 rev, the same point travels through arclengths of 143 m and 9.0×102 m, respectively.

What is the radius of the wheel?

Rigid System Rotating 0510:06, highSchool, numeric, > 1 min, normal.

The figure below shows a rigid systemwhich can rotate. M = 2 kg, L =1.2 m, and the connecting rod as negligiblemass. Treat the masses as point particles.

M

x

L

3M

0What is the moment of inertia about an axisperpendicular to the paper and through thecenter of mass?

SWCT Inertia10:06, highSchool, multiple choice, < 1 min,fixed.

A particular flywheel that rotates aboutits center of mass has a moment of inertia

I =3

4MR2, where R = the radius. What is

the moment of inertia if the flywheel is rotatedabout a point on its rim?

1.5

4MR2

2.3

4MR2

3.7

4MR2

4.3

2MR2

5. 3MR2

Three Masses 0310:06, highSchool, numeric,> 1min, wording-variable.

Assume: The masses are point particles;e.g., neglect the contribution due to momentsof inertia about their center of mass.

Three spherical masses are located in aplane at the positions shown in the figure be-low. A has mass 9.26 kg, B has mass 59.3 kg,and C has mass 27 kg.

-7 -6 -5 -4 -3 -2 -1 0 1 2 3-7

-6

-5

-4

-3

-2

-1

0

1

2

3

A

B

C

yDistance

(m)

x Distance (m)

Three Masses in a Plane

Figure: Drawn to scale.Calculate the moment of inertia (of the

three masses) with respect to the z-axisperpendicular to the xy plane and passingthrough the origin.

Chapter 10, section 7, Torque 331

Box on an Incline10:07, highSchool, multiple choice, < 1 min,fixed.

A box, with its center-of-mass off-center asindicated by the dot, is placed on an inclinedplane.

In which of the four orientations shown, ifany, does the box tip over?

1.

�

2.

�

3.

�

4.

�

5. None of the orientations will cause thebox to top over.


A friend incorrectly says that a body cannotrotate when the net torque acting on it is zero.

What is the correct statement?

1.Once a body starts rotating the net torqueis zero.

2. The original statement is actually cor-rect.

3. A body can rotate only when a non-zeronet torque acts on it.

4. A body’s rotation cannot change if thenet torque acting on it is zero.


How does the net torque change when apartner on a seesaw stands or hangs from herend instead of sitting?

1. The net torque decreases.

2. The net torque remains the same.

3. The net toque increases.

4. It depends on the mass.


When you pedal a bicycle with a constantdownward force, is maximum torque pro-duced when the pedal sprocket arms are inthe horizontal position, in the vertical posi-tion, or in the diagonal position?

1. horizontal position

2. vertical position

3. diagonal position

4. All torques are the same.


A spool (similar to a yo-yo) is pulled inthree ways, as shown below. There is suffi-


cient friction for rotation.

a b c

In what direction will each spool move (inthe order spool a, spool b, spool c)?

1. right; right; right

2. right; left; left

3. right; left; right

4. right; right; left

5. left; right; right

6. None of these is correct.


Which of the following is true about themost comfortable ride in a bus traveling on abumpy road, in a ship in a choppy sea, or inan airplane in turbulent air?

1. Objects closer to the center of mass expe-rience smaller movement.

2. Objects farther from the center of massexperience smaller movement.

3. The rough nature of the ride has nothingto do with position relative to the center ofmass.


Consider the three objects shown in the figure.

List the stabilities in order from least stableto most stable.

1. leftmost, middle, rightmost

2. leftmost, rightmost, middle

3. middle, rightmost, leftmost

4. middle, leftmost, rightmost

5. rightmost, middle, leftmost

6. rightmost, leftmost, middle

7. They are equally stable.


The centers of gravity of the three trucksparked on a hill are shown by the mark .

Which truck(s) will tip over?

1. Truck 1

2. Truck 2

3. Truck 3

4. Trucks 1 and 2

5. Trucks 1 and 3


6. Trucks 2 and 3

7. All three trucks

8. None of the trucks


When you push on an object such as awrench, a steel pry bar, or even the outeredge of a door, you produce a torque equal tothe force applied times the lever arm.

At what angle to the lever arm should aforce be applied to produce maximum torqueand why?

1. At any angle; the torque equals the forcetimes the lever arm, and both of these remainthe same.

2. 90◦; the force would be parallel to thelever arm, so the torque is constant.

3. 0◦; this maximizes the effective length ofthe lever arm.

4. 90◦; this maximizes the effective length ofthe lever arm.

5. 180◦; this maximizes the effective lengthof the lever arm.

6. At any angle; the torque is zero under allsituations.

7. 0◦; this maximizes the effective force.

8. 180◦; this maximizes the effectiveforce.

Dropping a Spool10:07, highSchool, multiple choice, > 1 min,fixed.

A student holds a piece of thread partiallyunwound from a spool. Holding the end of the

thread fixed, the students drops the spool, asshown

Choose the best statement.

1. The thread exerts a force in the verticaldirection on the spool, and creates a torqueabout the center of the spool.

2. The thread exerts a force slanted to theleft on the spool, and creates a torque aboutthe center of the spool.

3. The thread exerts a force slanted to theright on the spool, and creates a torque aboutthe center of the spool.

4. The thread exerts no force on the spool,but creates a clockwise torque about the cen-ter of the spool.

5. The thread exerts no force on the spool,but creates a counter-clockwise torque aboutthe center of the spool.

6. The thread exerts a force in the verticaldirection on the spool, but creates no torqueabout the center of the spool.

7. The thread exerts a force slanted to theright on the spool, but creates no torque aboutthe center of the spool.

8. The thread exerts neither force nor torqueabout the center of the spool since the spoolis falling.


Find the magnitude of the torque produced


by a 3.0 N force applied to a door at a perpen-dicular distance of 0.25 m from the hinge.


Part 1 of 2A simple pendulum consists of a 3.0 kg

point mass hanging at the end of a 2.0 m longlight string that is connected to a pivot point.

The acceleration of gravity is 9.81 m/s2 .a) Calculate the magnitude of the torque

(due to the force of gravity) around this pivotpoint when the string makes a 5.0◦ angle withthe vertical.

Part 2 of 2b) Repeat this calculation for an angle of15.0◦.


If the torque required to loosen a nut on thewheel of a car has a magnitude of 40.0N ·m,what minimum force must be exerted by amechanic at the end of a 30.0 cm wrench toloosen the nut?


A bucket filled with water has a mass of 54kg and is hanging from a rope that is woundaround a 0.050 m radius stationary cylinder.

The acceleration of gravity is 9.81 m/s2 .If the cylinder does not rotate and the

bucket hangs straight down, what is the mag-nitude of the torque the bucket producesaround the center of the cylinder?


A mechanic jacks up a car to an angle of

8.0◦ with the horizontal in order to change thefront tires. The car is 3.05 m long and has amass of 1130 kg. Its center of mass is located1.12 m from the front end. The rear wheelsare 0.400 m from the back end.

The acceleration of gravity is 9.81 m/s2 .Calculate the torque exerted by the car

around the back wheels.


Part 1 of 2The arm of a crane at a construction site is

15.0 m long, and it makes an angle of 20.0◦

with the horizontal. Assume that the max-imum load the crane can handle is limitedby the amount of torque the load producesaround the base of the arm.

a) What is the magnitude of the maximumtorque the crane can withstand if the maxi-mum load the crane can handle is 450 N?

Part 2 of 2b) What is the maximum load for this craneat an angle of 40.0◦ with the horizontal?


A wooden bucket filled with water has amass of 75 kg and is attached to a rope thatis wound around a cylinder with a radius of0.075 m. A crank with a turning radius of0.25 m is attached to the end of the cylinder.

The acceleration of gravity is 9.81 m/s2 .What minimum force directed perpendicu-

larly to the crank handle is required to raisethe bucket?


If the torque required to loosen a nut thatholds a wheel on a car has a magnitude of58 N ·m, what force must be exerted at the


end of a 0.35 m lug wrench to loosen the nutwhen the angle is 56◦?


In a canyon between two mountains, aspherical boulder with a radius of 1.4 m isjust set in motion by a force of 1600 N. Theforce is applied at an angle of 53.5◦ measuredwith respect to the radius of the boulder.

What is the magnitude of the torque on theboulder?


Part 1 of 2Hint: At 3:00 o’clock, the hour hand is

precisely 90◦ from vertical.Assume: The clock hands can be modeled

as uniform thin rods.The hour and minute hands of the clock in

the famous Parliament Clock Tower in Lon-don are 1.5 m and 3 m long and have massesof 85 kg and 60 kg , respectively.


3

2

112

11

10

9

8

76

5

4

Calculate the magnitude of the torquearound the center of the clock due to theweight of these hands indicating 3 hr and41 min; i.e., 3 :41 o’clock.

Part 2 of 2The torque is

1. counter-clockwise.

2. clockwise.

3. Cannot be determined from given infor-mation.


Part 1 of 2To tighten a bolt, you push with a force of

80 N at the end of a wrench handle that is0.25 m from the axis of the bolt.

What torque are you exerting?

Part 2 of 2If you move your hand inward to be only 0.1 mfrom the bolt, what force do you have to exertto achieve the same torque?

Second Time10:07, highSchool, numeric, > 1 min, normal.

A mechanic jacks up a car to an angle of8◦ with the horizontal in order to change thefront tires. The car is 3.05 m long and has amass of 1130 kg. Its center of mass is located1.12 m from the front end. The rear wheelsare 0.4 m from the back end.

The acceleration of gravity is 9.81 m/s2 .Calculate the torque exerted by the car

around the back wheels.

Chapter 10, section 8, Relationship Between Torque and Angular Acceleration 336


Part 1 of 2A potter’s wheel of radius 0.50 m and mass

100.0 kg is freely rotating at 50.0 rev/min.The potter can stop the wheel in 6.0 s bypressing a wet rag against the rim.

a) What is the angular acceleration of thewheel?

Part 2 of 2b) How much torque does the potter apply tothe wheel?


A bicycle tire of radius 0.33 m and mass 1.5kg is rotating at 98.7 rad/s.

What torque is necessary to stop the tire in2.0 s?


Part 1 of 2A light string 4.00 m long is wrapped

around a solid cylindrical spool with a ra-dius of 0.0750 m and a mass of 0.500 kg. A5.00 kg mass is then attached to the free endof the string, causing the string to unwindfrom the spool.

The acceleration of gravity is 9.81 m/s2 .a) What is the angular acceleration of the

spool?

Part 2 of 2b) How fast will the spool be rotating after allof the string has unwound?


A 30.0 kg uniform solid cylinder has a ra-dius of 0.180 m.

If the cylinder accelerates at 2.30 ×10−2 rad/s2 as it rotates about an axisthrough its center, how large is the torqueacting on the cylinder?


A 350 kg merry-go-round in the shape of ahorizontal disk with a radius of 1.5 m is set inmotion by wrapping a rope about the rim ofthe disk and pulling on the rope.

How large a torque would have to be ex-erted to bring the merry-go-round from restto an angular speed of 3.14 rad/s in 2.00 s?


Part 1 of 3A 12 kg mass is attached to a cord that is

wrapped around a wheel with a radius of 10.0cm, as shown. The acceleration of the massdown the frictionless incline is measured to be2.0 m/s2. Assume the axle of the wheel to befrictionless.

The acceleration of gravity is 9.81 m/s2 .10 cm

12kg

2 m/s

2

37◦

Note: Figure is not drawn to scalea) Find the force in the rope.

Part 2 of 3b) Find the moment of inertia of the wheel.

Part 3 of 3c) Find the angular speed of the wheel 2.0 safter it begins rotating, starting from rest.

Holt SF 08Rev 56



Part 1 of 2A cylindrical fishing reel has a mass of 0.85

kg and a radius of 4.0 cm. A friction clutch inthe reel exerts a restraining torque of 1.3 N ·mif a fish pulls on the line. The fisherman getsa bite, and the reel begins to spin with anangular acceleration of 66 rad/s2.

a) Find the force of the fish on the line.

Part 2 of 2b) Find the amount of line that unwinds fromthe reel in 0.50 s.


Part 1 of 3The combination of an applied force and a

frictional force produces a constant torque of36 N ·m on a wheel rotating about a fixedaxis. The applied force acts for 6.0 s, duringwhich time the angular speed of the wheelincreases from 0 to 12 rad/s.

a) What is the moment of inertia of thewheel?

Part 2 of 3The applied force is then removed, and thewheel comes to rest in 65 s.

b) What is the frictional torque?

Part 3 of 3c) How many revolutions does the wheel makeduring the entire 71 s interval?


A cable passes over a pulley. Because of thefriction, the force in the cable is not the sameon opposite sides of the pulley. The force onone side is 120.0 N, and the force on the otherside is 100.0 N.

Assuming that the pulley is a uniform disk

with a mass of 2.1 kg and a radius of 0.81m, determine the magnitude of the angularacceleration of the pulley.


Part 1 of 3A cylindrical 5.00 kg pulley with a radius of

0.600 m is used to lower a 3.00 kg bucket intoa well. The bucket starts from rest and fallsfor 4.00 s.

The acceleration of gravity is 9.81 m/s2 .a) What is the linear acceleration of the

falling bucket?

Part 2 of 3b) How far does it drop?

Part 3 of 3c) What is the angular acceleration of thecylindrical pulley?


Part 1 of 3A pulley has a moment of inertia of 5 kgm2

and a radius of 0.5 m . A cord is wrapped overthe pulley and attached to a hanging objecton either end. Assume the cord does not slip,the axle is frictionless, and the two hangingobjects have masses of 2 kg and 5 kg .

The acceleration of gravity is 9.81 m/s2 .a) Find the acceleration of each mass.

Part 2 of 3b) Find the force in the cord supporting thesmaller mass.

Part 3 of 3c) Find the force in the cord supporting thelarger mass.



Part 1 of 3A 4.0 kg mass is connected by a light cord to

a 3.0 kg mass on a smooth surface as shown.The pulley rotates about a frictionless axleand has a moment of inertia of 0.50 kg ·m2

and a radius of 0.30 m.The acceleration of gravity is 9.81m/s2 .

�

4kg

3kg

F1

F2

R

Note: Figure is not drawn to scale

Assume that the cord does not slip on thepulley.

a) What is the acceleration of the twomasses?

Part 2 of 3b) What is the magnitude of the force F1?

Part 3 of 3c) What is the magnitude of the force F2?

Torque on Pulley10:08, highSchool, multiple choice, < 1 min,fixed.

A pulley that has a moment of inertia3

4M R2 and radius R rotates about an axis

through its center. A string is wrappedaround the disk and exerts a constant force1

2M g tangential to the disk. Find the tan-

gential acceleration of a point on the rim ofthe disk.

1. g

2.g

2

3.4 g

3

4.3 g

4

5.3 g

2

6.2 g

5

7. 2 g

8.g

3

9.g

4

10.2 g

3

Torque vs Time10:08, highSchool, numeric,> 1min, wording-variable.

A cylindrical flywheel is initially at restand is free to pivot with negligible frictionabout the z-axis of the cylinder. Its momentof inertia with respect to the z-axis is I =1

2mr2, where its mass is 0.6 kg and its radius

is 0.05 m. The figure below shows the valueof an applied torque as a function of time.

−10

1

2

3

4

0 1 2 3 4 5 6 7 8 9 10

�

� �

� �

� �

� �

� �

� �

� �

� �

� �

� �

�

time ( s )∆t

Torque(Nm

)

Calculate the kinetic energyK of the cylin-der when it reaches 10 s.

Wheel and Axle 0110:08, highSchool, numeric, > 1 min, normal.

Two pulley wheels, or respective radii R1 =0.25 m and R2 = 1 m are mounted rigidly ona common axle and clamped together. Thecombined moment of inertia of the two wheelsis I + 3 kgm2.

Mass m1 = 36 kg is attached to a cordwrapped around the first wheel, and anothermass m2 = 15 kg is attached to another cord


wrapped around the second wheel:

1

2

m

R

1

m

R2

The acceleration of gravity is 9.8 m/s2 .Find the angular acceleration of the system.

Take clockwise direction as positive.

Chapter 10, section 9, Work, Power, and Energy in Rotational Motion 340

Atwood Machine 0110:09, highSchool, multiple choice, > 1 min,normal.

Part 1 of 2An Atwood machine is constructed using a

disk of moment if inertia of I. The masses arem1 and m2 with m1 being heavier than m2.


`

R

I

ω

m1

m2

T1

T2

Consider the free body diagrams

m1 m2

T1

T2

m1g

m2g

a a

Consider the following set of equations. Allvariables are positive.

I: m1 g − T1 = m1 aJ : T1 −m1 g = m1 aK: T1 = m1 a

X : m2 g − T2 = m2 aY: T2 −m2 g = m2 aZ: T2 = m2 a

A: (T2 − T1)R = Ia

RB: (T1 − T2)R = I

a

RC: (T2 − T1)R = I aD: (T1 − T2)R = I a

Choose the correct set of equations of mo-

tion.

1. I, Y, and B

2. I, X , and A

3. I, X , and B

4. I, X , and C

5. I, X , and D

6. J , Y, and A

7. J , Y, and B

8. K, Z, and A

9. K, Z, and B

10. K, Z, and C

Part 2 of 2Note: The moment of inertia is not given.

Let the mass on the left be 5.5 kg andthe mass on the right be 3.5 kg, and theacceleration be 1.30667 m/s2. The radius ofthe pulley is 0.1 m.

Determine the magnitude of the torque ex-erted on the pulley.

Ferris Wheel Motor 0210:09, highSchool, numeric, < 1 min, normal.

A motor keep a Ferris wheel (moment of in-ertia I = 3× 107 kgm2) rotating at 10 rev/hr.When the motor is terned off, the wheel slowsdown (because of friction) to 7 rev/hr in 20 s.

What was the power of the motor that keptthe wheel rotating at 10 rev/hr despite fric-tion?


A horizontal 800.0 N merry-go-round witha radius of 1.5 m is started from rest by aconstant horizontal force of 50.0 N applied

Chapter 10, section 9, Work, Power, and Energy in Rotational Motion 341

tangentially to the merry-go-round.The acceleration of gravity is 9.81 m/s2 .Find the kinetic energy of the merry-go-

round after 3.0 s. Assume it is a solid cylin-der.


A top has a moment of inertia of 4.00 ×10−4 kg ·m2 and is initially at rest. It is freeto rotate about a vertical stationary axis. Astring around a peg along the axis of the topis pulled, maintaining a constant tension of5.57 N in the string.

If the string does not slip while it is woundaround the peg, what is the angular speed ofthe top after 80.0 cm of string has been pulledoff the peg?


Part 1 of 2A car is designed to get its energy from

a rotating flywheel with a radius of 2.00 mand a mass of 500.0 kg. Before a trip, thedisk-shaped flywheel is attached to an electricmotor, which brings the flywheel’s rotationalspeed up to 1000.0 rev/min.

a) Find the kinetic energy stored in theflywheel.

Part 2 of 2b) If the flywheel is to supply as much energyto the car as a 7457 W motor would, findthe length of time the car can run before theflywheel has to be brought back up to speedagain.


A 10,000 N vehicle is stalled one-quarterthe way across the bridge.

Calculate the additional reaction forces

that are supplied at the supports on bothends of the bridge.

1. 6666 N at the left and 3333 N at theright.




Chapter 11, section 1, Rotational Plus Translational Motion: Rolling 342


Which will have the greater accelerationrolling down an incline: a bowling ball or avolleyball, and why?

1. the bowling ball; rotational inertia

2. the volleyball; rotational inertia

3. no difference

4. the bowling ball; mass

5. the volleyball; mass


What technique would help you to distin-guish between two identical-looking spheresof the same weight, one solid and the otherhollow?

1. Hit them and compare their reflectivesounds.

2.Plunge them into water and compare theirdensities.

3. Roll them down an incline and comparetheir speeds.

4. Launch them and compare their trajecto-ries.


Which will roll down an incline faster: acan of water or a can of ice?

1. the can of water

2. the can of ice

3. same speeds

4. It depends on the temperature.

Two wheels with fixed hubs11:01, highSchool, multiple choice, > 1 min,fixed.

Two wheels with fixed hubs, each having amass of 1kg, start from rest, and forces are ap-plies as shown. Assume the hubs and spokesare massless, so that the rotational inertia isI = mR2. In order to impart identical angu-lar accelerations, how large must F2 be?

�

F1 = 1N

R = 0.5m

m = 1kg �

F2 =?

R = 1m

m = 1kg

1. 0.25N

2. 0.5N

3. 1N

4. 2N

5. 4N

Chapter 11, section 2, The Kinetic Energy of Rolling 343

Conceptual rotation 0111:02, highSchool, multiple choice, < 1 min,fixed.

Consider two bicycle riders, A and B. Thetwo riders have equal masses M rider

A = M riderB

and their respective bicycles also have sim-ilar frames, M frame

A = M frameB . Finally,

the wheels of the two bicycles have equalmasses Mwheel

A = MwheelB and equal radii

RwheelA = Rwheel

B but different mass distribu-tions: the wheels of bike A have most of theirmasses at the rims,

Wheel A,

while the wheels of bike B have their masses‘spread’ evenly over the whole wheel area,

Wheel B.

The two cyclists travel at the same speedon level ground. They approach a low hill anddecide to coast up instead of hard pedalling.

At the top of the hill, which of the two bikeswill have a larger speed? Assume no frictionnor air resistance, and all the wheels roll onthe ground without slipping.

1. Bike A; its wheels have bigger moment ofinertia.

2. Bike B; its wheels have bigger moment ofinertia.

3. Bike A; its wheels have smaller momentof inertia.

4. Bike B; its wheels have smaller momentof inertia.

5. The same speed; conservation of energy.

6. The same speed; conservation of (linear)momentum.

7. The same speed; conservation of angularmomentum.

8. The height and the angle of the hill mustbe known.

9. The masses are necessary to answerthis.


A 35 kg bowling ball with a radius of 13 cmstarts from rest at the top of an incline 3.5 min height.

The acceleration of gravity is 9.81 m/s2 .Find the translational speed of the bowling

ball after it has rolled to the bottom of theincline. (Assume that the ball is a uniformsolid sphere.)


A solid 240 N ball with a radius of 0.200m rolls 6.0 m down a ramp that is inclined at37◦ with the horizontal.

The acceleration of gravity is 9.81 m/s2 .If the ball starts from rest at the top of the

ramp, what is the angular speed of the ball atthe bottom of the ramp?

Holt SF 08Rev 4411:02, highSchool, multiple choice, < 1 min,fixed.

Two spheres look identical and have thesame mass. One is hollow and the other issolid.

Which method would determine which iswhich?

Chapter 11, section 2, The Kinetic Energy of Rolling 344

1. Roll them down an incline.

2. Drop them from the same height.

3.Weigh them on a scale.

4. None of these

Chapter 11, section 6, Angular Momentum of a Particle 345


A basketball player wishes to balance a ballon his fingertip.

Will he be more successful with a spinningball or a stationary ball? What physical prin-ciple supports your answer?

1. the spinning ball; angular momentum

2. the spinning ball; inertia

3. the stationary ball; angular momentum

4. the stationary ball; inertia


When a car drives off a cliff, which physicsconcept explains why it rotates forward as itfalls?

1. torque

2. angular velocity

3. conservation of energy

4. conservation of momentum


Why does a car nose up when accelerating,and nose down when braking?

1. torque

2. momentum

3. gravity

4. center of mass


Why must you bend forward when carryinga heavy load on your back?

1. Inertia has changed.

2. Angular momentum has decreased.

3. The center of gravity has shifted.

4. The gravitational force has decreased.


Why is it easier to carry the same amountof water in two buckets, one in each hand,than in a single bucket?

1. The linear inertia of your body haschanged.

2. The center of gravity is in the center ofthe body.

3. Angular momentum has decreased.

4. Angular speed has increased.


What physics concept explains why a ballrolls down a hill?

1. center of gravity

2. friction

3. angular momentum

4. linear inertia



Why is it dangerous to roll open the topdrawers of a fully loaded file cabinet that isnot secured to the floor?

1. because of the angular momentum of thecabinet

2. because of the inertia of the cabinet

3. because of the angular velocity produced

4. because of the center of gravity of thecabinet


Why was the invention of rifling in a longgun or cannon barrel so important? (Riflingis a series of screw-like grooves etched into theinteior of a rifle barrel that imparts a spin tothe bullet.)

1. This slows the bullet, stabilizing theaccuracy.

2. This gives the bullet an angular momen-tum, stabilizing the trajectory.

3. This cools the barrel by decreasing fric-tion.

4. This makes the barrel more durable.

5. This saves more iron.

6. This slows the bullet, thus decreasing thedamage to the target.


Part 1 of 2a) Calculate the angular momentum of

Earth that arises from its spinning motionon its axis

(

IE = 0.331MER2E

)

.

Part 2 of 2b) Calculate the average angular momentumof Earth that arises from its orbital motionabout the sun.

Problems 08 1011:06, highSchool, numeric, < 1 min, fixed.

How much greater is the angular momen-tum of the Earth orbiting about the sunthan the moon orbiting about the Earth?(Mass of Earth is 6 × 1024 kg, mass ofmoon is 7.4 × 1022 kg, Earth-sun distanceis 1.5 × 1011 m, and Earth-moon distance is3.8× 108 m.)

Tennis Ball on a String11:06, highSchool, multiple choice, < 1 min,fixed.

A person spins a tennis ball on a string in ahorizontal circle (so that the axis of rotationis vertical). At the point indicated below, theball is given a sharp blow in forward direction.This causes a change in angular momentum∆L in the

L

z

y

x

1. +x direction

2. +y direction

3. +z direction

4. -x direction

5. -y direction


6. -z direction

Chapter 11, section 7, General Motion: Angular Momentum, Torque of a System 348

Disk and Spool over Pulley 0111:07, highSchool, multiple choice, > 1 min,fixed.

Hint: The moment of inertia for a uniform

disk is I =1

2mr2 .

Two uniform disks with the same mass areconnected by a light inextensible string sup-ported by a massless pulley, on a frictionlessaxis.

The string is attached to a point on thecircumference of disk A (on the left).

The string is wound around disk B (on theright) so that the disk will rotate like a yo-yowhen dropped.

A B

�

�

Describe the outcome when the disks aresimultaneously released from rest at the sameheight above the floor.

1. Both disks will reach the floor at the sametime.

2. Disk A (on the left) will reach the floorfirst.

3. Disk B (on the right) will reach the floorfirst.

4. Both disks will remain stationary.

Chapter 11, section 10, Conservation of Angular Momentum 349

Ball Flying Off Slide11:10, highSchool, multiple choice, < 1 min,fixed.

A child takes a ball and places it at thetop of a slide, at an initial height. The ballstarts from rest, rolls without slipping downthe slide and flies off the end into the air, withan initial angle of 32◦. Ignore loss to frictionand air resistance. Which statements are truethroughout the ball’s motion?

I. Angular momentum of the ball mustbe conserved.II. Linear momentum of the ball must beconserved.III. Mechanical energy of the ball mustbe conserved.IV. The ball will keep traveling upwarduntil it reaches its initial height.V. The ball will travel up to a maximumheight less than its initial height.

1. III and V only

2. III and IV only

3. I, II, III and IV only

4. I, II, III and V only

5. II, III and V only

6. II and IV only

7. II and V only

8. I and IV only

9. I and V only

10. I, II and IV only


A long track balanced like a seesaw sup-ports a mass m and another of mass 2m with

a compressed spring between them. Whenthe spring is released, the masses move awayfrom each other.

2m m

Does the track tip clockwise, tip counter-clockwise, or remain in balance as the massesmove outward? Why?

1. remain in balance; conservation of mo-mentum

2. tip clockwise; center of gravity

3. tip counterclockwise; angular inertia

4. remain in balance; angular frequency


You sit at the middle of a large turntable atan amusement park as it is set spinning andthen allowed to spin freely.

When you crawl toward the edge of theturntable, does the rate of the rotation in-crease, decrease, or remain unchanged, andwhy?

1. increases; conservation of energy

2. increases; conservation of momentum

3. decreases; conservation of energy

4. decreases; conservation of momentum


A sizable quantity of soil is washed downthe Mississippi River and deposited in theGulf of Mexico each year.

What effect does this tend to have on thelength of a day?


1. shorten the day

2. lengthen the day

1. no change

1. Impossible to determine


Strictly speaking, as more and moreskyscrapers are built on the surface of theEarth, does the day tend to become longeror shorter? And strictly speaking, does thefalling of autumn leaves tend to lengthen orshorten the 24-hour day? What physical prin-ciple supports your answers?

1. lengthen; shorten; conservation of kineticenergy

2. lengthen; shorten; conservation of angularmomentum

3. shorten; lengthen; conservation of inertia

4. shorten; lengthen; conservation of angulartorque


If the world’s populations move to the northand south poles, what effect would this haveon the length of the day?

1. longer

2. shorter

3. No change

4. It depends on the mass involved.

Concept 08 47


If the polar ice caps of the Earth were tomelt, the oceans would be deeper by about 30m.

What effect would this have on the Earth’srotation?

1. Faster

2. Slower

3. No change

4. It depends on mass.


A toy train is initially at rest on a trackfastened to a bicycle wheel, which is free torotate.

How does the wheel respond when the trainmoves clockwise? When the train backs up?Does the angular momentum of the wheel-train system change during these maneuvers?

1. Clockwise; counterclockwise; no

2. Clockwise; clockwise; yes

3. Counterclockwise; counterclockwise; no

4. Counterclockwise; clockwise; no


We believe our galaxy was formed from ahuge cloud of gas. The original cloud was farlarger than the present size of the galaxy, wasmore or less spherical, and was rotating verymuch more slowly than the galaxy is now.


original cloud of gas

present galaxy

In this sketch we see a representation ofthe original cloud and the galaxy as it is now(seen edgewise).

Explain how the law of gravitation and con-servation of angular momentum contribute tothe galaxy’s present shape and why it rotatesfaster now than when it was a larger, sphericalcloud.

1. Because of conservation of entropy.

2. Because of special relativity.

3. Because of energy conservation.

4. Because of angular momentum conserva-tion.


Why does a helicopter have a tail rotor?

1. This makes the helicopter move faster.

2. This keeps the helicopter from spinningout of control.

3. This increases safety if any of the rotorsbreaks down.

4. The tail rotor is just for decoration.

5. None of these

Conceptual 07 0611:10, highSchool, multiple choice, < 1 min,

fixed.

How does conservation of angular momen-tum affect the stability of a bike?

1. The bike plus the people on the bike havean angular momentum, which makes the bikemore stable when it is moving.

2. The rolling wheels have angular momen-tum; with no external torque applied, the bikeis more stable.

3. The rolling wheels have angular momen-tum; conservation of angular momentum sta-balizes a moving bike.

4. The rotating pedal has a angular momen-tum, which helps stabilize a moving bike.

5. The rider’s sense of balance stabilizes thebike.

Figure Skater11:10, highSchool, multiple choice, < 1 min,fixed.

Part 1 of 2A figure skater rotating on one spot with

both arms and one leg extended has momentof inertia Ii. She then pulls in her arms andthe extended leg, reducing her moment ofinertia to 0.75 Ii.

What is the ratio of her final to initial ki-netic energy?

1. 9/16

2. 16/9

3. 1

4. 1/2

5. 2

6. 3/4

7. 4/3


8. 3/8

9. 8/3

Part 2 of 2Consider the following statements for the fig-ure skater:

I. Angular momentum was conserved.II. Mechanical energy was conserved.III. The kinetic energy changed because of

energy dissipation due to friction.IV. Her rotation rate changed in response

to a torque exerted by pulling in her arms andleg.

Which is the correct combination of state-ments?

1. I

2. II

3. I and II

4. I, II, IV

5. I, II, III

Figure Skater Spin 0111:10, highSchool, multiple choice, < 1 min,fixed.

A figure skater on ice spins on one foot.She pulls in her arms and her rotational speedincreases.

Choose the best statement below:

1. Her angular speed increases because airfriction is reduced as her arms come in.

2. Her angular speed increases because herpotential energy increases as her arms comein.

3. Her angular speed increases because bypulling in her arms she creates a net torque inthe direction of rotation.

4. Her angular speed increases because she

is undergoing uniformly accelerated angularmotion.

5. Her angular speed increases because herangular momentum increases.

6. Her angular speed increases because herangular momentum is the same but her mo-ment of inertia decreases.

Figure Skater Spin11:10, highSchool, multiple choice, < 1 min,fixed.

Part 1 of 2A figure skater on ice spins on one foot.

She pulls in her arms and her rotational speedincreases.

Choose the best statement below:




4. Her angular speed increases because sheis undergoing uniformly accelerated angularmotion.


6. Her angular speed increases because herangular momentum is the same but her mo-ment of inertia decreases.

Part 2 of 2And again, choose the best statement below:

1.When she pulls in her arms, her rotationalkinetic energy is conserved and therefore staysthe same.


2. When she pulls in her arms, her rota-tional potential energy increases as her armsapproach the center.

3.When she pulls in her arms, her rotationalkinetic energy must decrease because of thedecrease in her moment of inertia.

4. When she pulls in her arms, her momentof inertia is conserved.

5. When she pulls in her arms, her angu-lar momentum decreases so as to conserveenergy.

6. When she pulls in her arms, the workshe performs on them turns into increasedrotational kinetic energy.

Figure Skater Spins11:10, highSchool, multiple choice, < 1 min,fixed.

A figure skater on ice spins on one foot.She pulls in her arms and her angular speedincreases.

Choose the best statement below.




4. Her angular speed increases because sheis undergoing uniformly accelerated angularmotion.


6. Her angular speed increases because herangular momentum remains the same but hermoment of inertia decreases.

7. Her angular speed is unrelated to herarms. She pulls them in at the same time asshe speeds up her spin because it looks betterthis way.


A merry-go-round rotates at the rate of0.30 rad/s with a(n) 80.0 kg man standing ata point 2.0 m from the axis of rotation.

What is the new angular speed when theman walks to a point 1.0 m from the center?Assume that the merry-go-round is a solid6.50 × 102 kg cylinder with a radius of 2.00m.


A 2.0 kg bicycle wheel with a radius of0.30 m turns at a constant angular speed of25 rad/s when a(n) 0.30 kg reflector is at adistance of 0.19 m from the axle.

What is the angular speed of the wheelwhen the reflector slides to a distance of 0.25m from the axle?


A solid, vertical cylinder with a mass of10.0 kg and a radius of 2.00 m rotates withan angular speed of 7.00 rad/s about a fixedvertical axis through its center. A 0.250 kgpiece of putty is dropped vertically at a point1.00 m from the cylinder’s center of rotationand sticks to the cylinder.

What is the final angular speed of the sys-tem?



As Halley’s comet orbits the sun, its dis-tance from the sun changes dramatically.

If the comet’s speed at a distance of 8.8 ×1010 m from the sun is 5.4 × 104 m/s andangular momentum is conserved, what is itsspeed when it is 5.2× 1012 m from the sun?


The entrance of a science museum featuresa funnel into which marbles are rolled one ata time. The marbles circle around the wall ofthe funnel, eventually spiraling down into theneck of the funnel. The internal radius of thefunnel at the top is 0.54 m. At the bottom,the funnel’s neck narrows to an internal radiusof 0.040 m. A 2.5 × 10−2 kg marble beginsrolling in a large circular orbit around thefunnel’s rim at 0.35 rev/s.

If it continues moving in a roughly circularpath, what will the marble’s angular speed beas it passes through the neck of the funnel?(Consider only the effects of conservation ofangular momentum.)


A 15.0 kg turntable with a radius of 25cm is covered with a uniform layer of dryice that has a mass of 9.00 kg. The angularspeed of the turntable and dry ice is initially0.75 rad/s, but it increases as the dry iceevaporates.

What is the angular speed of the turntableonce all the dry ice has evaporated?


A 65 kg woman stands at the rim of ahorizontal turntable with a moment of inertiaof 1.5×103 kg ·m2 and a radius of 2.0 m. Thesystem is initially at rest, and the turntable isfree to rotate about a frictionless vertical axle

through its center. The woman then startswalking clockwise (when viewed from above)around the rim at a constant speed of 0.75rad/s relative to Earth.

With what angular speed does theturntable rotate?


Part 1 of 2A skater spins with an angular speed of

12.0 rad/s with his arms outstretched. Helowers his arms, decreasing his moment ofinertia from 41 kg ·m2 to 36 kg ·m2.

a) Calculate his initial rotational kineticenergy.

Part 2 of 2b) Calculate his final rotational kinetic en-ergy.


The figure shows a system of fourm = 7 kgpoint masses that rotates at an angular speedof 2 rev/s . The masses are connected by light,flexible spokes of 5 m and 8 m length that canbe elongated or shortened.

x

y

5 m

8 m

m

m

m

m = 7 kg

2 rev/s

2 rev/s

What is the new angular speed if each ofthe spokes are shortened by 50 %?

An effect similar to this ocurred in the early


stages of the formation of our galaxy. As themassive cloud of gas and dust contracted, aninitially small rotation increased with time.


If a trapeze artist rotates once each secondwhile sailing through the air, and contracts toreduce her rotational inertia to one third ofwhat it was, how many rotations per secondwill result?

1. 1/9 rotations per second.

2. 1/3 rotations per second.

3. 3 rotations per second.

4. 9 rotations per second.

Spinning Flywheel in a Suitcase11:10, highSchool, multiple choice, > 1 min,fixed.

A suitcase containing a spinning flywheelis rotated about the vertical axis as shown in(a). As it rotates, the bottom of the suitcasemoves out and up, as in (b).

(a) (b)

beforerotation

afterrotation

From this, we can conclude that the fly-wheel as seen from the side of the suitcase asin (a), rotates

1. clockwise

2. counterclockwise

Chapter 11, section 11, Precession: Gyroscopes and Tops 356

Professor and Wheel11:11, highSchool, numeric, > 1 min, normal.

A professor holds a bicycle wheel rotatingat 300 rev/min by a string attached to aweightless axle 15 cm from the wheel.

The acceleration of gravity is 9.8 m/s2 .If all 4 kg of the wheel can be considered to

be at its 45 cm radius, at what frequency (inrpm) does it precess?

Chapter 11, section 13, Coriolis Effect 357


When a long-range cannonball is fired to-ward the equator from a northern (or south-ern) latitude, why does it land west of itsintended longitude?

1. The cannonball travels faster than thespeed of sound.

2. The Earth’s center of gravity is shifted bythe cannonball.

3. The Earth’s angular momentum ischanged.

4. The Earth rotates under the motion.

Coriolis Catch11:13, highSchool, multiple choice, < 1 min,fixed.

Part 1 of 2Two students decide to play a game of catch

on a merry-go-round which is rotating coun-terclockwise, as viewed from above. StudentA stands in the center of the merry-go-roundand student B stands near the edge. They arefacing each other.

Coriolis Catch

A B6 rad/s � �

At time t1, student A throws the ball di-rectly at student B. Student B will see theball

1. fly directly toward her.

2. curve away to her left.

3. curve away to her right.

4. Answer cannot be determined.

Part 2 of 2At time t2, student B throws the ball directlyat student A. Student A will see the ball

1. fly directly toward her.

2. curve away to her left.

3. curve away to her right.

4. Answer cannot be determined.

Chapter 12, section 1, The Conditions for Equilibrium of a Rigid Object 358


Nobody at the playground wants to play withan obnoxious boy, so he fashions a seesaw asshown so he can play by himself.

Explain how this is done.

1. The angular velocity of the boy is can-celled with that of the board.

2. The weight of the boy is balanced by theweight of the board.

3. The fulcrum is very far from the boy.

4. The weight of the boy is balanced with anunknown heavy metal.


Why does a typical helicopter with a singlemain rotor have a second small rotor on itstail?

1. The small rotor stops the rotation of thehelicopter body.

2. The small rotor provides a lifting force.

3.The small rotor acts as a rudder to steer.

4. The small rotor provides nothing.


Consider three types of rollers on a pair ofparallel tracks:

A) a cylinder;B) a pair of cups fastened at their narrow

ends; andC) a pair of cups fastened at their wide ends.When rolled along the track, one is very

unstable and rolls off the edge. Another ismoderately stable (for short distances). Theother is very stable and centers itself on thetrack.

Which roller has the best stability? (Thinkabout the wheels on a railroad car.)

1.

2.

3.

Chapter 12, section 2, Solving Statics Problems 359


Part 1 of 2A uniform 5.00 m long horizontal beam that

weighs 315 N is attached to a wall by a pinconnection that allows the beam to rotate. Itsfar end is supported by a cable that makes anangle of 53◦ with the horizontal, and a 545 Nperson is standing 1.50 m from the pin.

1.5m

5m

545N 315N

R FT

53◦

Note: Figure is not drawn to scale.

a) Assuming that the axis of rotation passesthrough the beam’s center of mass, find theforce FT in the cable.

Part 2 of 2b) Find the magnitude of the force R exertedon the beam by the wall if the beam is inequilibrium.


Part 1 of 3A floodlight with a mass of 20.0 kg is used to

illuminate the parking lot in front of a library.The floodlight is supported at the end of ahorizontal beam that is hinged to a verticalpole, as shown. A cable that makes an angle of30.0◦ with the beam is attached to the pole tohelp support the floodlight. Assume the massof the beam is negligible when compared withthe mass of the floodlight.


20 kg

30◦

Note: Figure is not drawn to scalea) Find the force FT provided by the cable.

Part 2 of 3b) Find the horizontal force exerted on thebeam by the pole.

Part 3 of 3c) Find the vertical force exerted on the beamby the pole.


Part 1 of 3A 1200.0 N uniform boom of length ` is

supported by a cable, as shown. The boom ispivoted at the bottom, the cable is attached

a distance3

4` from the pivot, and a 2000.0 N

weight hangs from the boom’s top.

FT

2000 N

25◦

65◦

Note: Figure is not drawn to scalea) Find the force FT applied by the sup-

porting cable.

Part 2 of 3b) Find the horizontal component of the reac-tion force on the bottom of the boom.


Part 3 of 3c) Find the vertical component of the reactionforce on the bottom of the boom.


Part 1 of 3A uniform 10.0 N picture frame is sup-

ported as shown.

FT,1FT,2

10 N

F

P

50◦30 cm

15 cm

Note: Figure is not drawn to scalea) Find the force FT,1 in the cord that is

required to hold the frame in this position.

Part 2 of 3b) Find the force FT,2 in the cord that isrequired to hold the frame in this position.

Part 3 of 3c) Find the magnitude of the horizontal forceat P that is required to hold the frame in thisposition.


A 23.0 cm screwdriver is used to pry opena can of paint.

If the axis of rotation is 2.00 cm from theend of the screwdriver blade and a force of 84.3N is exerted at the end of the screwdriver’shandle, what force is applied to the lid?


Part 1 of 2

A 0.1 kg meterstick is supported at its40 cm mark by a string attached to the ceil-ing. A 0.7 kg mass hangs vertically from the5 cm mark. A mass is attached somewhereon the meterstick to keep it horizontal and inboth rotational and translational equilibrium.The force applied by the string attaching themeterstick to the ceiling is 19.6 N.

The acceleration of gravity is 9.81 m/s2 .a) Find the value of the unknown mass.

Part 2 of 2b) Find the point where the mass attaches tothe stick.


Part 1 of 2A person is standing on tiptoe, and the per-

son’s total weight is supported by the force onthe toe. A mechanical model for the situationis shown, where T is the force in the Achillestendon and R is the force on the foot due tothe tibia. Assume the total weight is 700.0 N.

T

21.2◦

R15

◦

18 cm

25 cmFn

Note: Figure is not drawn to scalea) Find the value of T .

Part 2 of 2b) Find the value of R.


A uniform 6.0 m tall aluminum ladder isleaning against a frictionless vertical wall.The ladder has a weight of 250 N. The lad-der slips when it makes a 60.0◦ angle with the


horizontal floor.Determine the coefficient of static friction

between the ladder and the floor.


Part 1 of 3A ladder with a length of 15.0 m and a

weight of 520.0 N rests against a frictionlesswall, making an angle of 60.0◦ with the hori-zontal.

a) Find the horizontal force exerted on thebase of the ladder by Earth when an 800.0 Nfirefighter is 4.00 m from the bottom of theladder.

Part 2 of 3b) Find the vertical force exerted on the baseof the ladder by Earth when an 800.0 N fire-fighter is 4.00 m from the bottom of the lad-der.

Part 3 of 3c) If the ladder is just on the verge of slippingwhen the firefighter is 9.00 m up, what is thecoefficient of static friction between the ladderand the ground?


Neglect the weight of the meterstick andconsider only two weights hanging from itsends. One is a 1 kg mass the other has massof 3 kg.

How far from the end with the 1 kg mass isthe center of mass of this system?


A rock has a mass of 1 kg and hangs fromthe 0 cm end of a meter stick.

What is the mass of the measuring stickif it is balanced by a support force at theone-quarter mark?

1. 0.25 kg

2. 0.5 kg

3. 0.75 kg

4. 1 kg

5. 2 kg

6. 3 kg

7. 4 kg

Chapter 12, section 3, Stability and Balance: Center of Gravity 362

Bricks on the Brink 0312:03, highSchool, numeric, > 1 min, normal.

Part 1 of 2A uniform brick of length 20 m is placed

over the edge of a horizontal surface withthe maximum overhang x possible withoutfalling.

gx

20 m

Find x for a single block.

Part 2 of 2Two identical uniform bricks of length 20 mare stacked over the edge of a horizontal sur-face with the maximum overhang x possiblewithout falling.

gx

20 m

Find x for two blocks.

Bricks on the Brink 0412:03, highSchool, numeric, > 1 min, normal.

A uniform brick of length 20 m is placedover the edge of a horizontal surface withthe maximum overhang of x = 10 m possiblewithout the brick falling.

gx

20 m

Now, two identical uniform bricks of length20 m are stacked over the edge of a horizontalsurface with the maximum overhang x possi-ble without falling.

gx

20 m

Find x for two blocks.


If you walk along the top of a fence, whydoes holding your arms out help you to bal-ance?

1. Your momentum is decreased.

2. Your rotational inertia is decreased.

3. Your momentum is increased.

4. Your rotational inertia is increased.

Tipping a Block 0212:03, highSchool, numeric, > 1 min, normal.

A string provides a horizontal force whichacts on a 445 N rectangular block at top right-hand corner as shown in the figure below.

1m

0.85 m F

445 N

If the block slides with constant speed, findthe tension in the string required to start totip the block over.

Walking on a Beam off a Cliff

Chapter 12, section 3, Stability and Balance: Center of Gravity 363

12:03, highSchool, numeric, < 1 min, normal.

A student of mass 70 kg wants to walkbeyond the edge of a cliff on a heavy beam ofmass 280 kg and length 8 m. The beam is notattached to the cliff in any way, it simply layson the horizontal surface of the clifftop, withone end sticking out beyond the cliff’s edge:

d

The students want to position the beam soit sticks out as far as possible beyond the edge,but he also wants to make sure he can walk tothe beam’s end without falling down.

How far from the edge of the ledge can thebeam extend?

Chapter 12, section 4, Levers and Pulleys 364

Balancing Rock 0112:04, highSchool, multiple choice, < 1 min,normal.

A 1 kg rock is suspended by a masslessstring from one end of a 6 m measuring stick.

0 1 2 3 4 5 6

1 kg

What is the mass of the measuring stick ifit is balanced by a support force at the 1 mmark?

Balancing Rock 0212:04, highSchool, multiple choice, > 1 min,normal.

A 5 kg rock is suspended by a masslessstring from one end of a 8 m measuring stick.


0 1 2 3 4 5 6 7 8

5 kg

What is the weight of the measuring stickif it is balanced by a support force at the 1 mmark?

Diving Board 0112:04, highSchool, multiple choice, < 1 min,fixed.

A person (weight WP ) stands on the endof a diving board (weight WD) that has twosupports A and B that exert vertical forcesSA and SB:

A B

What is the free body diagram for the div-ing board?

1.SA SB

WD WP

2.

SA

SB

WD WP

3.

SA SB WD WP

4.

Chapter 12, section 4, Levers and Pulleys 365

SA

SB WD WP


Part 1 of 2A 400.0 N child and a 300.0 N child sit on

either end of a 2.0 m long seesaw.How far from the 400.0 N child should the

pivot be placed to ensure rotational equilib-rium? Disregard the mass of the seesaw.

Part 2 of 2Suppose a 225 N child sits 0.200 m from the400.0 N child.

How far from the pivot must a 325 N childsit to maintain rotational equilibrium?

Mobile12:04, highSchool, multiple choice, > 1 min,wording-variable.

A mobile consisting of four weights hangingon three rods of negligible mass.

10 N W1

W2

W3

6 m 9 m

6 m 5 m

5 m 7 m

Find the weight ofW3.

Chapter 12, section 5, Bridges and Scaffolding 366


Part 1 of 2A uniform bridge 20.0 m long and weighing

4.00×105 N is supported by two pillars located3.00 m from each end. A 1.96 × 104 N car isparked 8.00 m from one end of the bridge.

a) How much force does the pillar closer tothe car exert?

Part 2 of 2b) Howmuch force does the pillar farther fromthe car exert?


Part 1 of 2A 700.0 N window washer is standing on a

uniform scaffold supported by a vertical ropeat each end. The scaffold weighs 200.0 N andis 3.00 m long. Assume the window washerstands 1.00 m from one end.

a) What is the force on the farther rope?

Part 2 of 2b) What is the force on the closer rope?


Part 1 of 2A window washer is standing on a scaffold

supported by a vertical rope at each end. Thescaffold weighs 205 N and is 3.00 m long.Assume the 675 N worker stands 1.00 m fromone end of the scaffold.

a) What is the force on the rope fartherfrom the worker?

Part 2 of 2b) What is the force on the closer rope?

Chapter 12, section 8, Other Objects in Static Equilibrium 367


A uniform ladder 8.00 m long and weighing200.0 N rests against a smooth wall. Thecoefficient of static friction between the ladderand the ground is 0.600, and the ladder makesa 50.0◦ angle with the ground.

How far up the ladder can an 800.0 N personclimb before the ladder begins to slip?

Chapter 12, section 11, Fracturing 368


Suppose you’re making a balcony that ex-tends beyond the main frame of your house.

In a concrete overhanging slab, should steelreinforcing rods be embedded in the top, mid-dle, or bottom of the slab?

1. in the top

2. in the middle

3. in the bottom


Chapter 13, section 1, Simple Harmonic Motion 369

Angular Frequency SW13:01, highSchool, multiple choice, < 1 min,fixed.

An oscillator is described by

1 2 3 4 5 6 7 8 9 10 11 12

1

2

x(t)

t (sec)

What is the angular frequency ω?

1. 1.6 rad/s

2. 2.0 rad/s

3. 3.1 rad/s

4. 4.0 rad/s

5. 6.2 rad/s

Oscillating Object13:01, highSchool, multiple choice, < 1 min,fixed.

An object can oscillate ONLY around

1. any equilibrium point.

2. any stable equilibrium point.

3. certain stable equilibrium points.

4. any point, provided the forces exerted onit obey Hooke’s law.

5. any point

Chapter 13, section 2, Mass Attached to a Spring 370

Concept 19 0413:02, highSchool, numeric, < 1 min, normal.

Part 1 of 3A weight suspended from a spring is seen

to bob up and down over a distance of 20 cmtwice each second.

What is its frequency?

Part 2 of 3What is its period?

Part 3 of 3What is its amplitude?


A mass of 0.30 kg is attached to a springand is set into vibration with a period of 0.24s.

What is the spring constant of the spring?


When a mass of 25 g is attached to a certainspring, it makes 20 complete vibrations in4.0 s.

What is the spring constant of the spring?


A 125 N object vibrates with a period of3.56 s when hanging from a spring.

What is the spring constant of the spring?The acceleration of gravity is 9.81 m/s2 .


The body of a 1275 kg car is supportedon a frame by four springs. The spring con-

stant of a single spring is 2.00 × 104 N/m.Four people riding in the car have a combinedmass of 255 kg. When driven over a potholein the road, the frame vibrates and for thefirst few seconds the vibration approximatessimple harmonic motion.

What is the period of vibration of the car?


Part 1 of 6A spring with a spring constant of 30.0

N/m is attached to different masses, and thesystem is set in motion.

What is its period for a mass of 2.3 kg?

Part 2 of 6What is its frequency?

Part 3 of 6What is the period for a mass of 15 g?


Part 5 of 6What is the period for a mass of 1.9 kg?



Part 1 of 2A spring with a spring constant of 1.8×102

N/m is attached to a 1.5 kg mass and then setin motion.

What is the period of the mass-spring sys-tem?

Part 2 of 2What is the frequency of the vibration?

Chapter 13, section 3, Forces in Simple Harmonic Motion 371

Ball on a Spring13:03, highSchool, numeric,> 1min, wording-variable.

When a metal ball of unknown mass Mis suspended from a spring of unknown forceconstant k, the spring’s equilibrium lengthincreases by ∆Le. And when the ball is out ofequilibrium, it oscillates up and down with aperiod T .

Find ∆Le. The acceleration of gravity is9.8 m/s2 and the period is 0.4 s.

Chapter 13, section 4, Energy in Simple Harmonic Motion 372

Concept Harmonic Motion 0213:04, highSchool, multiple choice, < 1 min,fixed.

If almost any system in stable equilibrium isslightly disturbed, it will then exhibit simpleharmonic motion because

1. mechanical energy is conserved.

2. momentum is conserved.

3. momentum and mechanical energy areboth conserved.

4. the potential energy of a system near astate of static equilibrium is proportional tothe cube of the displacement from the equi-librium position.

5. the potential energy of a system neara state of static equilibrium is proportionalto the square of the displacement from theequilibrium position.

6. the potential energy of a system near astate of static equilibrium is linearly propor-tional to the displacement from the equilib-rium position.

7. the force on a system in stable equilibriumis zero.

8. the force on a system in unstable equilib-rium is zero.

9. the momentum of a system in stable equi-librium is zero.

10. the kinetic energy on a system in stableequilibrium is zero.

Concept Harmonic Motion13:04, highSchool, multiple choice, > 1 min,fixed.

If almost any system in stable equilibrium isslightly disturbed, it will then exhibit simple

harmonic motion because

1. mechanical energy is conserved.

2. momentum is conserved.

3. momentum and mechanical energy areboth conserved.

4. the change in potential energy is propor-tional to the cube of the displacement fromthe equilibrium position.

5. the change in potential energy is propor-tional to the square of the displacement fromthe equilibrium position.

6. the change in potential energy is propor-tional to the displacement from the equilib-rium position.

7. the force on a system in stable equilibriumis zero.

8. the force on a system in unstable equilib-rium is zero.

9. the momentum of a system in stable equi-librium is zero.

10. the kinetic energy on a system in stableequilibrium is zero.

Modified Mass on Spring13:04, highSchool, multiple choice, > 1 min,fixed.

A mass is placed on a spring and oscillateswith a period of 1 second.

Now a heavier mass is placed on the samespring.

Which statements are true?

Chapter 13, section 4, Energy in Simple Harmonic Motion 373

I. The heavier mass oscillates with ashorter period because the gravitationalforce on it is greater.

II. The heavier mass oscillates with thesame period because gravitational accel-eration is constant.

III. The heavier mass oscillates with a longerperiod because of its greater inertia.

IV. The heavier mass must have greater me-chanical energy than the first because itis heavier.

V. The heavier mass must have less me-chanical energy than the first because itmoves more slowly.

VI. One cannot reach any conclusion aboutmechanical energy without knowing theamplitude of motion in each case.

1. III and VI only

2. III and V only

3. III and IV only

4. II and VI only

5. II and V only

6. II and IV only

7. I and VI only

8. I and V only

9. I and IV only

Oscillations13:04, highSchool, multiple choice, < 1 min,fixed.

An object with a potential energy U(x) canoscillate around

1. any point provided that the restoringforce exerted on the object is given by Hooke’slaw.

2. any equilibrium point.

3. any point.

4. any unstable equilibrium point.

5. certain stable equilibrium points.

6. any stable equilibrium point.

Two Masses on a Spring 0213:04, highSchool, numeric, > 1 min, normal.

A mass, m1 = 9 kg, is in equilibriumwhile connected to a light spring of constantk = 100 N/m that is fastened to a wall (seea). A second mass, m2 = 7 kg, is slowlypushed up against mass m1, compressing thespring by the amount Ai = 0.2 m (see b).The system is then released, causing bothmasses to start moving to the right on thefrictionless surface. When m1 is at the equi-librium point, m2 loses contact with m1 (seec) and moves to the right with speed vmax.

m1

m1

m1

m1 2m

2m

2m

k

k

k

k

A

D

v

v

(a)

(b)

(c)

(d)

Determine the value of vmax.

Chapter 13, section 5, The Simple Pendulum 374

Conceptual 14 Q0113:05, highSchool, numeric, < 1 min, fixed.

Part 1 of 2Jim and Gina are swinging on adjacent,

equal length swings at the school playground.Jim weights about twice as much as Gina

Who, if either, will take less time to swingback and forth?

1. Same for both

2. Jim

3. Gina

Part 2 of 2What, if anything, will change if Jim swingswhile standing on the seat of his swing?

1. Jim’s period will decrease.

2. Gina’s period will decrease.

3. No change to the periods


You need to know the height of a tower, butdarkness obscures the ceiling. You note thata pendulum extending from the ceiling almosttouches the floor and that its period is 24 s.

The acceleration of gravity is 9.81 m/s2 .How tall is the tower?

Holt SF 12B 0213:05, highSchool, numeric, > 1 min, fixed.

You are designing a pendulum clock to havea period of 1.0 s.

The acceleration of gravity is 9.81 m/s2 .How long should the pendulum be?


A trapeze artist swings in simple harmonicmotion with a period of 3.8 s.

The acceleration of gravity is 9.81 m/s2 .Calculate the length of the cables support-

ing the trapeze.


Part 1 of 6Consider a pendulum of length 3.500 m.The acceleration of gravity is 9.832 m/s2 .a) What is its period at the North Pole?

Part 2 of 6b) What is its frequency?

Part 3 of 6c) What is its period in Chicago, where g =9.803 m/s2?

Part 4 of 6d) What is its frequency?

Part 5 of 6e) What is its period in Jakarta, Indonesia,where g = 9.782 m/s2?

Part 6 of 6f) What is its frequency?


The acceleration of gravity is 9.81 m/s2 .Find the length of a pendulum that oscil-

lates with a frequency of 0.16 Hz.


A visitor to a lighthouse wishes to deter-mine the height of the tower. The visitor tiesa spool of thread to a small rock to make asimple pendulum, then hangs the pendulum


down a spiral staircase in the center of thetower. The period of oscillation is 9.49 s.

The acceleration of gravity is 9.81 m/s2 .What is the height of the tower?

Holt SF 12Rev 2113:05, highSchool, multiple choice, > 1 min,wording-variable.

Part 1 of 3A pendulum that moves through its equilib-

rium position once every 1.000 s is sometimescalled a “seconds pendulum.”

a) What is the period of any seconds pen-dulum?

1. 2.000 s

2. 1.000 s

3. 4.000 s

4. 0.500 s

5. 0.250 s

6. None of these

Part 2 of 3In Cambridge, England, a seconds pendulumis 0.9942 m long.

b)What is the free-fall acceleration in Cam-bridge?

1. 9.81236 m/s2

2. 9.79756 m/s2

3. 9.81341 m/s2

4. 9.79651 m/s2

5. 9.81 m/s2

6. None of these

Part 3 of 3In Tokyo, Japan, a seconds pendulum is0.9927 m long.

c) What is the free-fall acceleration inTokyo?

1. 9.79756 m/s2

2. 9.81236 m/s2

3. 9.81341 m/s2

4. 9.79651 m/s2

5. 9.81 m/s2

6. None of these


What is the free-fall acceleration in a lo-cation where the period of a 0.85 m longpendulum is 1.86 s s?


A simple 2.00 m long pendulum oscillates.The acceleration of gravity is 9.8 m/s2 .How many complete oscillations does this

pendulum make in 5.00 min?


Part 1 of 3A certain pendulum clock that works per-

fectly on Earth is taken to the moon, whereg = 1.63 m/s2.

The acceleration of gravity is 9.81 m/s2 .The clock is started at 12:00:00 A.M. and

runs for 24 h.a) What will be the reading for the hours?

Part 2 of 3b) What will be the reading for the minutes?

Part 3 of 3c) What will be the reading for the seconds?


Oscillations in a swing13:05, highSchool, multiple choice, < 1 min,fixed.

A child in a swing oscillates with a certainfrequency of oscillation (the child is sittingstill). Another child sits next to the firstchild.

How does the swing’s frequency of oscilla-tion change when the second child sits next tothe first child?

1. increases

2. decreases

3. stays the same

4. more information is needed

Pendulum of Fun13:05, highSchool, numeric, < 1 min, normal.

A simple pendulum has a period of 2.5 s.The acceleration of gravity is 9.8 m/s2 .What is its length?

Chapter 14, section 1, Newton’s Law of Gravity 377


Part 1 of 2Compare the gravitational force on a 1 kg

mass at the surface of the Earth (with ra-dius 6.4× 106 m and mass 6× 1024 kg) with

that on the surface of the Moon(

with mass

1

81.3ME and radius 0.27RE

)

.

What is the force on the Earth?

Part 2 of 2What is it on the Moon?

Conceptual 05 Q1214:01, highSchool, numeric, > 1 min, normal.

Part 1 of 3Consider two planets of mass m and 2m,

respectively, orbiting the same star in circularorbits. The more massive planet is 2 times asfar from the star as the less massive one.

What is the ratio F1 : F2 of the gravita-tional forces exerted on the star by the twoplanets?

Part 2 of 3What is the ratio v1 : v2 of the speeds of thetwo planets?

Part 3 of 3What is the ratio T1 : T2 of the orbital periodsof the two planets?


If our Sun were four times as massive as itis, how many times faster or slower should theEarth move in order to remain in the sameorbit?


fixed.

Which of the objectsa. a bookb. the nearest starc. the Sund. a distant galaxyexert(s) a gravitational force on you?

1. a

2. b

3. c

4. a and d

5. a and b

6. a, b and c

7. b, c and d

8. c and d

9. a, b, c and d

10. Another combination


According to some nineteenth-century geo-logical theories (now largely discredited), theEarth has been shrinking as it gradually cools.

If so, how would g have changed over geo-logical time?

1. It would not change; the mass of theEarth remained the same.

2. It would decrease; the Earth’s radius isdecreasing.

3. It would increase; g is inversely pro-portional to the square of the radius of theEarth.


Conceptual 05 Q4 Q514:01, highSchool, multiple choice, > 1 min,wording-variable.

Two iron spheres of mass m and 2m,respectively, and equally spaced points “rapart” are shown in the figure.

A m B C D 2m E

r r r r r r

At which location would the net gravita-tional force on an object due to these twospheres be a minimum?

1. A

2. B

3. C

4. E

5. D


What did Newton discover about gravity?

1.Gravity is universal, which means it is nota phenomenon unique to Earth.

2. All objects near the Earth free fall withthe same acceleration.

3. Gravity only happens on Earth.

4. The stars, planets, and moon move indivine circles.

5. Any force on a planet would be directedalong its path.


What is the Newtonian synthesis?

1. The union of terrestrial laws and cosmiclaws

2. The combination of forces on each planetdirected towards the Sun

3. The combination of all forces on a planetdirected along its path

4. Gravity only happens on Earth.

5. All objects near the Earth free-fall withthe same acceleration.


How does the force of gravity between twobodies change when the distance betweenthem doubles?

1. remains the same

2. doubles

3. quadruples

4. drops to one quarter of its original value

5. halves

6. Unable to determine; the mass isneeded.

Holt SF 07I 0114:01, highSchool, numeric,> 1min, wording-variable.

Two balls, each with a mass of 0.800 kg,exert a gravitational force of 8.92 × 10−11 Non each other.

How far apart are the balls? The valueof the universal gravitational constant is6.673× 10−11 Nm2/kg2.


Holt SF 07I 0214:01, highSchool, numeric, > 1 min, normal.

Mars has a mass of about 6.4× 1023 kg,and its moon Phobos has a mass of about9.6× 1015 kg.

If the magnitude of the gravitational forcebetween the two bodies is 4.6× 1015 N, howfar apart are Mars and Phobos? The valueof the universal gravitational constant is6.673× 10−11 N ·m2/kg2.

Holt SF 07I 0314:01, highSchool, numeric, > 1 min, normal.

Part 1 of 3Find the magnitude of the gravitational

force a 67.5 kg person would experiencewhile standing on the surface of Earth witha mass of 5.98× 1024 kg and a radius of6.37× 106 m. The universal gravitationalconstant is 6.673× 10−11 N ·m2/kg2.

Part 2 of 3Find the magnitude of the gravitational forceon Mars, with a mass of 6.34× 1023 kg and aradius of 3.43× 106 m.

Part 3 of 3Find the magnitude of the gravitational forceon Pluto, with a mass of 1.32× 1022 kg and aradius of 1.15× 106 m.


The gravitational force of attraction be-tween two students sitting at their desks inphysics class is 3.2× 10−8 N.

If one student has a mass of 50 kg and theother has a mass of 60 kg, how far apart arethe students sitting? The universal gravita-tional constant is 6.673× 10−11 N ·m2/kg2.


If the gravitational force between the elec-tron (of mass 9.11× 10−31 kg) and the proton

(of mass 1.67× 10−27 kg) in a hydrogen atomis 1× 10−47 N, how far apart are the two par-ticles? The universal gravitational constant is6.673× 10−11 N ·m2/kg2.


Part 1 of 3During a solar eclipse, the moon (of

mass 7.36× 1022 kg), Earth (of mass5.98× 1024 kg), and Sun (of mass1.99× 1030 kg) lie on the same line, with themoon between Earth and the Sun.

What gravitational force is exerted on themoon by the Sun? The universal gravita-tional constant is 6.673× 10−11 N ·m2/kg2,the Earth-moon distance is 3.84× 108 m, andthe Earth-Sun distance is 1.496× 1011 m.

Part 2 of 3What gravitational force is exerted on themoon by Earth?

Part 3 of 3What gravitational force is exerted on Earthby the Sun?

New Planet 0114:01, highSchool, multiple choice, > 1 min,wording-variable.

Planet X has four times the diameter andnine times the mass of the earth.

What is the ratio gX : ge of gravitationalacceleration at the surface of planet X to thegravitational acceleration at the surface of theEarth?

1.gxge

=9

16

2.gxge

=7

4

3.gxge

=1

16

4.gxge

=7

81


5.gxge

=1

32

6.gxge

=1

12

7.gxge

=4

9

8.gxge

=9

25

9.gxge

=7

64

10.gxge

=2

9

New Planet 0214:01, highSchool, numeric,> 1min, wording-variable.

Planet X has four times the diameter andnine times the mass of the earth.

What is the ratio gX : ge of gravitationalacceleration at the surface of planet X to thegravitational acceleration at the surface of theEarth?

Chapter 14, section 2, Gravitational Force Due to a System of Particles 381


Two planets with the same diameter areclose to each other, as shown. One planet hastwice the mass as the other planet.

Am

B C2m

D

At which locations would both planets’gravitational force pull on you in the samedirection? From among these four locations,where would you stand so that the force ofgravity on you is a maximum; i.e., at whichpoint would you weigh the most?

1. B; D

2. C; A

3. D; D

4. B and C; D

5. A and D; D

6. A and D; A

7. B and C; C

8. A and B; D

9. None of these

Chapter 14, section 3, Free Fall Acceleration and the Gravitational Force 382

Astronauts14:03, highSchool, numeric, > 1 min, normal.

On the way from a planet to a moon, as-tronauts reach a point where that moon’sgravitational pull is stronger than that of theplanet. The masses of the planet and themoon are, respectively, 5.98× 1024 kg and7.36× 1022 kg. The distance from the cen-ter of the planet to the center of the moon is3.84× 108 m.

Determine the distance of this point fromthe center of the planet. The value of theuniversal gravitational constant is 6.67259 ×10−11 N·m2/kg2.


The Earth and the moon are attracted toeach other by gravitational force.

The more massive Earth attracts the lessmassive moon with a force that is (greaterthan, less than, the same as) the force withwhich the moon attracts the Earth.

1. less than

2. greater than

3. the same as



The mass of a certain neutron star is6× 1030 kg (3 solar masses) and its radiusis 3000 m.

What is the acceleration of gravity at thesurface of this condensed, burned-out star?The value of the universal gravitational con-stant is 6.67× 10−11 N ·m2/kg2.

Conceptual 05 0314:03, highSchool, numeric,> 1min, wording-

variable.

You weigh 800 N.What would you weigh if the Earth were

four times as massive as it is and its radiuswere two times its present value?


Part 1 of 2You weigh 150 lb.How much would you weigh if you were

standing on a mountain 200 km tall (equiva-lent to standing still at about the altitude of aspace shuttle orbit)? 4.45 N = 1 lb, the grav-itational constant is 6.67× 10−11 N ·m2/kg2,the radius of the Earth is 6.4× 106 m, and themass of the Earth is 6× 1024 kg.

Part 2 of 2How much does this differ from your weight

on the surface of the Earth?


Part 1 of 4Calculate the force of gravity on a 65 kg

person at the surface of the Earth. The accel-eration of gravity is 9.8 m/s2.

Part 2 of 4What force of gravity exists at two times theEarth’s radius?

Part 3 of 4What force of gravity exists at four times theEarth’s radius?

Part 4 of 4What is the relationship exhibited on a gravi-tational force vs distance graph?

1. inverse square

2. direct


3. exponential

4. quadratic


How much less would you weigh on the topof Mount Everest (elevation 8850 m) than atsea level? The value of the universal gravita-tional constant is 6.67× 10−11 N ·m2/kg2.

1. 0.5%

2. 0.3%

3. 4%

4. 2%

5. 3%

6. 5%

7. 0.2%

8. 0.4%

9. 0.1%

10. 1%


Part 1 of 2Calculate the weight of a solid rocket

booster of the space shuttle with mass590000 kg on Earth. The Earth has a mass of6× 1024 kg and a radius of 6.4× 106 m.

Part 2 of 2What would this weight be on Mars, withmass 0.11mE and radius 0.53RE? Thevalue of the universal gravitational constantis 6.67× 10−11 N ·m2/kg2.

Conceptual 05 1514:03, highSchool, multiple choice, > 1 min,wording-variable.

The height of a mountain is limited by theability of the atoms at the bottom to sustainthe weight of the materials above them. As-suming that the tallest mountains on Earth(at about 8850 m) are near this limit, how tallcould that mountain be on Mars, with mass0.11Me, and radius 0.53Re?

1. 22667.9 m

2. 52610.2 m

3. 1488.73 m

4. 3455.22 m

5. 26548.7 m

6. 26305.1 m

7. 105220.4 m

8. 46587.2 m


If you moved to a planet that has the samemass as the Earth but twice the diameter,how would your weight be affected?

1. 2 times as much

2.1

4as much

3. the same

4.1

2as much

5. 4 times as much

6. 8 times as much


7.1

6as much

8. None of these


If you moved to a planet that has twice themass of the Earth and also twice the diameter,how would your weight be affected?

1. 2 times as much

2.1

4as much

3. the same

4.1

2as much

5. 4 times as much

6. 8 times as much

7.1

6as much


The environment in a satellite or space sta-tion orbiting the Earth is often referred toas weightless environment; however, we havedefined weight as the force of gravity on anobject.

In this sense, what statement is not correctconcerning an object on board an orbitingsatellite?

1. There is a force of gravity on the object.

2. The object is weightless.

3. The weight of an object in orbit is only afew percent less than it is on the Earth.

4.We refer to the object in orbit as weight-less because it is accelerating toward the

Earth, but it is not actually weightless.

Figuring Physics 1114:03, highSchool, multiple choice, < 1 min,wording-variable.

When at rest on the launching pad, theforce of gravity on the space shuttle is quitehuge.

When in orbit, some 200 km above Earth’ssurface, what is the force of gravity on theshuttle? Neglect changes in the weight of thefuel carried by the shuttle.

1. nearly as much

2. about half as much

3. nearly zero (micro-gravity)

4. zero


Consider a giant flat plate that touches theEarth at one point and extends out into space.Suppose you slide an iron block along theplane, where it makes contact with the Earth.Suppose also, that the plate is perfectly fric-tionless, air drag is absent, and vo < vescape.

The block will

1. continue at constant velocity, according


to the law of inertia.

2. increase in speed as the force of gravityweakens with distance.

3. decrease in speed due to the pull of grav-ity.

4. oscillate to and fro.


In what sense does the moon “fall”?

1. The moon moves in a straight line towardthe Earth.

2.The moon falls away from the straight lineit would follow if there were no forces actingon it.

3. Some stones on the moon drop from ittoward the Earth.


What do we call the gravitational force be-tween the earth and your body?

1. weight

2. mass

3. Newton

4. gravitation

5. velocity

Two Satellites14:03, highSchool, multiple choice, > 1 min,fixed.

Two satellites A and B with the same massorbit the Earth in concentric orbits. The

distance of satellite B from the earth’s centeris four times that of satellite A.

What is the ratio of the tangential speed ofsatellite B to that of satellite A?

1.vBvA

=1

2

2.vBvA

=1

64

3.vBvA

=1

16

4.vBvA

=1

4

5.vBvA

= 2

6.vBvA

= 4

7.vBvA

= 16

8.vBvA

= 64

Two Satellites in Orbit 0114:03, highSchool, multiple choice, > 1 min,fixed.

Part 1 of 2Two satellites A and B orbit the Earth in

the same plane. Their masses are m and6m, respectively, and their radii r and 3 r,respectively.

3 r

r

6m

B m

A

What is the ratio of the orbital speeds?

1.vBvA

=1√3


2.vBvA

= 9

3.vBvA

=1

9

4.vBvA

=1

2

5.vBvA

=1

3

6.vBvA

= 3

7.vBvA

=1√2

8.vBvA

=√2

9.vBvA

=√3

10.vBvA

= 2

Part 2 of 2Let 10RE be the distance of the satellite Afrom the center of the Earth, where RE is theradius of the Earth.

What is the gravitational acceleration dueto the Earth at satellite A? g is the gravita-tional acceleration at the surface of the Earth.

1. gA =g

100

2. gA =g

121

3. gA = g

4. gA =g

10

5. gA =g√10

6. gA =g

11

7. gA =g√11

8. gA =g

81

9. gA =g

9

10. gA =g

3

Two Satellites in Orbit 0314:03, highSchool, multiple choice, > 1 min,

wording-variable.

Part 1 of 2Two satellites A and B orbit the Earth in

the same plane. Their masses are 4m and7m, respectively, and their radii 3 r and 7 r,respectively.

7 r

3 r

B

7m

A

4m

What is the ratio of their orbital speeds?

1.vBvA

=

√

3

7

2.vBvA

=

√

7

3

3.vBvA

=

√

7

4

4.vBvA

=

√

4

7

5.vBvA

=

√

49

12

6.vBvA

=

√

12

49

7.vBvA

=

√

4

3

8.vBvA

=

√

3

4

9. None of these

Part 2 of 2Let the distance of the satellite A from thecenter of the Earth be 10RE , where RE is theradius of the Earth.


What is the gravitational acceleration dueto the Earth at satellite A? Denote the grav-itational acceleration at the surface of theEarth by g.

1. gA =g

121

2. gA = g

3. gA =g

10

4. gA =g√10

5. gA =g

100

6. gA =g

11

7. gA =g√11

8. gA =g

81

9. gA =g

9

10. gA =g

3

Two Satellites in Orbit 0414:03, highSchool, multiple choice, > 1 min,wording-variable.

Two satellites A and B orbit the Earth inthe same plane. Their masses are 5m and6m, respectively, and their radii 4 r and 5 r,respectively.

5 r

4 r

B

6m

A

5m

What is the ratio of their orbital speeds?

1.vBvA

=

√

4

5

2.vBvA

=

√

5

4

3.vBvA

=

√

6

5

4.vBvA

=

√

5

6

5.vBvA

=

√

3

2

6.vBvA

=

√

2

3

7.vBvA

=

√

25

24

8.vBvA

=

√

24

25

9. None of these

Chapter 14, section 4, Gravitation Inside the Earth 388


If the earth were of uniform density, whatwould be the value of g inside the earth at halfits radius? (The value of g at the surface ofearth is 9.8 m/s2.)

1. 4.9 m/s2

2. 9.8 m/s2

3. 19.6 m/s2

4. 39.2 m/s2

Chapter 14, section 5, Kepler’s Laws: Planetary and Satellite Motion 389


The eccentricity of an ellipse is a measure ofhow elongated (or oval) it is. It is defined fora planet’s orbit as the distance between thetwo foci divided by twice the average distanceto the sun, which resides at one of the foci.

focusSun

a

b

The eccentricity of a planetary orbit is de-fined as the ratio of the distance between thefoci and twice the average distance to the sun.A perfect circle has an eccentricity of zerosince the two foci are in the same position.

The eccentricities for several solar systemobjects are shown in the table below. All dataare in terms of the average distance of theEarth from the Sun, called the astronomicalunit (AU).

Object f1 + f2 Average(AU) Distance

Earth 0.017 1.0Mars 0.14 1.52Pluto 9.8 39.5

Halley’s comet 17.4 17.9

Which object has the most nearly ellipticalorbit?

1. Halley’s Comet

2. Mars

3. Pluto

4. Earth

Conceptual 03 09


Consider the orbit of a typical cometaround the sun, which is marked at five dif-ferent positions, X , S, Z, P, and U .

Sun

a

bP

SU

X

Z

Using Kepler’s second law of planetary mo-tion, rank those positions in order of their rel-ative speeds, with the position for the fastestspeed first.

1. P S U X Z

2. Z X U S P

3. U S P Z X

4. X Z P S U

5. Z P S X U

6. U X S P Z


The four Galilean moons of Jupiter are Io,Europa, Ganymede, and Callisto. Their aver-age distances from Jupitor and orbital periodsare listed below in terms of Io’s values.

Moon Relative Relativeaverage distance obital period

Io 1.00 1.00Europa 1.59 2.00

Ganymede 2.54 4.05Callisto 4.46 9.42


After plotting the square of the relative or-bital period versus the cube of the relativeaverage distance for each moon and identify-ing the pattern you find in your graph, doyou agree or disagree that Kepler’s third law(as applied to the moons of Jupiter) holds forJupiter’s four Galilean moons?

1. In agreement with Kepler’s third law.

2. Cannot be determined from given data.

3. Not in agreement with Kepler’s thirdlaw.

4. Kepler’s third law does not require ex-perimental verification since time cannot berelated to distance.


How long would our year be if our Sunwere half its present mass and the radius ofthe Earth’s orbit were two times its presentvalue?


When Galileo first observed the four largestmoons orbiting the planet Jupiter, he quicklydetermined the time it took for each moon tocomplete one orbit but didn’t determine themasses of the moons.


1. He couldn’t determine the masses of themoons because the orbital period of satellitedepends on the mass of the planet or star it isorbiting, not on the satellite’s mass.

2. If we knew the distance from Jupiter toone of its moons and the orbital period ofthat moon, we could determine the mass ofJupiter.

3. We can determine the mass of Jupiterwithout knowing the orbital period of itsmoons.


How is Newton’s law of gravitation relatedto Kepler’s third law of planetary motion?

1.Newton’s law of gravitation contains moreinformation than Kepler’s third law.

2. Kepler’s third law contains more informa-tion than Newton’s law of gravitation.

3. The two laws contain exactly the sameinformation.

4. There is no relationship.

Conceptual gravity14:05, highSchool, multiple choice, < 1 min,fixed.

Given:

k =4π2

GMs,

whereMs is the mass of the Sun.Suppose that the gravitational force law

between two massive objects is

Fg =Gm1m2

r2+ε,

where ε is a small number.Which of the following would be the rela-

tionship between the period T and radius r ofa planet in circular orbit?

1. T 2 = k r 3+2 ε

2. T 2 = k r 3+ε

3. T 2 = k r 3−ε

4. T 2 = k r 3−2 ε

5. T 2 = k r 3+2/ε


6. T 2 = k r 3/ε

7. T 2 = k r 2+3 ε

8. T 2 = k r 2−3 ε

9. T 2 = k r 3 ε

10. T 2 = k r 3


Since the moon is gravitationally attractedto the Earth, why doesn’t it simply crash intothe Earth?

1.When the moon moves close to the Earth,the air on the Earth repels it.

2. The moon does not have enough speed tocrash into the Earth.

3. The moon’s tangential velocity keeps themoon coasting around the Earth rather thancrashing into it.

4. The Sun attracts the moon so that themoon cannot move closer the Earth.


When the space shuttle coasts in a circularorbit at constant speed about the Earth, is itaccelerating? If so, in what direction?

1. No acceleration

2. Yes; toward the Earth’s center.

3. Yes; in a direction from the Earth to themoon.

4. Yes; in a direction from the moon to theSun.


Which planets have a period of rotationaround the Sun greater than 1 Earth year?

1. Those closer to the sun

2. Those farther from the sun

3. Additional information is needed.

4. It depends on the planet’s mass.


Would the speed of a satellite in close circu-lar orbit about Jupiter be greater than, equalto, or less than 8 km/s?

1. greater than

2. equal to

3. less than



Two planets are never seen at midnight.Which two?

1. Jupiter and Mars

2. Neptune and Pluto

3. Saturn and Jupiter

4. Neptune and Mercury

5. Venus and Mercury

Hewitt CP9 10 E32



What is the shape of the orbit when thevelocity of the satellite is everywhere perpen-dicular to the force of gravity?

1. rectangle

2. parabola

3. hyperbola

4. circle

5. ellipse


If the Space Shuttle circled the Earth ata distance equal to the Earth-moon distance,how long would it take for it to make a com-plete orbit?

1. 28 days

2. 35 days

3. 365 days

4. 7 days

5. 24 hours


A “geosynchronous” Earth satellite can re-main directly overhead in which of the follow-ing cities?

1. San Francisco

2. Singapore

3. Sidney

4. London

5. Moscow


If you stopped an Earth satellite dead in itstracks, it would simply crash into the Earth.

Why, then, don’t the communications satel-lites that hover motionless above the samespot on Earth crash into the Earth?

1. The satellites are not attracted by theEarth.

2. The satellites’ orbital period coincideswith the daily rotation of the Earth.

3. The moon attracts the satellites at thesame time.

4. There is no power on the satellites.


Part 1 of 2What astronomical event would be seen by

observers on the moon at the time the Earthwas seeing a lunar eclipse?

1. The Sun is in the shadow of the Earth.

2. The Earth is behind the Sun.

3. The observer is in the middle of the Earthand the Sun.

4. None of these

Part 2 of 2What astronomical event would be seen byobservers on the moon at the time the Earthwas seeing a solar eclipse?


1. The Sun is in the shadow of the Earth.

2. The Earth is behind the Sun.

3. The observer is in the middle of the Earthand the Sun.

4. None of the above is correct.

Kepler14:05, highSchool, multiple choice, < 1 min,fixed.

Which are the correct statements regardingKepler’s laws?A. They were obtained first by Tycho Brahe.B. They were obtained by Kepler from

Brahe’s observations combined with New-ton’s second law.

C. They were deduced by Kepler fromBrahe’s observations.

D. They were derived by Newton from hisgravitational and second laws.

E. They were derived by Newton using hisgravitational and second law togetherwith Brahe’s data.

1. A, B, and C

2. C and D

3. A and D

4. B and D

5. C and E

6. A and E

7. B and E

Solar System 0114:05, highSchool, multiple choice, > 1 min,fixed.

When considering only the Sun, Earth,Mercury, and Mars in a planetary system,which statement is correct?

1. None of these is correct.

2. The Sun is fixed and the Earth goesaround it.

3. The Earth is fixed and the Sun goesaround it.

4. Neither the Earth nor the Sun go aroundone another.

5. The Earth only goes around the Sun dur-ing daylight.

6. The Sun only goes around the Earth dur-ing daylight.

Solar System 0214:05, highSchool, multiple choice, > 1 min,fixed.

When considering only the Sun, Earth,Mercury, and Mars in a planetary system,which statement is correct?

1.Mars and Mercury go around the Earth.

2. The Sun, Earth, Mars, and Mercury allgo around each other with the same angularmomentum.

3.Mars goes around the Sun in the oppositeangular direction from Mercury.

4.Mars goes around the Earth but Mercurydoesn’t go around the Earth since its orbit issmaller.

5. At night the Earth stops until morningand then goes around the Sun during daytimeonly.

6. At night the Sun stops until morning andthen goes around the Earth during daytimeonly.

Solar System 0314:05, highSchool, multiple choice, < 1 min,fixed.


Kepler’s third law states that the orbitalperiod squared T 2 is propotional to the semi-major axis cubed R3 ; i.e.,

T 2 ∝ R3 .

For convenience let us assume an imaginarysolar system and choose orbits for the planetswhose periods are integral multiples of eachother, for example

RMercury = 1.9842511315 ≈ 2 ,

REarth = 5 ,

RMars = 7.93700526 ≈ 8 ,

TMercury

TEarth=

√

( REarth

RMercury

)3

= 4 ,

TEarth

TMars=

√

(RMars

REarth

)3

= 2 .

The upper diagram shows a Sun concentricdiagram of a solar system. This diagramwas proposed by Galileo Galilei (an Italianscientist 1564-1642).

What is the lower diagram?

1. A coordinate transform from the upperdiagram to the Earth’s frame of reference sothe lower diagram is a physical description ofthis solar system.

2. The Sun is fixed and the Earth goesaround it so the lower diagram is an imag-inary artist conception of the Earth at thecenter of the universe and is an unphysicaldescription of this solar system.

3. The Earth is fixed and the Sun goesaround it so the lower diagram is a physi-cal description of this solar system.

4. Neither the Earth nor the Sun go aroundone another so the lower diagram is an un-physical description of this solar system.

5. The Earth only goes around the Sun dur-ing daylight so the lower diagram is an un-physical description of this solar system.

6. The Sun only goes around the Earth dur-ing daylight so the lower diagram is an un-physical description of this solar system.

Chapter 14, section 6, The Gravitational Field 395


Why will the gravitational field intensityincrease on the surface of a shrinking star?

1. The matter increases.

2. The density becomes larger.

3. The matter becomes more compact.

4. The star rotates faster.

Chapter 14, section 7, Gravitational Potential Energy 396

Potentials of 2 Reference Pnts14:07, highSchool, multiple choice, > 1 min,fixed.

Part 1 of 2G is the universal gravitational constant. g

is the free fall acceleration at Earth’s surface.RE is the mean radius of the Earth. ME isthe mass of the Earth.

Very near the Earth’s surface, the gravita-tional attraction of the Earth on a body ofmass m can be stated in terms of either g orG.

Since potential energy is defined only up toan arbitrary constant, only changes in poten-tial energy are meaningful; therefore, when wetalk about potential, we must give a referencevalue for the potential. Let Uo be the gravi-tational potential energy set equal to zero atthe surface of the Earth; let U∞ be the grav-itational potential energy set equal to zeroinfinitely far from the earth.

Which of the following correctly state thevalues of Uo and U∞ at an altitude h abovethe Earth’s surface?

1. Uo = mgh and U∞ = −mGME

REh

2. Uo = −mgh and U∞ = −mGME

RE + h


RE + h


R2E

h

Part 2 of 2Consider Uo and U∞. Which of the followingstatements are correct for h¿ RE .

Hint:1

1 + ε≈ 1− ε for ε¿ 1.

1. U∞(h)− U∞(h = 0) = Uo(h)

2. Uo increases with h, but U∞ decreaseswith h

3. the derivativesdUo

dh(h = 0) and

dU∞

dh(h =

0) are different

4. U∞(h)− U∞(h = 0) =GMEm

REh

Chapter 14, section 8, Escape Velocity 397

Estimate a Black Hole 0114:08, highSchool, numeric, > 1 min, normal.

A black hole is an object so heavy thatneither matter nor even light can escape theinfluence of its gravitational field. Since nolight can escape from it, it appears black.Suppose a mass approximately the size of theEarth’s mass 5.98 × 1024 kg is packed into asmall uniform sphere of radius r.

Use:

The speed of light c = 2.99792× 108 m/s .The universal gravitational constant G =6.67259× 10−11 Nm2/kg2 .

Hint: The escape speed must be the speedof light.

Based on Newtonian mechanics, determinethe limiting radius r0 when this mass (approx-imately the size of the Earth’s mass) becomesa black hole.


Of all the United States, why is Hawaiithe most efficient launching site for non-polarsatellites?

1. Hawaii is the warmest place in the US;less energy is needed.

2. There is not any strong cold wind inHawaii.

3. Hawaii is composed of small islands;launch failures can easily go into the sea in-stead of damaging residential areas.

4. Hawaii has a greater tangential speedabout the polar axis.


If the Earth shrank in size, with all otherfactors remaining the same, how would the

escape velocity from its surface change?

1. greater

2. smaller

3. the same


Chapter 14, section 9, Energy: Planetary and Satellite Motion 398

Rise to a Maximum Height14:09, highSchool, numeric, > 1 min, normal.

Consider an airless, non-rotating planet ofmass M and radius R. An electromagneticlauncher standing on the surface of this planetshoots a projectile with initial velocity v0 di-rected straight up. Unfortunately, due tosome error, v0 is less than the planet’s escapevelocity ve. Specifically, v0 = 0.5 ve.

Unable to escape the planet’s gravitationalpull, the projectile rises to a maximal heighth above the ground, then falls back to theground.

Calculate the ratio h/R of the projectile’smaximal height to the planet’s radius.

Chapter 15, section 1, States of Matter 399


In gaseous form, oxygen consists of O2

molecules and hydrogen consists of H2

molecules. Suppose that instead of H2

molecules, gaseous hydrogen consisted of Hatoms.

If this were the case, how much hydrogengas would be produced for each liter of oxygengas when water (H2O) is separated by anelectric current?

1. 1 liter

2. 2 liters

3. 4 liters

4. 0.5 liter


Aluminum electroplating is a process bywhich aluminum is coated onto a metal ob-ject. The object is submerged in a liquid solu-tion containing Al2O3 molecules. An electriccurrent breaks up these molecules into oxy-gen gas and aluminum atoms. The aluminumis attracted to the object to be coated andforms a thin aluminum film on its surface.

If a car bumper needs to be plated with300 g of aluminum using this electroplatingprocess, what mass of oxygen gas is produced?Assume a mass of 27 atomic mass units (amu)for each aluminum atom and 16 amu for eachoxygen atom.


Ammonia is a liquid that consists ofmolecules of (NH3) (one nitrogen atom withthree hydrogen atoms attached). Supposeammonia is separated into nitrogen (N2) gas

and hydrogen (H2) gas.If 1 liter of nitrogen is produced, what vol-

ume of hydrogen is produced?

1. 1 liter

2. 2 liter

3. 3 liter

4. 0.5 liter

5. 1.5 liter


Diamond and graphite are both solids com-posed of only carbon atoms.

Since all carbon atoms are chemically iden-tical, what accounts for the vastly differentproperties of graphite and diamond?

1. different shapes

2. different ordering of atoms

3. different movement of atoms


Which molecules have more average kineticenergy?

1. Those in 10 grams of ice

2. Those in 10 grams of steam

3. They have the same average kinetic en-ergy.


Why does crushed ice melt so much faster

Chapter 15, section 1, States of Matter 400

than an equal mass of ice cubes?

1. Crushed ice is smaller.

2. The crushing process raised the tempera-ture of the crushed ice.

3. Crushed ice has more exposed surface.

Chapter 15, section 2, Density and Specific Gravity 401


Why do ice cubes float?

1. Ice cubes are lighter than water.

2. Ice cubes are less dense than water.

3. Ice cubes are in a solid state.


If you mixed oil and vinegar in one con-tainer, which would you expect to end up ontop?

1. vinegar

2. oil

3. They couldn’t separate from each other.

4. They form a new substance which has adifferent property from oil and vinegar.

Chapter 15, section 3, Pressure 402


Why is the gas pressure inside an inflatedballoon always greater than the air pressureoutside?

1.Warmer air is inside the balloon.

2. The balloon is made of stretchy rubberthat pushes inward on the gas.

3. Cooler air is inside the balloon.

4. The pressure is actually less; that’s whyinflated balloons rise. The stretched rubbersupplies an inward force (and pressure).


Part 1 of 2You blow up an ordinary party balloon with

air until it has a diameter of 6 inches. Yourfriend blows up another balloon with heliumgas until it has a diameter of 12 inches. Airconsists mostly of O2 and N2 molecules, whilehelium gas consists of He atoms. Assume thepressure in each balloon is the same.

What is the ratio the number of heliumatoms to the total number of O2 and N2

molecules?

Part 2 of 2Air is about 80% nitrogen and 20% oxygen.

What is the ratio of the weight of the he-lium balloon to the weight of the air-filledballoon? (Hint: Imagine that there are 80helium atoms in the helium balloon. Calcu-late the mass, in atomic mass units, of thisamount of helium, and then compare it to themass of the corresponding number of oxygenand nitrogen molecules.)


Why does the pressure of a gas double (pro-vided the temperature and volume of the con-tainer remain the same) if the number of gasatoms in container is doubled?

1. The frequency of the molecular collisionsdoubles when the number of molecules dou-bles.

2. The speed of the molecules doubles whenthe number of molecules doubles.

3. The attraction among the molecules dou-bles when the number of molecules dou-bles.

Conceptual 09 Q1515:03, highSchool, numeric, < 1 min, normal.

Atmospheric pressure is approximately15 lb/in2.

How much force does the air exert on100 in2 ?


Part 1 of 2A medic applies a force of 85 N to a 0.03 m2

area that is bleeding.What pressure did she apply?

Part 2 of 2What is this pressure in pounds per squareinch?


Part 1 of 2How much pressure is applied to the ground

by a 104 kg man who is standing on squarestilts that measure 0.05 m on each edge?

Part 2 of 2What is this pressure in pounds per squareinch?



Which situation is likely to hurt you more?

1. Your bare foot was stepped on by a 270-lbman wearing flat-soled loafer.

2. Your bare foot was stepped on by a 130-lbwoman wearing high heels.

3. Either



Part 1 of 2In a car lift, compressed air exerts a force on

a piston with a radius of 5 cm. This pressureis transmitted to a second piston with a radiusof 15 cm.

How large a force must the compressed airexert to lift a 13300 N car?

Part 2 of 2What pressure produces this force? Neglectthe weight of the pistons.


A 1.5 m wide by 2.5 m long water bedweighs 1025 N.

Find the pressure that the water bed exertson the floor. Assume that the entire lowersurface of the bed makes contact with thefloor.


The four tires of an automobile are inflatedto an absolute pressure of 200000 Pa. Eachtire has an area of 0.024 m2 in contact withthe ground.

Determine the weight of the automobile.


A pipe contains water at 500000 Pa aboveatmospheric pressure.

If you patch a 4 mm diameter hole in thepipe with a piece of bubble gum, how muchforce must the gum be able to withstand?


How much force does the atmosphere exerton 1.00 km2 of land at sea level?


A 70 kg man sits in a 5 kg chair so thathis weight is evenly distributed on the legs ofthe chair.Assume that each leg makes contactwith the floor over a circular area with aradius of 1 cm.

The acceleration of gravity is 9.81 m/s2 .What is the pressure exerted on the floor

by each leg?


Part 1 of 3A physics book has a height of 26 cm, a

width of 21 cm, and a thickness of 3.5 cm.The acceleration of gravity is 9.81 m/s2 .What is the density of the physics book if

it weighs 19 N?

Part 2 of 3Find the pressure that the physics book exertson a desktop when the book lies face up.

Part 3 of 3Find the pressure that the physics book exertson the surface of a desktop when the book isbalanced on its spine.



In testing a new material for shieldingspacecraft, 150 small ball bearings, each mov-ing at a supersonic speed of 400.0 m/s, collidehead-on and elastically with the material dur-ing a 1.00 min interval.

If the bearings each have a mass of 8.0 gand the area of the tested material is 0.75 m2,what pressure is exerted on the material?

Chapter 15, section 4, Fluids at Rest: Variation of Pressure with Depth 405

Barge in Fresh Water15:04, highSchool, numeric, < 1 min, normal.

Part 1 of 2A loaded flatbottom barge floats in fresh

water. The bottom of the barge is 3.5 m belowthe water line. When the barge is empty thebarge’s bottom is only 2.5 m below the waterline.

What is the difference between the pressureon the bottom of the loaded barge and thepressure at the water line?

Part 2 of 2If the surface area of the bottom of the bargeis 300 m2 what is the weight of the load in thebarge?


At what level (vertically) should you hold acut finger to reduce bleeding?

1. at the same level as your heart

2. as low as possible

3. as high as possible

4. as far from your heart as possible at anylevel

Concept 13 1a15:04, highSchool, numeric, < 1 min, normal.

A water pool is 220 m deep. The density ofwater is 1000 kg/m3.

What is the pressure at the base of the pool?(Neglect the pressure due to atmosphere.)

Concept 13 715:04, highSchool, multiple choice, > 1 min,fixed.

You want a blood pressure reading as closeas possible to that of your heart.

Where should you place the cuff?

1. at a level even with the heart

2. anywhere the cuff will fit

3. at a level below the heart

4. at a level above the heart

Concept 13 E0115:04, highSchool, numeric, > 1 min, normal.

The depth of water behind the Hoover Damin Nevada is 220 m.

What is the water pressure at a depth of220 m? The weight density of water is 9800N/m3.


Where would it be the most difficult todraw soda through a straw?

1. the top of a very high mountain

2. sea level

3. the bottom of a deep mine

4. The elevation makes no difference atall.


Put the following heights in the order of airdensity with the most dense point first:A) Earth surfaceB) low atmosphere (just above high moun-

tains)C) high atmosphere (way above jet flights)D) deep mineE) the bottom of an imaginary hole drilled to

the center of the Earth


1. ABDEC

2. ABDCE

3. EDABC

4. DACEB

5. DACBE

6. DAEBC


When an air bubble rises in water, whathappens to its mass, volume, and density?

1. All three are conserved.

2. Mass doesn’t change; volume decreasesand density increases.

3. Mass doesn’t change; volume increasesand density decreases.

4. Volume doesn’t change; mass and densitydecrease.

5. Volume doesn’t change; mass anddesnisty increase.

6. Density doesn’t change; mass and volumeincrease.

7. Density doesn’t change; mass and volumedecrease.


Part 1 of 3A column of water has a diameter of 2 m

and a depth of 10 m.How much pressure is at the bottom of the

column?

Part 2 of 3

What is the weight of this column of water?

Part 3 of 3What would be the pressure if the column hada radius of 8 m and the same depth?


Would the pressure at the bottom of a 3-foot holding tank be different if the tank heldmotor oil instead of water?

1. Yes; the pressure at the bottom will begreater.

2. Yes; the pressure at the bottom will beless.

3. No; the pressures would be the same.

4. It depends on the brand of motor oil.


The pressure in a 3-foot-deep lake is P1.The pressure in a 3-foot-deep hot tub 2 metersin diameter is P2.

What relationship would P1 and P2 have?

1. P1 > P2

2. P1 < P2

3. P1 = P2



In a deep dive, a whale is appreciably com-pressed by the pressure of the surroundingwater.

What happens to the whale’s density?



2. Its density remains the same as before.

3. Its density decreases.

4. Its density increases.


Part 1 of 2A person rides up a lift to a mountain top,

but the person’s ears fail to “pop”; that isthe pressure of the inner ear does not equalizewith the outside atmosphere. The radius ofeach eardrum is 0.4 cm. The pressure ofthe atmosphere drops from 101000 Pa at thebottom of the lift to 99800 Pa at the top.

What is the net pressure on the inner earat the top of the mountain?

Part 2 of 2What is the magnitude of the net force oneach eardrum?

Holt SF 09C 0115:04, highSchool, numeric, > 1 min, fixed.

The Mariana Trench, in the Pacific Ocean,is about 11 km deep.

The acceleration of gravity is 9.81 m/s2 .If atmospheric pressure at sea level is

101000 Pa and the density of sea water is1025 kg/m3, how much pressure would a sub-marine need to be able to withstand to reachthis depth?


Part 1 of 2A container is filled with water to a depth

of 20 cm. On top of the water floats a 30 cmthick layer of oil with a density of 700 kg/m3.

The acceleration of gravity is 9.81 m/s2 .What is the absolute pressure at the surface

of the water?

Part 2 of 2What is the absolute pressure at the bottomof the container?


A beaker containing mercury is placed in-side a vacuum chamber in a laboratory. Thepressure at the bottom of the beaker is27000 Pa.

The acceleration of gravity is 9.81 m/s2 .What is the height of the mercury in the

beaker?

Holt SF 09C 0415:04, highSchool, numeric, > 1 min, fixed.

The acceleration of gravity is 9.81 m/s2 .Calculate the depth in the ocean at which

the pressure is three times atmospheric pres-sure.


Part 1 of 2A submarine is at an ocean depth of 250 m.

Assume that the density of sea water is1025 kg/m3 and the atmospheric pressure is101000 Pa .

The acceleration of gravity is 9.81 m/s2 .Calculate the absolute pressure at this

depth.

Part 2 of 2Calculate the magnitude of the force exertedby the water at this depth on a circular sub-marine window with a diameter of 30 cm.


Part 1 of 2A circular swimming pool at sea level has

a flat bottom and a 6 m diameter. It is filledwith water to a depth of 1.5 m.

What is the absolute pressure at the bot-


tom? The acceleration of gravity is 9.81 m/s2 .

Part 2 of 2Two people with a combined mass of 150 kgfloat in the pool.

What is the resulting increase in the aver-age absolute pressure at the bottom?

Pressure vs Depth15:04, highSchool, multiple choice, < 1 min,fixed.

Part 1 of 2Two open-top containers, #1 on the left

and #2 on the right, with equal base area Aare placed on two scales. The #2 containeron the right has an lower diameter twice thatof its upper diameter and the height of itslower (larger) diameter is half that of its waterheight. Both containers are filled with waterto the same height H, as shown below.

ScaleScale

H = 2h

h

D = 2 dD = 2 d

d

left right#1 #2

What is the relationship between the forceexerted by the water on the bottom surface ofthe containers?

1. F left > F right

2. F left = F right

3. F left < F right

4. cannot be determined

Part 2 of 2

What is the relationship between the weightsexerted by the flasks on the scales supportingthe containers?

1.W left =W right

2.W left = 2W right

3.W left =3

2W right

4.W left =4

3W right

5.W left =5

3W right

6.W left =7

4W right

7.W left =8

5W right

8.W left =7

5W right

9.W left =6

5W right


Chapter 15, section 5, Pressure Measurements (Atmospheric, Gauge) 409


If a liquid only half as dense as mercurywere used in a barometer, how high wouldits level be on a day of normal atmosphericpressure (when the mercury barometer reads76 cm)?

1. 19 cm

2. 38 cm

3. 76 cm

4. 152 cm

5. 304 cm


A mercury barometer reads 760 mm at sealevel. When it is carried to an altitude of 5.6km, the height of the mercury column is 380mm.

If the barometer is taken to an altitude 11.2km, what will the reading be?

1. 760 mm

2. 380 mm

3. zero

4. less than 760 mm, but more than 380mm

5. less than 380 mm, but more than zero

Chapter 15, section 6, Pascal’s Principle (Hydraulics) 410


A piston A has a diameter of 0.64 cm, asshown. A second piston B has a diameter of3.8 cm.

A

B

500 NF

In the absence of friction, determine theforce ~F necessary to support the 500.0 Nweight.


An engineer weighs a sample of mercury(ρ = 13.6 × 103 kg/m3) and finds that theweight of the sample is 4.5 N.

The acceleration of gravity is 9.81 m/s2 .What is the sample’s volume?


A hydraulic brake system is shown. Thearea of the piston in the master cylinder is6.40 cm2, and the area of the piston in thebrake cylinder is 1.75 cm2. The coefficient ofkinetic friction between the brake shoe andthe wheel drum is 0.500.

Master cylinderBrake cylinder

Brake shoe

µk = 0.5

Wheel drum

Pedal

How large is the frictional force between thebrake shoe and the wheel drum when a forceof 44 N is exerted on the pedal?

Chapter 15, section 7, Buoyant Forces and Archimedes’ Principle 411

An Ax and a Piston15:07, highSchool, multiple choice, > 1 min,fixed.

Consider a steel ax and an aluminum pis-ton. (Note that steel is denser than alu-minum.) When weighed in water, the ax andthe piston have the same apparent weight.

But when the same ax and the same pistonare weighed in air,

1. they again have equal weights, but bothare heavier than they are in water.

2. the ax is heavier than the piston.

3. they again have equal weights, but bothare lighter than they are in water.

4. the piston is heavier than the ax.

5. the longer object weighs more than theother.

6. the wider object weighs more than theother.

Balloon trick15:07, highSchool, multiple choice, < 1 min,fixed.

Note: Helium is lighter than air.Imagine you are on a bus with a helium

balloon tied on a string tied to the seat infront of you. The bus stops short to avoidrunning over a rabbit and you are thrownforward.

What happens to the balloon in relation tothe bus?

Hint: Try it!

1. The balloon moves forward.

2. The balloon moves backward.

3. The balloon’s position does not change.

4. The balloon pops.

Bricks Under Water15:07, highSchool, multiple choice, < 1 min,fixed.

Imagine holding two identical bricks underwater. Brick A is just beneath the surface ofthe water, while brick B is at a greater depth.

What is the force needed to hold brick B inplace? (Assume the density of water doesn’tchange with height.)

1. larger

2. the same as

3. smallerthan the force required to hold brick A in

place.


A block of aluminum with a volume of 1cm3 is placed in a beaker of water filled to thebrim and sinks. Water overflows. The samehappens in another beaker with a 1 cm3 blockof lead.

The lead will displace (more, less, the sameamount of) water than the aluminum blockdoes.

1. more

2. less

3. the same

4. It cannot be determined without a directmeasurement.


A block of aluminum with a mass of 1 kgis placed in a beaker of water filled to thebrim and sinks. Water overflows. The same


happens in another beaker with a 1 kg blockof lead.

The lead will displace (more, less, the sameamount of) water than the aluminum blockdoes.

1. more

2. less

3. the same

4. It cannot be determined without a directmeasurement.


Assume you are floating in water with yourlungs full of air. When you exhale, you sinklower in the water.

What is a possible explanation of the sink-ing effect?

I) Your volume decreases and so does thebuoyant force.

II) Your mass decreases as you let the airout of your lungs making it easier foryou to sink.

III) Your overall density decreases.IV) Your overall density increases.

1. I only

2. II only

3. III only

4. IV only

5. I and II only

6. I and III only

7. I and IV only

8. II and III only

9. II and IV only

10. I, II, and III only


Do the stones hurt your feet less or more inthe water than on the stony beach? Explain.

1. It feels exactly the same; our mass doesn’tchange, so we press down on our feet in thesame way.

2. The stones hurt more in the water; thebuoyant force increases as we go deeper.

3. The stones hurt less in the water; thebuoyant force lifts us up.

4. As you enter the water they hurt moreat first and then less; until we start floatingwe “sink” onto the stones, but once we startfloating the displaced water lifts us up.


If liquid pressure were the same at alldepths, would there be a buoyant force onan object submerged in the liquid?

1. No; buoyant force is the result of differ-ences in pressure.

2. Yes; directed down

3. Yes; it is determined by the volume of thesubmerged object.

4. Yes; it pushes an object out of liquid.

5. Yes; but it will be very small.



Why does a can of diet drink float in water,while a can of regular soda sinks?

1. Regular soda has fewer gas bubbles.

2. Sugar is heavier than a sugar substitute.

3. Diet soda is less dense than a regularsoda.

4. It depends on the brand and the actualingredients.

5. Diet soda cans are slightly smaller.


Do light objects tend to sink or float? Cansomething similar be concluded about heavyobjects?

1. All light objects float.

2. Most heavy objects sink.

3. Weight is not the critical factor; it alsodepends on volume.

4. There is a critical mass for each mate-rial that determines whether or not it willfloat.


A piece of iron is sitting on a block of woodfloating in water.

If the iron were instead suspended beneaththe wood, would the wood float at the samelevel, lower, or higher?

1. Definitely lower, because the iron is underthe wood.

2. Higher, because there is a buoyant forceacting on the iron now.

3. It would float only slightly lower, becausethe iron displaces a little water and the overallwater level rises.

4. It depends on the ratio of iron and woodvolumes.

5. It would float at the same level.


Compared to an empty ship, would a shiploaded with a cargo of Styrofoam sink deeperor rise in the water?

1. Since Styrofoam pushes down on the shipwith its weight, the ship sinks deeper.

2. Since Styrofoam is less dense than water,the ship rises.

3. The ship will float at the same level be-cause its density hasn’t changed.

4. It depends on the weight of the Styro-foam.


Part 1 of 2A barge filled with scrap iron is in a canal

lock.If the iron is thrown overboard, does the

water level rise, fall or remain unchanged?

1. It falls.

2. It rises.

3. It remains unchanged.

4. It depends on the amount of iron.

Part 2 of 2


If the barge were to sink what would happento the water level?

1. It would fall.

2. It would rise.

3. It would remain unchanged.

4. It would depend on its mass.


A balloon is weighted so that it is barelyable to float in water.

What will happen if it is pushed beneaththe surface?

1. It will come back up.

2. It will stay at the depth to which it ispushed.

3. It will sink.

4. It depends on the speed it was pushedbeneath the surface.

5. It depends on how deep it was pushedbeneath the surface.


Bodies float higher in salt water than infresh water.

Which of the following is incorrect?

1. Fresh water is denser than salt water.

2. A body floats higher in a denser fluid.

3. A body does not have to sink as far in adenser fluid to displace a weight of fluid equalto its own weight.

4. A smaller volume of the displaced denserfluid is able to match the weight of the floatingbody.


A ship sailing from the ocean into a freshwater harbor sinks slightly deeper into thewater.

How does the buoyant force on it change?

1. It increases slightly.

2. It increases a lot.

3. It decreases slightly.

4. It decreases a lot.

5. It doesn’t change at all.


The weight of the human brain is about 15N. The buoyant force supplied by the fluidsurrounding the brain is about 14.5 N.

What can you conclude about the weight offluid surrounding the brain?

1. The fluid weighs 14.5 N.

2. The fluid weighs at least 14.5 N.

3. The fluid weighs less than 14.5 N.

4. The fluid weighs 0.5 N.

5. The fluid weighs at least 0.5 N.

6. The fluid weighs less than 0.5 N.

7. The information provided says nothingabout the weight of the brain fluid.

Concept 13 38



The relative densities of water, ice, andalcohol are 1.0, 0.9, and 0.8 respectively.

Which of the following is true about icecubes floating in a mixed alcoholic drink?

1. Ice cubes will sink to the bottom of amixed drink.

2. Ice cubes will float in a mixed drink, butnot as high as they would in water.

3. In a drink that is predominantly alcoholice cubes will float the highest.


How does the water level in a glass changewhen a floating ice cube melts?

1. It rises.

2. It falls.

3. It remains unchanged.

4. It depends on the size of the piece of ice.

5. It depends on how many air bubbles weretrapped inside of the ice cube.


A bucket of water is on a spring scale.How will the scale reading change if a fish

is placed in the bucket?

1. Increases if the bucket does not overflow;remains the same otherwise.

2. Increases if the bucket does not overflow;decreases otherwise.

3. Increases in both cases.

4. Decreases in both cases.


Would a fish float to the surface, sink, orstay at the same depth if the gravitationalfield of the Earth increased?

1. float

2. sink

3. stay at the same level

4. Neither. The fish would collapse or ex-plode.


Which of the following would you experi-ence when swimming in water in an orbitingspace habitat where simulated gravity is halfthat of our gravity?

1. float in the water as you do on Earth

2. float lower than you would on Earth

3. float higher than you would on Earth

4. sink to half of the depth of the “spacepool”

5. sink to the bottom

Concept 13 E0215:07, highSchool, numeric, < 1 min, normal.

A 6 kg piece of metal displaces 1 L of waterwhen submerged.

What is its density?

Concept 13 E03



Part 1 of 2A rectangular barge 5 m long and 2 m

wide floats in fresh water. Water density is1000 kg/m3.

How much deeper will it float when loadedwith a 400 kg horse?

Part 2 of 2If the barge can only be pushed 27 cm deeperinto the water before water overflows to sinkit, how many 400 kg horses can it carry?


You lower a 1 kg solid gold statue into acontainer of water and measure the volume ofdisplaced water.

What volume will verify that it is pure goldif the density of gold is 19.3 g/cm3?

Concept 13 E0715:07, highSchool, numeric, > 1 min, normal.

An ice cube measures 10 cm on the side,and floats in water. One cm extends abovethe water level.

If you shave off the 1 cm above the water,how many cm of the remaining ice wouldextend above water level?


A partially filled plastic container floats inthe ocean with 90% of its volume below thesurface. The density of the ocean water is1025 kg/m3.

What it the container’s average density?

Concept 13 E1015:07, highSchool, multiple choice, > 1 min,wording-variable.

A salvage ship is able to raise a containerfilled with unknown material from the oceanfloor to the water surface, but cannot raise it

above the water. The ship captain knows thatthe overall density of the container is 5 timesthe density of water, and he wonders whetherone other ship with a crane of equal capacitywill be enough to help him lift the containerabove the water, or whether he will need thehelp of more than one additional ship.

How many ships with equal lifting capacitywill be required to lift the container?

1. two

2. three

3. four

4. five

5. six

6. seven

7. one

8. None of these


On a sensitive balance, weigh an empty flatthin plastic bag. Then weigh the bag whenair is in it.

Will the readings differ?

1. No, assuming the air is not compressed.

2. Yes, an empty bag weighs less because airinside would contribute to its weight.

3. Yes, an empty bag weighs more becausethe air inside tries to rise.

4. It depends on how much air is in thebag.

5. It depends on the type of plastic.

Concept 14 28


15:07, highSchool, multiple choice, > 1 min,fixed.

Put the following objects in order by theirweights with the heaviest first.

A) a glass bottle filled with air at atmo-spheric pressure;

B) a glass bottle filled with helium at at-mospheric pressure;

C) an empty glass bottle (vacuum inside).

1. A, B, C

2. A, C, B

3. B, C, A

4. B, A, C

5. C, A, B

6. C, B, A


A balloon’s size doesn’t change when he-lium in the balloon is replaced with less densehydrogen.

Does the buoyant force on the balloonchange?

1. Yes, because the balloon is now lighter.

2. Yes, because the buoyant force dependson the density.

3. No, because the volume is still the same.

4. It’s impossible to tell without a measure-ment.


A balloon filled with helium rises in the air.Will a steel tank rise if filled with helium?

1. Yes; if the tank has the same volume asthe balloon.

2. Yes; if the amount of helium is the sameas that in the balloon.

3. Yes; but it will take a lot more helium.

4. Yes; but the density of helium should bemuch less than that in the balloon.

5. No; to make the tank rise a different gasshould be used.

6. No; there is nothing you can fill the tankwith that will make it rise.


Two identical balloons of the same volumeare pumped up with air to more than atmo-spheric pressure and suspended on oppositeends of a stick that is horizontally balanced.One of the balloons is then punched.

Will the balance stick be upset?

1. No, because the balloons weigh the samewith or without air.

2. No, because the air inside of the balloonweighs as much as the displaced air.

3. No, because the punched balloon islighter, but at the same time the buoyantforce is smaller on it.

4. Yes, the remaining balloon will drop.

5. Yes, the remaining balloon will rise.


Two balloons with the same weight and vol-ume are filled with equal amounts of helium.


One is rigid and the other is free to expand asthe pressure outside decreases.

Which one will rise higher when released?

1. the rigid one

2. the expandable one

3. They will rise to the same level.

4. It’s impossible to predict.


You are hovering at low altitude in a hot-air balloon, neither accelerating upward nordownward. The total weight of the balloon(including its load) is 30,000 N.


1. The balloon displaces no air, because airis not a liquid.

2.The balloon displaces 30,000 liters of air.

3. The air displaced by the balloon weighs30,000 N.

4. The volume of the displaced air is 30,000cubic meters.

5. The air displaced by the balloon weighs30,000 liters times the density of air.


A dense plastic toy of mass 3 kg is floatingjust beneath the surface of a pond.

What is the buoyant force on it?


A piece of wood from a nearby constructionsite floats near the shore of a lake. It floats in

very calm water with half of its volume justabove the surface. The density of water is1000 kg/m3.

What is the density of this piece of wood?

1. 500 kg/m3

2. 2000 kg/m3

3. 125 kg/m3

4. 4000 kg/m3



Why do some iron objects such as shipsfloat when placed in water while other ironobjects such as nails sink?

1. They are composed of different types ofiron.

2. Iron ships have large air pockets insidethem, making them less dense than water andthus able to float.

3. The same reason that makes planes fly inthe sky.


If you submerge a flexible air-filled balloonunder water, what happens to the balloon’sdensity?

1. increases

2. decreases

3. remains the same

4. increases at first, then decreases


5. decreases at first, then increases



A flexible helium-filled party balloon is re-leased in the atmosphere.

As it gains altitude, what happens to thedensity of the balloon?

1. increases

2. decreases

3. remains the same





A helium-filled party balloon is released inthe atmosphere. Imagine that the balloon isrigid, so that its volume cannot change.

What happens to the buoyant force on theballoon as it gains altitude?

1. increases

2. decreases

3. remains the same





fixed.

Suppose that a volleyball A and a bowlingball B are completely submerged in water andhave the same volume, as in the figure. (Ofcourse, you would have to hold the volleyballbeneath the water to keep it from popping upto the surface.)

A B

Which feels a greater buoyant force?

1. volleyball A

2. bowling ball B

3. They feel the same buoyant force.



Suppose that a volleyball A floats on thewater, and a bowling ball B, being denserthan water, is completely submerged in water.Assume they have the same volume.

A

B

Which feels a greater buoyant force?

1. volleyball A

2. bowling ball B


3. They feel the same buoyant force.



Part 1 of 2A 20-N rock hangs from a spring scale. The

rock is lowered into a beaker of water that sitson another spring scale, but is not allowed totouch the bottom of the beaker.

How does the reading on the scale Achange?

B

A

1. increases

2. decreases

3. remains the same


Part 2 of 2How does the reading on scale B change?

1. increases

2. decreases

3. remains the same



Where would it be easiest to float, a verysalty sea or a fresh-water lake?

1. a very salty sea

2. a fresh-water lake

3. There is no difference.



Helga says that although it’s impossible towalk on a sea of water, it is possible to walkon a sea of mercury. She claims that if youstep into a pool of mercury, you will onlysink enough so that about half of your calfmuscles is submerged. Ali disagrees with herstatement.

Who is right and why?

1. Helga; mercury is much denser than wa-ter.

2. Ali; water and mercury have similar prop-erties. You’ll sink in the mercury, too.

3. Helga; mercury is a kind of metal butwater is not.


A wedge-shaped piece of wood floats in wa-ter with the widest part on the bottom andthe narrowest part on top.

water

If we want the wood to displace the least


amount of water, what should we do?

1. Turn it over.

2. Leave it as is.

3. Rotate it 90◦.

4. It doesn’t matter.

Cork in water15:07, highSchool, numeric, > 1 min, normal.

A cork is held at the bottom of a bucket ofwater by a piece of string. The actual depthof the cork is 0.7 m below the surface of thewater.

0.7 m

If the density of the cork is 200 kg/m3 andthe volume of the cork is 3 cm3, then whatis the tension in the string? g = 9.8 m/s2.Assme the density of water is 1000 kg/m3.

1. 0.02352 N

2. 0.2352 N

3. 0.01176 N

4. 2.352 N

Cube in Liquid and Oil e115:07, highSchool, numeric, > 1 min, normal.

A cube of wood whose edge is 12 mm is inequlibrium just submerged in a liquid with alayer of oil on top of the liquid as shown in thepicture.

Wood

air

oil

liquid

ho

h`

12 mm

The cube of wood has one of its faces par-allel to the liquid surface. The density ofwood is 1000 kg/m3, that of the liquid is1296 kg/m3, and that of the oil is 606 kg/m3.Determine the thickness,ho, of the layer ofoil.

Figuring Physics 1015:07, highSchool, multiple choice, > 1 min,fixed.

When you gently push down on the panof the scale, the display show an increase inforce. Likewise if you do the same on the rimof a beaker full of water.

scale

However, what if you immerse you finger inthe water, without touching the beaker?

Then the scale reading

1. shows an increase.

2. doesn’t change.

3. shows a decrease.



Consider a solid brass cube and a solid brasssphere that have equal surface areas.

When both are completely submerged inwater, the one experiencing the greater buoy-ant force is the

1. cube.

2. sphere.

3. Both the same

4. Not enough information given


A pair of identical balloons are inflated withair and suspended on the ends of a stick thatis horizontally balanced. When the balloonon the left is punctured, the balance of thestick is

1. upset and the stick rotates clockwise.

2. upset and the stick rotates counter-clockwise.

3. unchanged.

Floats in Water Sinks in Oil15:07, highSchool, multiple choice, > 1 min,fixed.

Consider an object that floats in water butsinks in oil. When the object floats in water,half of the object is submerged.

If oil is poured slowly onto the top of the ob-

ject until the oil completely covers the object,the object will

1. rise

2. stay at the same position

3. lower

4. more information on the density of theobject and fluids is needed.


What is wrong?

1.A piece of solid copper sinks in a containerof molten copper.

2. A piece of solid iron sinks in a containerof molten iron.

3. A piece of solid aluminum sinks in a con-tainer of molten aluminum.

4. A piece of ice sinks in a container ofmolten water.


Part 1 of 2A piece of metal weighs 50.0 N in air, 36.0

N in water, and 41.0 N in an unknown liquid.a) Find the density of the metal.

Part 2 of 2b) Find the density of the unknown liquid.


A 2.8 kg rectangular air mattress is 2.00 mlong, 0.500 m wide, and 0.100 m thick.

What mass can it support in water before


sinking?


A ferry boat is 4 m m wide and 6 m m long.When a truck pulls onto it, the boat sinks 4.00cm in the water.

The acceleration of gravity is 9.81 m/s2 .What is the weight of the truck?


Part 1 of 2An empty rubber balloon has a mass of

0.0120 kg. The balloon is filled with heliumat 0◦C, 1 atm pressure, and a density of 0.179kg/m3. The filled balloon has a radius of0.500 m.

The acceleration of gravity is 9.81 m/s2 .What is the magnitude of the buoyant force

acting on the balloon?

Part 2 of 2What is the magnitude of the net force actingon the balloon?


Part 1 of 2An object weighs 315 N in air. When tied

to a string, connected to a balance, and im-mersed in water, it weighs 265 N. When it isimmersed in oil, it weighs 269 N.

a) Find the density of the object.

Part 2 of 2b) Find the density of the oil.


A sample of an unknown material weighs

300.0 N in air and 200.0 N when submergedin an alcohol solution with a density of 0.700×103 kg/m3.

What is the density of the material?


A frog in a hemispherical bowl, as shown,just floats in a fluid with a density of1350 kg/m3.

�

�

If the bowl has a radius of 6 cm and negli-gible mass, what is the mass of the frog?


When a load of 1.0 × 106 N is placed on abattleship, the ship sinks only 2.5 cm in seawater.

The acceleration of gravity is 9.81 m/s2 .Estimate the cross-sectional area of the ship

at water level.


Part 1 of 2A 1.1 kg beaker containing 2 kg of oil with

a density of 916 kg/m3 rests on a scale. A 2 kgblock of iron with a density of 7860 kg/m3 issuspended from a spring scale and completelysubmerged in the oil, as shown.



2 kg

Find the equilibrium reading of the springscale (the upper scale).

Part 2 of 2Find the equilibrium reading of the lowerscale.


A raft is constructed of wood having a den-sity of 600.0 kg/m3. The surface area of thebottom of the raft is 5.7 m2, and the volumeof the raft is 0.600 m3.

When the raft is placed in fresh water hav-ing a density of 1.0× 103 kg/m3, how deep isthe bottom of the raft below water level?


A 2.0 cm thick bar of soap is floating inwater, with 1.900 cm of the bar underwater.Bath oil with a density of 899.0 kg/m3 isadded and floats on top of the water.

What is the depth of the oil layer when thetop of the soap is just level with the upper

surface of the oil?


Oil having a density of 930 kg/m3 floats onwater. A rectangular block of wood 4.00 cmhigh and with a density of 960 kg/m3 floatspartly in the oil and partly in the water. Theoil completely covers the block.

How far below the interface between thetwo liquids is the bottom of the block?


A block of wood weighs 50.0 N in air. Asinker is hanging from the block, and theweight of the wood-sinker combination is200.0 N when the sinker alone is immersedin water. When the wood-sinker combinationis completely immersed, the weight is 140.0 N.

Find the density of the block.


A light spring with a spring constant of90.0 N/m rests vertically on a table, as shown.A 2.00 g balloon is filled with helium (0 ◦C and1 atm pressure) to a volume of 5.00 m3 andconnected to the spring, causing the spring tostretch. The magnitude of the force withinthe spring that pulls it back toward its un-stretched position is equal to k∆x.



kk

(b)(a)

∆x

How much does the spring stretch when thesystem is in equilibrium?


A light balloon is filled with helium at0.0 ◦C and 1.0 atm and then released fromthe ground.

The acceleration of gravity is 9.81 m/s2 .Determine its initial acceleration. Disre-

gard the air resistance on the balloon.


A 1.0 kg hollow ball with a radius of 0.10 mis filled with air and is released from rest atthe bottom of a 2.0 m deep pool of water.

The acceleration of gravity is 9.81 m/s2 .How high above the water does the ball

rise? Disregard friction and the ball’s motionwhen it is only partially submerged.


A small ball 0.6 times as dense as water isdropped from a height of 10 m m above thesurface of a smooth lake.

Determine the maximum depth to whichthe ball will sink. Disregard any energy trans-ferred to the water during impact and sink-ing.


Part 1 of 2A thin, rigid, spherical shell with a mass of

4.00 kg and diameter of 0.200 m is filled withhelium at 0 ◦C and 1 atm pressure. It is thenreleased from rest on the bottom of a pool ofwater that is 4.00 m deep.

The acceleration of gravity is 9.81 m/s2 .a) Determine the upward acceleration of

the shell.

Part 2 of 2b) How long will it take for the top of the shellto reach the surface? Disregard frictionaleffects.


A light spring with a spring constant of16.0 N/m rests vertically on the bottom of alarge beaker of water, as shown in (a).

The acceleration of gravity is 9.81 m/s2 .A 5.00 × 10−3 kg block of wood with a

density of 650.0 kg/m3 is connected to thespring, and the mass-spring system is allowedto come to static equilibrium, as shown in (b).The magnitude of the force pulling the springback to its unstretched position equals k∆x.

k

m

(b)(a)

k

∆x

How much does the spring stretch?

Submerged Ping Pong Ball 0215:07, highSchool, numeric, > 1 min, normal.


A Ping-Pong ball has a diameter of 3.8 cmand average density of 0.084 g/cm3.

The acceleration of gravity is 9.8 m/s2 and

the volume of a ball is V =4

3πR3, where R is

the radius of the ball.What force would be required to hold it

completely submerged under water?

Testing Brine with an Egg 0215:07, highSchool, multiple choice, > 1 min,fixed.

When pickling cucumbers or other vegeta-bles, it’s very important to use the rightamount of salt. An old recipe recommendsputting an egg into the pickling solution andmaking sure it neither sinks nor floats: A sink-ing egg indicates too little salt while an eggthat floats on the surface indicates too muchsalt.

What is the assumption behind this recipe?

1. All eggs have the same density.

2. All eggs have the same weight.

3. All eggs have the same volume.

4. All eggs have the same shape.

5. The salt tends to neutralize the choles-terol in the egg.

Two Glasses15:07, highSchool, multiple choice, < 1 min,fixed.

Two identical glasses are filled to the samelevel with water. One of the two glasses hassome ice cubes floating in it.

Which glass weighs more?

1. The glass without ice cubes.

2. The glass with ice cubes.

3. They weigh the same.

4. Not enough information is given.

Which Level is Higher15:07, highSchool, multiple choice, < 1 min,fixed.

Two identical glasses are filled to the samelevel with water. One of the two glasses hasice cubes floating in it.

When the ice cubes melt, in which glass isthe level of the water higher?

1. The glass without ice cubes.

2. The glass with ice cubes.

3. It is the same in both.

Chapter 15, section 8, Fluid Dynamics 427


A child sits in a car at a traffic light hold-ing a helium-filled balloon. The windows areup and the car is relatively airtight. Whenthe light turn green and the car acceleratesforward, her head pitches backward but theballoon pitches forward.

Which of the following explains why cor-rectly?

1. When the car accelerates forward, thegirl’s head tends to stay where it was andpitches backwards. But the balloon is pushedforward by the air inside of the car that isaccelerating with the car.

2. The girl’s head is much denser than theballoon, so it reacts more severely to the ac-celeration.

3. Buoyant forces act on both the girl’s headand the balloon, but they act in oppositedirections.

4. The law of inertia acts on both the girl’shead and the balloon, but in opposite direc-tions.

5. Inertia acts on the girl’s head but a pres-sure difference acts on the balloon.

Chapter 15, section 9, Streamlines and the Equation of Continuity 428

Blood flow15:09, highSchool, multiple choice, < 1 min,fixed.

Blood flows through a coronary artery thatis partially blocked by deposits along theartery wall.

bloodflow

Through which part of the artery is the flux(mass of blood per unit time) largest?

1. The narrow part

2. The wide part

3. The flux is the same in both parts.


A natural-gas pipeline with a diameter of0.250 m delivers 1.55 m3 of gas per second.

What is the the flow speed of the gas?


Part 1 of 2The aorta in an average adult has a cross-

sectional area of 2.0 cm2.Calculate the flow rate (in grams per sec-

ond) of blood of 1.0 g/cm3 in the aorta if theflow speed is 42 cm/s.

Part 2 of 2Assume that the aorta branches to form alarge number of capillaries with a combinedcross-sectional area of 3.0× 103 cm2.

What is the flow speed in the capillaries?


The approximate inside diameter of theaorta is 1.6 cm, and that of a capillary is1.0×10−6 m. The average flow speed is about1.0 m/s in the aorta and 1.0 cm/s in the cap-illaries.

If all the blood in the aorta eventually flowsthrough the capillaries, estimate the numberof capillaries in the circulatory system.


A cowboy at a ranch fills a water troughthat is 1.5 m long, 65 cm wide, and 45 cmdeep. He uses a hose having a diameter of2.0 cm, and the water emerges from the hoseat 1.5 m/s.

How long does it take the cowboy to fill thetrough?

Two Hoses 0215:09, highSchool, multiple choice, < 1 min,fixed.

Two hoses, one 20 mm in diameter, theother 15 mm in diameter are connected onebehind the other to a faucet. At the openend of the hose, the flow of water measures 10liters per minute.

Through which hose is the velocity of waterv faster?

1. the 20 mm hose.

2. the 15 mm hose.

3. the velocity of water is the same in bothcases.

4. the answer depends on which of the twohoses comes first in the flow.

Two Hoses Connected15:09, highSchool, multiple choice, > 1 min,fixed.

A 4 meter long hose of 2 cm diameter isconnected to a faucet, and a 3 meter long

Chapter 15, section 9, Streamlines and the Equation of Continuity 429

hose, which has a diameter of 4 cm diameter,is connected to the end of the first hose. Atthe open end of the second hose water flowsout at a rate of 2.5 liters/minute. The openend of the second hose is 2 meters higher thanthe faucet.

What is the ratio of the speed of the waterin the second hose to the speed of the waterflowing in the first hose?

1. 1/8

2. 1/4

3. 1/2

4. 1

5. 3/2

6. 2

7. 4

8. 8

Chapter 15, section 10, Bernoulli’s Equation 430

Bernoulli Derivation 0215:10, highSchool, multiple choice, < 1 min,fixed.

Bernoulli’s equation can be derived fromconservation of:

1. pressure

2. linear momentum

3. angular momentum

4. potential energy

5. total mechanical energy

6. kinetic energy

Bernoulli Principle15:10, highSchool, multiple choice, > 1 min,wording-variable.

Part 1 of 4Assume: The fluid is incompressible and

non-viscous.Shown below is a cross-section of a ver-

tical view of a pipe discharging a fluid intothe atmosphere at its highest elevation. Thepipe diameter increases and then remains con-stant. Pi is the pressure and ‖~vi‖ is the speedof the fluid, at locations i = y, u, x, and w.

y u

x

w

The relationship between the magnitude ofthe velocity v ≡ ‖~v‖ at position y and u is

1. ‖~vu‖ < ‖~vy‖ .

2. ‖~vu‖ > ‖~vy‖ .

3. ‖~vu‖ = ‖~vy‖ .

4. indeterminable, not enough informationavailable.

Part 2 of 4The relationship between the pressure P atposition u and x is

1. Px > Pu .

2. Px < Pu .

3. Px = Pu .


Part 3 of 4The relationship between the pressure P atposition y and w is


2. Pw > Py .

3. Pw < Py .

4. Pw = Py .

Part 4 of 4The relationship between the pressure P atposition y and u is

1. Pu > Py .

2. Pu < Py .

3. Pu = Py .


Figuring Physics 1915:10, highSchool, multiple choice, < 1 min,


fixed.

You’re driving in a convertible car with thetop up and the windows closed. You note thatthe fabric top puffs up.

To explain this interesting phenomenon itis easiest to invoke

1. Bernoulli’s principle.

2. Newton’s laws.

3. Both

Fireman and Hose 0215:10, highSchool, numeric, > 1 min, normal.

A fireman standing on a 10 m high ladderoperates a water hose with a round nozzle ofdiameter 2 inch. The lower end of the hose(10 m below the nozzle) is connected to thepump outlet of diameter 3 inch. The gaugepressure of the water at the pump is

P(gauge)pump = P

(abs)pump − Patm

= 43.2 PSI = 297.854 kPa.

Calculate the speed of the water jet emerg-ing from the nozzle. Assume that water isincompressible liquid of density 1000 kg/m3

and negligible viscosity. The acceleration ofgravity is 9.8 m/s2.


Part 1 of 2A large storage tank, open to the atmo-

sphere at the top and filled with water, devel-ops a small hole in its side at a point 16 mbelow the water level. The rate of flow ofwater from the leak is 2.5× 10−3 m3/min.

The acceleration of gravity is 9.81 m/s2 .Determine the speed at which the water

leaves the hole.

Part 2 of 2Determine the diameter of the hole.


When a person inhales, air moves down thewindpipe at 15 cm/s. The average flow speedof the air doubles when passing through aconstriction in the bronchus.

Assuming incompressible flow, determinethe pressure drop in the constriction.


A dairy farmer notices that a circular watertrough near the barn has become rusty andnow has a hole near the base. The hole is0.30 m below the level of the water that is inthe tank.

The acceleration of gravity is 9.81 m/s2 .If the top of the trough is open to the

atmosphere, what is the speed of the water asit leaves the hole?

Assume that the trough is large enoughthat the relocity of the water at the top iszero.


Part 1 of 2The wind blows with a speed of 30.0 m/s

over the roof of your house.Assuming the air inside the house is rela-

tively stagnant, what is the pressure differ-ence at the roof between the inside air andthe outside air?

Part 2 of 2What net force does this pressure differenceproduce on a roof having an area of 175 m2?



A bag of blood with a density of 1050 kg/m3

is raised 1.00 m higher than the level of apatient’s arm.

The acceleration of gravity is 9.81 m/s2 .How much greater is the blood pressure

at the patient’s arm than it would be if thebag were at the same height as the arm?Assume there is no change in drip speed atthe different heights.


A water tank with a valve at the bottomis shown. Assume the cross-sectional area atA is very large compared with that at B, andthe acceleration of gravity is 9.81 m/s2 .

value

A

B

9.5m

6m

45◦

∆ymax

If this valve is opened, what is the maxi-mum height ∆ymax (above the opening of thespigot) attained by the water stream comingout of the discharge spigot (at B)?


Water flows through a 0.300 m radius pipeat the rate of 0.200 m3/s. The pressure in thepipe is atmospheric. The pipe slants downhilland feeds into a second pipe with a radius of0.150 m, positioned 0.600 m lower.

The acceleration of gravity is 9.81 m/s2 .What is the gauge pressure in the lower

pipe?

Chapter 15, section 12, Other Applications of Fluid Dynamics 433


How much lift is exerted on the wings ofan airplane that have a total surface area of100 m2 when the difference in air pressure be-low and above the wings is 4% of atmosphericpressure? Normal atmospheric pressure is100000 N/m2.


A plane usually extends flaps from its wingsduring takeoff and landing.

What is a reasonable explanation?

1. From the Bernoulli effect, this will createa larger upward force.

2. From Archimedes’ principle, this will cre-ate more buoyant force.

3. The appearance of the plane would begreat.

4. This is a safety precaution and has noth-ing to do with the lift on takeoff.


As a plane climbs, the angle of attack (theangle that a wing makes with the ground)increases.

Is there an angle beyond which it becomesdetrimental to the lift?

1. Yes; if the angle is more than 60◦, theupward lift will change to downward force.

2. Yes; the upward lift may be insufficient tomaintain altitude and the plane may stall.

3. No; the upward lift won’t change as theattack increases.

4. No; the upward lift may change, but itis always able to support the weight of theplane.


What explains why a baseball pitcher couldthrow a curve ball?

1. Archimedes’ principles

2. Bernoulli effect


4. The ideal gas law

Siphon 0215:12, highSchool, multiple choice, > 1 min,normal.

Part 1 of 2A siphon consists of a flexible tube with the

same cross section throughout the tube. It isused to drain a special liquid from a tank. Letthe density of the liquid be 750 kg/m3 andthe diameter of the tube be 7.5 cm . Let thesiphon discharge a distance 4.5 m below thesurface of the liquid.

The acceleration of gravity is 9.8 m/s2 andPatm = 101300 N/m2 .

h

4.5m

7.5 cm

What is the maximum height h; i.e., thevertical distance between the surface of theliquid to the point at the top of the siphon,for this siphon to work?

Chapter 15, section 12, Other Applications of Fluid Dynamics 434

Part 2 of 2Consider the operation for the siphon wherethe height h = 0.75 m , less than the maxi-mum as defined in Part 1.

Find the speed of liquid flow at the exit ofthe siphon tube.

Siphon 0315:12, highSchool, multiple choice, > 1 min,normal.

A siphon consists of a flexible tube with thesame cross section throughout the tube. It isused to drain a special liquid from a tank. Letthe density of the liquid be 750 kg/m3 andthe diameter of the tube be 7.5 cm . Let thesiphon discharge a distance 4.5 m below thesurface of the liquid.

The acceleration of gravity is 9.8 m/s2 andPatm = 101300 N/m2 .

h

4.5m

7.5 cm

What is the maximum height h; i.e., thevertical distance between the surface of theliquid to the point at the top of the siphon,for this siphon to work?

Siphon 0415:12, highSchool, multiple choice, > 1 min,fixed.

A siphon (a flexible tube with a circularcross section) is used to drain water from atank.Assume:

1. a steady flow within the tube, at least fromthe water surface through the bend to theexit end;

2. no friction for the water;

3. the water cannot sustain a negative pres-sure.

y

yB

yA

yC

0

A

B

C

b

h

What is the maximum vertical distance hbetween the top of the bend B and the exitend C, beyond which water flow is not possi-ble?

1. h =Patm

ρ g+ b

2. h = b− Patm

ρ g

3. h =Patm

ρ g− b

4. h =Patm

ρ g

Chapter 16, section 1, Wave Characteristics and Propagation 435


What is the period that corresponds to fre-quency 0.2 Hz?


What is the frequency corresponding to aperiod of 5 s?


Radio waves travel at the speed of light:300000 km/s.

What is the wavelength of radio waves re-ceived at 100.1 MHz on your FM radio dial?


Toss a stone in still water and concentriccircles are formed.

What form will waves have in the water if astone is tossed into smoothly flowing water?

1. The same circles will form and traveldownstream.

2. Plane waves will form and travel down-stream.

3. Elliptical waves will form and will traveldownstream.

4. The moving water will have no effect onthe concentric circles.

5. Standing elliptical waves will beformed.


You push your little sister on a swing andin 1.5 minutes you make 45 pushes.

What is the frequency of your swing?


Andrea was watching her brother in theocean and noticed that the waves were cominginto the beach at a frequency of 0.933333 Hz.

How many waves hit the beach in 15 s?


Andrea asked her brother to take a 6 ftfloating raft out of the water near the wave-swept shore. Using this raft as a measuringtool, she estimated that the wavelengths ofthese particular ocean waves were about 9 ft.

How fast are these surface ocean waves if

the frequency remains1

3Hz?


Part 1 of 2If an ocean wave passes a stationary point

every 3 s and has a velocity of 12 m/s, whatis the wavelength of the wave?

Part 2 of 2Can the amplitude be determined?

1. Not enough information is provided.

2.Yes; the amplitude can be calculated fromthis information.


Two waves have the same speed. The firsthas twice the frequency of the second.

Compare the wavelength of the two waves.

1. The first has half the wavelength of the


second.

2. The second has half the wavelength of thefirst.

3. They have the same wavelength.

4. The first has one third the wavelength ofthe second.

5. The second has one third the wavelengthof the first.


Part 1 of 2What happens to a piece of driftwood in a

lake with waves?

1. It will move up and down as a result ofthe waves.

2. It moves in the direction the waves aremoving.


Part 2 of 2How is energy transferred by a wave?

1. Energy is transferred by the up and downmotion of the wave.

2. Energy is transferred by the longitudinalmotion of the wave.



Why do waves break as they approach theshore?

1. The wave speed decreases as the watergets shallow; the top of the wave gets ahead of

the bottom of the wave, causing it to break.

2. The wave speed increases as the watergets shallow; the bottom of the wave getsahead of the top of the wave causing it tobreak.


How many nodes are in the standing wavepattern shown?

1. 5

2. 3

3. 6

4. 4

5. 2

6. 7


What type of unique information might aDoppler radar give you that ordinary radarwould not?

1. the speed of the object and its location

2. the speed of the object

3. the location of the object


If the speed of a wave doubles while the


wavelength remains the same, what happensto the frequency?

1. The frequency doubles.

2. The frequency remains the same.

3. The frequency reduces by half.



What requires a physical medium in whichto travel?

1. sound

2. light

3. Both sound and light

4. Neither sound nor light


Part 1 of 2A piano emits frequencies that range from

a low of about 28 Hz to a high of about 4200Hz.

a) Find the maximum wavelength in airattained by this instrument when the speedof sound in air is 340 m/s.

Part 2 of 2b) Find the minimum wavelength in air at-tained by this instrument.


Part 1 of 3The speed of all electromagnetic waves in

empty space is 3.00× 108 m/s.

a) What is the wavelength of radio wavesemitted at 88.0 MHz?

Part 2 of 3b) What is the wavelength of visible lightemitted at 6.0× 108 MHz?

Part 3 of 3c) What is the wavelength of X rays emittedat 3.0× 1012 MHz?

Holt SF 12D 0316:01, highSchool, numeric, > 1 min, fixed.

The red light emitted by a He-Ne laser hasa wavelength of 633 nm in air and travels at3.00× 108 m/s.

Find the frequency of the laser light.


Part 1 of 2A tuning fork produces a sound with a fre-

quency of 256 Hz and a wavelength in air of1.35 m.

a) What value does this give for the speedof sound in air?

Part 2 of 2b) What would be the wavelength of the waveproduced by this tuning fork in water in whichsound travels at 1500 m/s?


Microwaves travel at the speed of light,3.00× 108 m/s.

When the frequency of microwaves is 9.00×109 Hz, what is their wavelength?


Part 1 of 2Green light has a wavelength of 5.20× 10−7


m and travels through the air at a speed of3.00× 108 m/s.

Calculate the frequency of green light waveswith this wavelength.

Part 2 of 2Calculate the period of green light waves withthis wavelength.


Part 1 of 3You dip your finger into a pan of water twice

each second, producing waves with crests thatare separated by 0.15 m.

Determine the frequency of these waterwaves.

Part 2 of 3Determine the period of these water waves.

Part 3 of 3Determine the speed of these water waves.


Part 1 of 2The notes produced by a violin range in

frequency from approximately 196 Hz to 2637Hz.

a) Find the maximum wavelength in airproduced by this instrument when the speedof sound in air is 340 m/s.

Part 2 of 2b) Find the minimum wavelength producedby this instrument.


Yellow light travels through a certain glassblock at a speed of 1.97 × 108 m/s. Thewavelength of the light in this particular typeof glass is 3.81× 10−7 m (381 nm).

What is the frequency of the yellow light inthe glass block?


The distance between two successive crestsof a certain transverse wave is 1.20 m. Eightcrests pass a given point along the directionof travel every 12.0 s.

Calculate the wave speed.


A harmonic wave is traveling along a rope.The oscillator that generates the wave com-pletes 40.0 vibrations in 30.0 s. A given crestof the wave travels 425 cm along the rope in atime period of 10.0 s.

What is the wavelength?

Wave Fronts16:01, highSchool, multiple choice, < 1 min,fixed.

Part 1 of 2A ray always intersects its wave front at a

right angle.

1. True

2. False

Part 2 of 2Wave fronts are closer together where thewave length is smaller.

1. True

2. False

Chapter 16, section 2, Transverse and Longitudinal Waves 439


If a single disturbance some unknown dis-tance away sends out both transverse andlongitudinal waves that travel with distinctlydifferent speeds in the medium, such as in theground during earthquakes, how could thedistance to the disturbance be determined?How could the location of the disturbance bedetermined?

1. distance: the difference in wavelength ofthe waves as they arrive; location: measure-ments from three different locations.

2. distance: the difference in frequency ofthe waves as they arrive; location: measure-ments from two different locations.

3. distance: the difference in time of thewaves as they arrive; location: measurementsfrom two different locations.

4. distance: the difference in time of thewaves as they arrive; location: repeated mea-surements of the event from the same loca-tion.


“Doing the wave” is a common activity inlarge football stadiums.

What type of wave is this?

1. Transverse wave.

2. Longitudinal wave.

2. Cannot be determined from the informa-tion.

Chapter 16, section 3, Speed of a Traveling Wave 440


A sound wave traveling at 343 m/s is emit-ted by the foghorn of a tugboat. An echo isheard 2.60 s later.

How far away is the reflecting object?

Chapter 16, section 5, One-Dimensional Traveling Waves 441

Moving Pulse Wave16:05, highSchool, multiple choice, < 1 min,fixed.

A wave is moving, as illustrated, with uni-form speed v along a rope.

Which graph correctly shows the relationbetween the displacement s of point P andtime t?

v

P

1.

s

t

2.

t

s

3.

s

t

4.

t

s

Chapter 16, section 7, Superposition and Interference of Waves 442

Superposition 0116:07, highSchool, multiple choice, > 1 min,normal.

You are given two waves, a transverse wavethat moves to the right f1(x) and a transversewave that moves to the left f2(x), on a string.As the problem begins, the wave f1(x) is mov-ing to the right at v1 = +1 m/s and the wavef2(x) is moving to the left at v2 = −1 m/s.

v1 v2

0 1 2 3 4 5 6 7 8 9 10-3

-2

-1

0

1

2

3

Amplitude(centimeter)

Distance (meter)

What is the shape of the wave on the stringafter 3 s?

1.

0 1 2 3 4 5 6 7 8 9 10-3

-2

-1

0

1

2

3

Distance (meter)

2.

0 1 2 3 4 5 6 7 8 9 10-3

-2

-1

0

1

2

3

Distance (meter)

3.

0 1 2 3 4 5 6 7 8 9 10-3

-2

-1

0

1

2

3

Distance (meter)

4.

0 1 2 3 4 5 6 7 8 9 10-3

-2

-1

0

1

2

3

Distance (meter)

5.

0 1 2 3 4 5 6 7 8 9 10-3

-2

-1

0

1

2

3

Distance (meter)

6.

0 1 2 3 4 5 6 7 8 9 10-3

-2

-1

0

1

2

3

Distance (meter)


7.

0 1 2 3 4 5 6 7 8 9 10-3

-2

-1

0

1

2

3

Distance (meter)

8.

0 1 2 3 4 5 6 7 8 9 10-3

-2

-1

0

1

2

3

Distance (meter)

9.

0 1 2 3 4 5 6 7 8 9 10-3

-2

-1

0

1

2

3

Distance (meter)

10.

0 1 2 3 4 5 6 7 8 9 10-3

-2

-1

0

1

2

3

Distance (meter)

Superposition 02



v1 v2

0 1 2 3 4 5 6 7 8 9 10-3

-2

-1

0

1

2

3


Distance (meter)

What is the shape of the wave on the stringafter 2.5 s?

1.

0 1 2 3 4 5 6 7 8 9 10-3

-2

-1

0

1

2

3

Distance (meter)

2.

0 1 2 3 4 5 6 7 8 9 10-3

-2

-1

0

1

2

3

Distance (meter)


3.

0 1 2 3 4 5 6 7 8 9 10-3

-2

-1

0

1

2

3

Distance (meter)

4.

0 1 2 3 4 5 6 7 8 9 10-3

-2

-1

0

1

2

3

Distance (meter)

5.

0 1 2 3 4 5 6 7 8 9 10-3

-2

-1

0

1

2

3

Distance (meter)

6.

0 1 2 3 4 5 6 7 8 9 10-3

-2

-1

0

1

2

3

Distance (meter)

7.

0 1 2 3 4 5 6 7 8 9 10-3

-2

-1

0

1

2

3

Distance (meter)

8.

0 1 2 3 4 5 6 7 8 9 10-3

-2

-1

0

1

2

3

Distance (meter)

9.

0 1 2 3 4 5 6 7 8 9 10-3

-2

-1

0

1

2

3

Distance (meter)

10.

0 1 2 3 4 5 6 7 8 9 10-3

-2

-1

0

1

2

3

Distance (meter)

Superposition 03




v1 v2

0 1 2 3 4 5 6 7 8 9 10-3

-2

-1

0

1

2

3


Distance (meter)


1.

0 1 2 3 4 5 6 7 8 9 10-3

-2

-1

0

1

2

3

Distance (meter)

2.

0 1 2 3 4 5 6 7 8 9 10-3

-2

-1

0

1

2

3

Distance (meter)

3.

0 1 2 3 4 5 6 7 8 9 10-3

-2

-1

0

1

2

3

Distance (meter)

4.

0 1 2 3 4 5 6 7 8 9 10-3

-2

-1

0

1

2

3

Distance (meter)

5.

0 1 2 3 4 5 6 7 8 9 10-3

-2

-1

0

1

2

3

Distance (meter)

6.

0 1 2 3 4 5 6 7 8 9 10-3

-2

-1

0

1

2

3

Distance (meter)


7.

0 1 2 3 4 5 6 7 8 9 10-3

-2

-1

0

1

2

3

Distance (meter)

8.

0 1 2 3 4 5 6 7 8 9 10-3

-2

-1

0

1

2

3

Distance (meter)

9.

0 1 2 3 4 5 6 7 8 9 10-3

-2

-1

0

1

2

3

Distance (meter)

10.

0 1 2 3 4 5 6 7 8 9 10-3

-2

-1

0

1

2

3

Distance (meter)

Superposition 04



v1 v2

0 1 2 3 4 5 6 7 8 9 10-3

-2

-1

0

1

2

3


Distance (meter)


1.

0 1 2 3 4 5 6 7 8 9 10-3

-2

-1

0

1

2

3

Distance (meter)

2.

0 1 2 3 4 5 6 7 8 9 10-3

-2

-1

0

1

2

3

Distance (meter)


3.

0 1 2 3 4 5 6 7 8 9 10-3

-2

-1

0

1

2

3

Distance (meter)

4.

0 1 2 3 4 5 6 7 8 9 10-3

-2

-1

0

1

2

3

Distance (meter)

5.

0 1 2 3 4 5 6 7 8 9 10-3

-2

-1

0

1

2

3

Distance (meter)

6.

0 1 2 3 4 5 6 7 8 9 10-3

-2

-1

0

1

2

3

Distance (meter)

7.

0 1 2 3 4 5 6 7 8 9 10-3

-2

-1

0

1

2

3

Distance (meter)

8.

0 1 2 3 4 5 6 7 8 9 10-3

-2

-1

0

1

2

3

Distance (meter)

9.

0 1 2 3 4 5 6 7 8 9 10-3

-2

-1

0

1

2

3

Distance (meter)

10.

0 1 2 3 4 5 6 7 8 9 10-3

-2

-1

0

1

2

3

Distance (meter)

Chapter 16, section 8, The Speed of Waves on Strings 448


Explain how you can lower the pitch of atone on a guitar by altering (a) the length ofthe string, (b) the tension of the string, or (c)the thickness or the mass of the string.

1. longer, looser, and more massive

2. shorter, looser, and more massive

3. longer, looser, and lighter

4. shorter, tighter, and lighter

5. longer, tighter, and more massive


Why should guitars be played before theyare brought on stage for a concert?

1. Guitars have softer sound after pre-playing.

2. The guitarist should practice before theconcert.

3. Strings warm up and expand during play,so they should be tuned while warm.

4. There is no special reason to do so.

Harmonic Wave in a Wire16:08, highSchool, numeric, > 1 min, normal.

Part 1 of 2A harmonic wave in a wire has amplitude

5 mm, wavelength 1 m, and frequency 500 Hz.What is the propagation speed of the wave?

Part 2 of 2The wire has linear mass density of 10 g/m.

Determine the wire’s tension.

Sine Wave in a Wire16:08, highSchool, numeric, < 1 min, normal.

A sinusoidal transverse wave travels alonga wire of linear density 5 g/m. The wavehas amplitude 1 cm, frequency 300 Hz andwavelength 2 m.

What is the tension of the wire?

Wave in a Copper Wire16:08, highSchool, numeric, < 1 min, normal.

A transverse wave runs along a copper wireof radius 0.5 mm at speed 50 m/s. Copperhas density 8920 kg/m3.

What is the tension of the wire?

Chapter 16, section 9, Reflection and Transmission of Waves 449

Fixed End Pulse Reflection16:09, highSchool, multiple choice, < 1 min,fixed.

A pulse moves on a string at 1 m/s, trav-eling to the right. At point A, the string istightly clamped and cannot move.

1 m/s

1 m

A

Which of the following shows how the stringwould look soon after 2 seconds?

1.A

2.A

3.A

4.A

5.A

6.A

7.A

8.A

Reflection 0116:09, highSchool, multiple choice, > 1 min,normal.

You are given f1(x), a transverse wave thatmoves on a string that ends and is FIXED inplace at x = 5 m. As the problem begins, thewave is moving to the right at v = 1 m/s.

v

0 1 2 3 4 5 6 7 8 9 10−3−2−10

1

2

3


Distance (meter)

Consider the image of the wave reflectedabout the FIXED point x = 5 m in the fol-lowing diagram. The image will be movingto the left at v′ = −1 m/s (in the oppositedirection from the real wave).

v v′

0 1 2 3 4 5 6 7 8 9 10−3−2−10

1

2

3


Distance (meter)



1.

0 1 2 3 4 5 6 7 8 9 10−3−2−10

1

2

3

Distance (meter)

2.

0 1 2 3 4 5 6 7 8 9 10−3−2−10

1

2

3

Distance (meter)

3.

0 1 2 3 4 5 6 7 8 9 10−3−2−10

1

2

3

Distance (meter)

4.

0 1 2 3 4 5 6 7 8 9 10−3−2−10

1

2

3

Distance (meter)

5.

0 1 2 3 4 5 6 7 8 9 10−3−2−10

1

2

3

Distance (meter)

6.

0 1 2 3 4 5 6 7 8 9 10−3−2−10

1

2

3

Distance (meter)

7.

0 1 2 3 4 5 6 7 8 9 10−3−2−10

1

2

3

Distance (meter)

8.

0 1 2 3 4 5 6 7 8 9 10−3−2−10

1

2

3

Distance (meter)


9.

0 1 2 3 4 5 6 7 8 9 10−3−2−10

1

2

3

Distance (meter)

10.

0 1 2 3 4 5 6 7 8 9 10−3−2−10

1

2

3

Distance (meter)



v

0 1 2 3 4 5 6 7 8 9 10−3−2−10

1

2

3


Distance (meter)

Consider the image of the wave reflectedabout the FIXED point x = 5 m in the fol-lowing diagram. The image will be movingto the left at v′ = −1 m/s (in the oppositedirection from the real wave).

v v′

0 1 2 3 4 5 6 7 8 9 10−3−2−10

1

2

3


Distance (meter)


1.

0 1 2 3 4 5 6 7 8 9 10−3−2−10

1

2

3

Distance (meter)

2.

0 1 2 3 4 5 6 7 8 9 10−3−2−10

1

2

3

Distance (meter)

3.

0 1 2 3 4 5 6 7 8 9 10−3−2−10

1

2

3

Distance (meter)


4.

0 1 2 3 4 5 6 7 8 9 10−3−2−10

1

2

3

Distance (meter)

5.

0 1 2 3 4 5 6 7 8 9 10−3−2−10

1

2

3

Distance (meter)

6.

0 1 2 3 4 5 6 7 8 9 10−3−2−10

1

2

3

Distance (meter)

7.

0 1 2 3 4 5 6 7 8 9 10−3−2−10

1

2

3

Distance (meter)

8.

0 1 2 3 4 5 6 7 8 9 10−3−2−10

1

2

3

Distance (meter)

9.

0 1 2 3 4 5 6 7 8 9 10−3−2−10

1

2

3

Distance (meter)

10.

0 1 2 3 4 5 6 7 8 9 10−3−2−10

1

2

3

Distance (meter)




v

0 1 2 3 4 5−3−2−10

1

2

3Amplitude(centimeter)

Distance (meter)


1.

0 1 2 3 4 5−3−2−10

1

2

3

Distance (meter)

2.

0 1 2 3 4 5−3−2−10

1

2

3

Distance (meter)

3.

0 1 2 3 4 5−3−2−10

1

2

3

Distance (meter)

4.

0 1 2 3 4 5−3−2−10

1

2

3

Distance (meter)

5.

0 1 2 3 4 5−3−2−10

1

2

3

Distance (meter)

6.

0 1 2 3 4 5−3−2−10

1

2

3

Distance (meter)

7.

0 1 2 3 4 5−3−2−10

1

2

3

Distance (meter)


8.

0 1 2 3 4 5−3−2−10

1

2

3

Distance (meter)

9.

0 1 2 3 4 5−3−2−10

1

2

3

Distance (meter)

10.

0 1 2 3 4 5−3−2−10

1

2

3

Distance (meter)



v

0 1 2 3 4 5−3−2−10

1

2

3


Distance (meter)


1.

0 1 2 3 4 5−3−2−10

1

2

3

Distance (meter)

2.

0 1 2 3 4 5−3−2−10

1

2

3

Distance (meter)

3.

0 1 2 3 4 5−3−2−10

1

2

3

Distance (meter)


4.

0 1 2 3 4 5−3−2−10

1

2

3

Distance (meter)

5.

0 1 2 3 4 5−3−2−10

1

2

3

Distance (meter)

6.

0 1 2 3 4 5−3−2−10

1

2

3

Distance (meter)

7.

0 1 2 3 4 5−3−2−10

1

2

3

Distance (meter)

8.

0 1 2 3 4 5−3−2−10

1

2

3

Distance (meter)

9.

0 1 2 3 4 5−3−2−10

1

2

3

Distance (meter)

10.

0 1 2 3 4 5−3−2−10

1

2

3

Distance (meter)

Wave on a Guitar String 0216:09, highSchool, numeric, < 1 min, normal.

Part 1 of 2Consider a guitar string of length L =

630 mm. Let the x axis run from one endof the string to the other end, thus 0 ≤ x ≤ L.

Suppose you pluck the string by sharplypulling it up at point x0 and letting go. Thissets pulses travelling in both directions; atthe ends of the string, the pulses are reflectedback, and eventually they meet again at pointx?.


Given x0 = 180 mm, calculate x?.

Part 2 of 2When the pulses meet and superpose, is thestring above or below its relaxed position?

1. Below

2. Above

3. At rest (The pulses cancel.)

4. It depends on the x0.

Wave Reflection16:09, highSchool, multiple choice, > 1 min,wording-variable.

The figure below shows a complex wavepattern on a string moving towards a rigidhook at the wall on the right. After sometime, the wave is reflected from the wall.

v

Select the wave pattern for the reflected wave.

1.

v

2.

v

3.

v

4.

v

5.

Chapter 16, section 10, Refraction of Waves 457


Would the refraction of sound be possible ifthe speed of sound were unaffected by wind,temperature, and other conditions? Defendyour answer.

1. If the speed of sound were unaffected bysome conditions, refraction would not occur.

2. Refraction is the result of changing wavefrequencies; even if the speed of sound wereaffected by some conditions, refraction wouldnot occur.

3. Refraction is the result of changing wavefrequencies; when sound travels into differentmediums, there is a change in its frequency,so even if the speed of sound were unaffectedby some conditions, refraction would still oc-cur.

4. Refraction always occurs.

Chapter 16, section 12, Sinusoidal Waves 458

Sine Wave in a Wire 0216:12, highSchool, numeric, < 1 min, normal.

A transverse wave in a wire with lineardensity 5 g/m has the form

y(x, t) = (1 cm) sin[

(5 m−1)x

− (3000 s−1) t]

What is its tension?

Sinusoidal Wave on a String 0216:12, highSchool, numeric, > 1 min, normal.

Part 1 of 3A sinusoidal wave of wavelength 2 m and

amplitude 0.1 m travels with a speed of 1 m/son a string. Initially, the left end of the stringis at the origin and the wave moves from leftto right. Find the angular frequency.

Part 2 of 3Find the angular wave number.

Part 3 of 3What is the maximum speed of any point onthe string?

Wave Form16:12, highSchool, multiple choice, < 1 min,fixed.

A transverse wave has a wave function

y = (0.2 m) sin{

2π[

(2 m−1)x− (2 s−1) t]}

where x and y are in meters and t is in seconds.This wave is

1. a travelingwave of amplitude 0.2 m, wave-length 0.5 m and frequency 2 Hz.

2. a standing wave of maximal amplitude0.2 m, wavelength 0.5 m and frequency2 Hz.

3. a travelingwave of amplitude 0.2 m, wave-length 2 m and frequency 2 Hz.

4. a travelingwave of amplitude 0.2 m, wave-length 0.5 m and frequency 0.5 Hz.

5. a traveling wave of amplitude 0.2 m,wavelength 4πm = 12.5m and frequency2πHz = 6.28Hz.

6. a travelingwave of amplitude 0.5 m, wave-length 0.2 m and frequency 2 Hz.

7. a standing wave of maximal amplitude2 m, wavelength 0.2 m and frequency 4πHz =6.28Hz.

8. a standing wave of maximal amplitude0.2 m, wavelength 0.25 m and frequency2πHz = 3.14 Hz.

9. a standing wave of maximal amplitude

0.4 m, wavelength1m

4π= 0.08m and fre-

quency 2 Hz.

10. a traveling wave of amplitude 2 m, wave-length 0.4 m and frequency 60 Hz.

Wave Length 0316:12, highSchool, multiple choice, > 1 min,wording-variable.

A harmonic wave

y = A sin[k x− φ] ,

where A = 1 meter, k has units of m−1, and φhas units of radians, is plotted in the diagrambelow.

+1

−1

A(m

eters)

x (meters) 82 m 164 m 246 m

Chapter 16, section 12, Sinusoidal Waves 459

Which wavelength corresponds best to thediagram?

1. λ = 123 m

2. λ = 39 m

3. λ = 9 m

4. λ = 15 m

5. λ = 21 m

6. λ = 33 m

7. λ = 51 m

8. λ = 57 m

9. λ = 93 m

10. λ = 69 m

Chapter 16, section 13, Energy Transmitted by Waves on Strings 460

Waves on a Rope 0316:13, highSchool, multiple choice, > 1 min,fixed.

A transverse wave is being generated on arope under constant tension.

The power transmitted by the wave is in-creased or decreased by what factor if the ropeis replaced by an identical rope twice as long?Assume the mass density and all other prop-erties of the rope and wave are unchanged.

1. P = 2P0

2. P = P0

3. P = 4P0

4. P =1

2P0

5. P =1

4P0

Chapter 17, section 1, Characteristics of Sound Waves 461


Why do flying bees buzz?

1. They have special wings that makesounds.

2. They move their wings at audible fre-quencies.

3. The buzz comes from their heads. Theymake a buzzing noise to communicate witheach other.


Cats can hear sound frequencies up to70,000 Hz. Bats send and receive ultrahigh-frequency squeaks up to 120,000 Hz.

Which hears the sound of shorter wave-lengths?

1. cats

2. bats

3. Neither; the wavelength is independent offrequency.


When a sound wave moves past a point inair, what happens to the density of air at thispoint?

1. The density of air increases and thendecreases as the sound wave passes.

2. There is no change in the density of air.

3. The air is compressed after the soundwave passes.

4. There is no air after the sound wavepasses.


The frequency range for a telephone is be-tween 500 and 4000 Hz.

Why does a telephone not do a very goodjob of transmitting music?

1. A telephone cuts off the higher-frequencyovertones of music that contribute to its qual-ity.

2. A telephone speaker has a bad quality.

3. A telephone cuts off the lower-frequencyovertones of music that contribute to its qual-ity.

4. Special earpieces can be used to allow youto enjoy music.

5. The small speaker cannot produce goodmusic.


In what ways are sound waves similar towater waves?

I) Both carry energy in the form of an os-cillating medium;

II) Both carry energy in the form of vibra-tion.

1. I only

2. II only

3. I and II

4. None of these

Conceptual 15 Q02

Chapter 17, section 1, Characteristics of Sound Waves 462


What kind of wave is created if a tree fallsin a forest?

1. sound wave

2. electromagnetic wave

3. transverse wave

4. polarized wave

5. None of these


What physical features make an echo lakeproduce echos?

1. The sound must travel across the lake andback.

2. The sound must travel across the lake.

3. The sound must travel beyond the lake.

4. The sound must travel beyond the lakeand back.

5. None of these


For most vibrating systems, the amplitudeof vibrations does not affect the frequency aslong as the amplitude is not too high.

Why does this fact makes the constructionand use of musical instruments possible?

1. You have to strike the key with preciselythe right force.

2. You just have to strike the key.

3. You have to strike the key very hard.

4. You have to strike the key very softly.

5. None of these

Chapter 17, section 2, Speed of Sound Waves 463


Middle C has a speed of 1500 m/s in waterand 340 m/s in air.

Does it have a longer or shorter wavelengthin water than in air and why?

1. Shorter; water is denser than air.

2. Shorter; the speed of sound is greater inwater than in air.

3. Longer; water is denser than air.

4. Longer; the speed of sound is greater inwater than in air.


Sound from Source A has twice the fre-quency of sound from Source B.

Compare the wavelengths of sound from thetwo sources.

1. The wavelength of sound from Source Bis half the wavelength of sound from SourceA.

2. The wavelength of sound from Source Ais√2 times the wavelength of sound from

Source B.

3. The wavelength of sound from Source Bis the same as the wavelength of sound fromSource A.

4. The wavelength of sound from Source Ais half the wavelength of sound from SourceB.


If the speed of sound depended on its fre-quency, would you enjoy a concert from thesecond balcony?

1. The music would be even better.

2. The farther a listener is from the musicsource, the more jumbled the sound wouldbe.

3.The closer a listener is to the music source,the more jumbled the sound would be.

4. A listener could still enjoy a concert atany distance.


If the frequency of sound is doubled, howwill its speed change? How will its wavelengthchange?

1. There will be no change in its speed andwavelength.

2. Its speed will halve, and its wavelengthwill double.

3. Its speed will double, and its wavelengthwill not change.

4. Both speed and wavelength will double.

5. Its speed will not change, and its wave-length will halve.


Why does sound travel faster in warm air?

1. In warm air the frequency of sound ishigher.

2. In warm air the air molecules travelfaster.


3. In warm air the wavelength of sound isshorter.


Why does sound travel faster in moist air?(Hint: At the same temperature, water va-por molecules have the same average kineticenergy as the heavier nitrogen and oxygenmolecules in the air. How, then, do the av-erage speeds of H2O molecules compare withthose of N2 and O2 molecules?)

1. The more massive water vapor moleculestravel faster than the less massive nitrogenand oxygen molecules in the air.

2. The less massive water vapor moleculestravel faster than the more massive nitrogenand oxygen molecules in the air.

3. Sound traveling in moist air experiencesno refraction and no deflection.

4. At the same temperature, water vapormolecules have a greater average kinetic en-ergy than oxygen and nitrogen molecules.


Why can the tremor of the ground from adistant explosion be felt before the sound ofthe explosion can be heard?

1. The wavelength of the sound is smaller inthe ground than in air.

2. The amplitude of the sound is bigger inthe solid ground than in air.

3. The frequency of the sound is higher inthe solid ground than in air.

4. Sound travels faster in solid ground than

in air.


Why will marchers at the end of a longparade following a band be out of step withmarchers near the front?

1. They are likely to loose their attention.

2. They cannot see the marchers near thefront.

3. They have difficulty in hearing the soundof a band.

4. They hear a delayed sound.

5. Usually the least experienced marchersare at the end of a parade.

Concept 20 P0117:02, highSchool, numeric,< 1min, wording-variable.

What is the wavelength of a 34000 Hz tonein air? THe sped of sound in air is 340 m/s.


For years, marine scientists were mystifiedby sound waves picked up by underwater mi-crophones in the Pacific Ocean. These so-called T-waves were among the purest soundsin nature. Eventually they traced the sourceto underwater volcanoes whose rising columnsof bubbles resonated like organ pipes.

What is the wavelength of a typical T-wavewhose frequency is 7 Hz? The speed of soundis seawater is 1530 m/s .


Imagine a Rip-van-Winkle type who livesin the mountains. Just before going to sleep


he yells ”WAKE UP” and the sound echoesoff the nearest mountain and returns 12 hourslater.

How far away is that mountain? The speedof sound is 340 m/s.


A grunting porpoise emits a scund of 57 Hzsound.

What is the wavelength of this sound in wa-ter, where the speed of sound is 1500 m/s?

Concept 21 0217:02, highSchool, numeric, < 1 min, fixed.

Part 1 of 2The highest frequencies humans can hear is

about 20000 Hz.What is the wave length of sound in air

at this frequency? (The speed of sound is340 m/s.)

Part 2 of 2What is the wavelength for the lowest soundswe can hear, about 20 Hz?


A person who talks after inhaling heliumgas has a high-pitched voice. One of thereasons for this is the higher speed of soundin helium than in air.

Why does sound travel faster in helium?

1. Sound travels faster in a pure gas.

2. A helium molecule has a smaller size thanother gases.

3. A helium molecule has a small number ofelectrons which reduce the speed of sound.

4. A helium molecule has a small mass.

5. A helium molecule has a greater kinetic

energy.

Conceptual 15 02 0317:02, highSchool, numeric, > 1 min, normal.

Part 1 of 5Rosa and Jon were asked by their physi-

cal science teacher to determine the speed ofsound. While walking to their dormitories af-ter class, Jon clapped his hands, which Rosaand Jon heard a moment later as an echo. Theecho bounced off a building that was 300 ftaway. They knew that they could not mea-sure the brief time for a single clap to return,so they had a brillant idea. Jon clapped andthen started to clap as soon as he heard theecho, and he then continued this synchronizedclapping so that Rosa could measure the fre-quency. Rosa counted 56 of Jon’s claps in onehalf minute.

What is the frequency of Jon’s clapping?

Part 2 of 5What is the speed of sound as determined byRosa and Jon?

Part 3 of 5Rosa and Jon decided to test their results, sothey walked an additional 100 ft away fromthe wall.

What is the new clapping frequency?

Part 4 of 5What is the new time between successiveclaps?

Part 5 of 5How many claps will Jon have to make in onehalf minute?


Anna was on vacation and came across anecho lake. Wanting to know how far she hadto swim to get across the lake to the otherside, she yelled across “Hello!”

How wide is the lake if 5 seconds later sheheard her own echo? Assume that the tem-


perature is 20◦C and the speed of sound is344 m/s.

Conceptual 15 06a 06b17:02, highSchool, numeric, < 1 min, normal.

Assume that the speed of a sound waveproduced by an elephant at 20◦C is 344 m/sand its frequency is 25 Hz.

What is the wavelength of this wave?

Conceptual 15 0817:02, highSchool, numeric,< 1min, wording-variable.

A dog can hear sounds in the range from 15to 50,000 Hz.

What wavelength corresponds to the uppercut off point of the sounds at 20◦C?


A stringed instrument has a maximumstring length of 0.3 m and is tuned so thata wave travels along the string at 120 m/s.

What is the string’s fundamental frequencyat this length and wave speed?


If an atomic bomb was detonated on thesurface of the Moon, how long would it beuntil we heard the explosion here on Earth?

1. 8 min

2.We would not hear anything.

3. 16 min

4. 0.5 min

5. None of these


fixed.

Runners line up side by side at the startingline of a road race.

About how long would the starting linehave to be to have a one-second delay betweenthe sound of the starting gun reaching thecloset runner and the farthest runner from thegun? The speed of sound is about 340 m/s.

1. 340 m

2. 34 m

3. 9.8 m

4. 3× 108 m

5. 1 m


Part 1 of 2Why does sound move faster in water or

rock than in air?

1. Atoms and molecules are packed closertogether in water and rock.

2. Atoms and molecules are farther apart inwater or rock.

3. More heat generated in water or rockhelps sound to move faster than in air.

4. All of these

5. None of these

Part 2 of 2What might be happening at a molecular levelthat accounts for this?

1. It takes less time for the vibration of oneatom to vibrate a neighboring atom.

2. The generated heat excites the electrons


in the atoms.

3. The atomic bonds prevents the atomsfrom moving.

4. All of these

5. None of these


Part 1 of 2How does sound travel at very high alti-

tudes compared to sea level?

1. slower at high altitude

2. faster at high altitude

3. same in both

Part 2 of 2How would sound travel in outer space?

1. faster in outer space than on earth

2. slower in outer space than on earth

3. Sound does not travel in outer space.


Why does sound travel faster in warmertemperature?

1. Molecules bump into each other morefrequently at warmer temperatures.

2. Molecules are more loosely packed atwarmer temperatures, allowing sound traveleasier.

3. Warmer temperatures excite the elec-trons, allowing sound to move faster.

4. None of these


A guitar and a flute are in tune with eachother.

How could a change in temperature affectthis situation?

I) changes the speed of sound;II) changes the length of instruments;III) changes the speed of sound;IV) does not affect the tune.

1. I and II only

2. II and III only

3. I only

4. II only

5. III only

6. IV only

7. I and III only


Part 1 of 2The velocity v of a sound wave traveling in

the air depends on B, the bulk modulus, andρ, the density of the air. The bulk modulusis defined by the variation of pressure ∆P =

−B ∆V

V, where

∆V

Vis the fractional change

of the volume.If v = Bx ρy, choose the correct set of equa-

tions. The powers of x and y may be de-termined based on a dimensional analysis byequating the powers ofM , of L and of T .

1. 0 = x+ y, 1 = −x− 3 y and −1 = −2x

2. 0 = x+ y, 1 = −x+ 3 y and −1 = −2x


3. 0 = x− y, 2 = x+ 3 y and −1 = −2x

4. 0 = x− y, −1 = x− 3 y and −1 = −2x

5. 0 = x+ y, 1 = x− 3 y and 1 = −2x

6. 0 = x+ y, 1 = x+ 3 y and 1 = −2x

7. 0 = x− y, 1 = x+ 3 y and 1 = −2x

8. 0 = x− y, 1 = x− 3 y and 1 = −2x

9. 1 = x+ y, 0 = x− 3 y and 1 = −2x

10. 0 = x+ y, 0 = x− 3 y and 1 = −2x

Part 2 of 2What are the values of x and y?

1. x =1

2, y = −1

2

2. x = −1

2, y = −1

2

3. x =1

2, y =

1

2

4. x = −1, y = −1

5. x = 1, y = −1

6. x = 1, y = 1

7. x = −1, y = 1

8. x = 0, y = 1

9. x = 1, y = 0

10. x = −1

2, y =

1

2


The velocity v of a sound wave traveling inthe air depends on B, the bulk modulus, andρ, the density of the air. The bulk modulusis defined by the variation of pressure ∆P =

−B ∆V

V, where

∆V

Vis the fractional change

of the volume.If v = Bx ρy, choose the correct set of equa-

tions. The powers of x and y may be de-termined based on a dimensional analysis byequating the powers ofM , of L and of T .

1. 0 = x+ y, 1 = −x− 3 y and −1 = −2x

2. 0 = x+ y, 1 = −x+ 3 y and −1 = −2x

3. 0 = x− y, 2 = x+ 3 y and −1 = −2x

4. 0 = x− y, −1 = x− 3 y and −1 = −2x

5. 0 = x+ y, 1 = x− 3 y and 1 = −2x

6. 0 = x+ y, 1 = x+ 3 y and 1 = −2x

7. 0 = x− y, 1 = x+ 3 y and 1 = −2x

8. 0 = x− y, 1 = x− 3 y and 1 = −2x

9. 1 = x+ y, 0 = x− 3 y and 1 = −2x

10. 0 = x+ y, 0 = x− 3 y and 1 = −2x


Part 1 of 2The range of human hearing extends from

approximately 20 Hz to 20000 Hz.a) Find the wavelength for 20 Hz when the

speed of sound in air is equal to 343 m/s.

Part 2 of 2b) Find the wavelength for 20000 Hz when thespeed of sound in air is equal to 343 m/s.


A dolphin in 25◦C sea water emits a sounddirected toward the bottom of the ocean 150m below.


How much time passes before it hears anecho? The speed of sound in sea water is1530 m/s.


The greatest value ever achieved for thespeed of sound in air is about 1.0 × 104 m/s,and the highest frequency ever produced isabout 2.0× 1010 Hz.

Find the wavelength of this wave.


Some studies indicate that the upper fre-quency limit of hearing is determined by thediameter of the eardrum. The wavelengthof the sound wave and the diameter of theeardrum are approximately equal at this up-per limit.

If this is so, what is the diameter of theeardrum of a person capable of hearing 2.0 ×104 Hz? Assume 340 m/s is the speed ofsound in the ear.

Pier Construction17:02, highSchool, numeric, > 1 min, normal.

You are watching a pier being constructedon the far shore of a saltwater inlet whensome blasting occurs. You hear the sound inthe water 4.5 s before it reaches you throughthe air, which has a temperature of 20◦C.

The velocity of sound in air is 343 m/s andin saltwater 1533 m/s.

How wide is the inlet?

Sound in a Liquid17:02, highSchool, numeric, < 1 min, normal.

Sound waves travel through a liquid of den-sity 1000 kg/m3 at a speed of 1500 m/s.

What is the bulk modulus of this liquid?

Chapter 17, section 3, Periodic Sound Waves 470


At the instant that a high-pressure region iscreated just outside the prongs of a vibratingtuning fork, what is being created betweenthe prongs?

1. A high pressure region

2. A low pressure region

3. No change in pressure

4. Low-high-low pressure

5. High-low-high pressure

Chapter 17, section 4, Energy and Intensity of Sound Waves 471


Why is it so quiet after a snowfall?

1. There are few cars out there after a snow-fall.

2. The temperature increases after a snow-fall.

3. The temperature decreases after a snow-fall.

4.Our ears become insensitive to sound aftera snow fall.

5. Snow is a good absorber of sound.


Why is the moon described as the “silentplanet?”

1. The moon orbits without sound.

2. There is no life in the moon.

3. Sound from the moon cannot be heard onthe earth.

4. The moon always apears at night.

5. The moon has no atmosphere to transmitsounds.


What kinds of wind conditions would makesound more easily heard at long distances?

1. The wind travels in the same directionthe sound travels.

2. The wind travels in the opposite directionthe sound travels.

3. The wind traveling toward the listenerat elevations above ground level travels fasterthan wind near the ground.

4. The waves are bent upward.


Why is an echo weaker than the originalsound?

1. The echo has a longer wavelength thanthe original sound due to the reflection.

2. The echo has a smaller amplitude thanthe original sound because sound spreads andits intensity decreases with distance.

3. The echo has a higher frequency than theoriginal sound due to the reflection.

4. The echo has a shorter wavelength thanthe original sound due to the reflection.


The yellow-green light emitted by streetlights matches the yellow-green color to whichthe human eye is most sensitive. Conse-quently, a 100-watt street light emits lightthat is better seen at night. Similarly, themonitored sound intensities of television com-mercials are louder than the sound from reg-ular programming, yet don’t exceed the regu-lated intensities.

At what frequencies do advertisers concen-trate the commercial’s sound?

1. The sound of commercials is concentratedat the low-frequency region of audible soundfrequencies.


2. The sound of commercials is concentratedat the high-frequency region of audible soundfrequencies.

3. The sound of commercials is concentratedat frequencies to which the ear is most sensi-tive.

4. The sound of commercials is concentratedat the frequency of 60 Hz.


A loudspeaker produces a musical sound bymeans of the oscillation of a diaphragm.

On what does the loudness of producedsound depend?

1. the frequency of oscillation only

2. the amplitude of oscillation only

3. the kinetic energy of oscillation only

4. the frequency of oscillation and the kineticenergy of oscillation

5. the frequency of oscillation and the am-plitude of oscillation

6. the amplitude of oscillation and the ki-netic energy of oscillation

7. the frequency of oscillation, the ampli-tude of oscillation, and the kinetic energy ofoscillation


One person has a threshold of hearing of 5dB, and another of 10 dB.

Which person has the more acute hearing?

1. The one who can hear 5 dB.

2. The one who can hear 10 dB.



How much more intense is sound at 40 dBthan at 0 dB?


How much more intense is a sound at 40 dBthan a sound 30 dB?

Four Shouts17:04, highSchool, multiple choice, > 1 min,fixed.

The sound of a man shouting at the topof his lungs from a rather large distance awayfrom your ear has loudness of only 20 decibels.What would be the decibel level of four menshouting at the top of their (equally powerful)lungs from the same distance away from youear? Assume that there is no interferencefrom superposed waves and round off youranswer to the nearest integer.

1. 26 db

2. 20 db

3. 14 db

4. 40 db

5. 160 db

6. 80 db

7. 6 db

8. 60 db

9. 10 db


10. 5 db

Hearing Loss17:04, highSchool, multiple choice, > 1 min,fixed.

Sustained sound intensity levels on the or-der of can cause permanent hearingloss.

1. 90 dB

2. 20 dB

3. 30 dB

4. 40 dB

5. 50 dB

6. 60 dB

7. 70 dB

8. 55 dB

9. 75 dB


Part 1 of 3An electric guitar’s amplifier is at a distance

of 5.0 m.a) Find the intensity of its sound waves

when its power output is 0.25 W.

Part 2 of 3b) Find the intensity of the sound waves whenthe amplifier’s power output is 0.50 W.

Part 3 of 3c) Find the intensity of the sound waves whenthe amplifier’s power output is 2.0 W.


At a maximum level of loudness, the poweroutput of a 75-piece orchestra radiated assound is 70.0 W.

What is the intensity of these sound wavesto a listener who is sitting 25.0 m from theorchestra?


If the intensity of a person’s voice is 4.6 ×10−7 W/m2 at a distance of 2.0 m, how muchsound power does that person generate?


How much power is radiated as sound froma band whose intensity is 1.6× 10−3 W/m2 ata distance of 15 m?


The power output of a tuba is 0.35 W.At what distance is the sound intensity of

the tuba 1.2× 10−3 W/m2?


A baseball coach shouts loudly at an umpirestanding 5.0 meters away.

If the sound power produced by the coachis 3.1 × 10−3 W, what is the intensity of thesound when it reaches the umpire?


A stereo speaker represented by P in thefigure emits sound waves with a power outputof 100.0 W.


P x� �10 m

What is the intensity of the sound waves atpoint x, 10.0 m away?


A rock group is playing in a club. Soundemerging outdoors from an open door spreadsuniformly in all directions.

If the decibel level is 60 dB at a distanceof 1.0 m from the door, at what distance isthe music just barely audible to a person witha normal threshold of hearing? Disregardabsorption.


A typical decibel level for a buzzingmosquito is 40 dB, and normal conversationis approximately 50 dB.

Howmany buzzing mosquitoes will producea sound intensity equal to that of normalconversation?


Part 1 of 2The decibel level of the noise from a jet

aircraft is 130 dB when measured 20.0 m fromthe aircraft.

a) How much sound power does the jetaircraft emit?

Part 2 of 2

b) How much sound power would strike theeardrum of an airport worker 20.0 m fromthe aircraft? (Assume the diameter of theworker’s eardrum is 1.7× 10−2m).

Intensity of a Sound Wave 0217:04, highSchool, numeric, > 1 min, normal.

The intensity of a sound wave at a fixeddistance from a speaker vibrating at 1.5 kHzis 0.6 W/m2. Calculate the intensity if thefrequency is reduced to 0.5 kHz and the dis-placement amplitude is doubled.

Sinusoidal Sound Wave 0217:04, highSchool, numeric, < 1 min, normal.

Part 1 of 2A sinusoidal sound wave in a gas of density

1.2 kg3/m has molecular displacement

s(x, t) = sm cos(kx− ωt) ,

where sm = 2 µm, k = 500 m−1, and ω =170000 s−1.

What is the speed of this wave?

Part 2 of 2What is the intensity of this wave?

Sound level17:04, highSchool, multiple choice, > 1 min,normal.

Part 1 of 2Given an harmonic sound wave which has a

sound level, β1 = 100 dB.What is its corresponding sound intensity

I1?

Part 2 of 2If the frequency and maximum amplitude ofthe sound wave are both tripled, what is theintensity, I2, of this new sound wave in termsof the original intensity, I1?

1. I2 = 81 I1

2. I2 = 54 I1


3. I2 = 27I1

4. I2 = 24 I1

5. I2 = 12 I1

6. I2 = 9 I1

7. I2 = 6 I1

8. I2 = 3 I1

9. I2 = 2 I1

10. I2 = I1

Two Bells17:04, highSchool, numeric, < 1 min, normal.

Consider two loud bells: The sound inten-sity of the first bell is β1 = 90 db (loud!)and the sound intensity of the second bellβ2 = 110 db (even louder!).

Assume each bell produces a harmonicsound wave or respective pressure amplitudesδPmax

1 and δPmax2 , and calculate the ratio

δPmax2

δPmax1

of the two pressure amplitudes.

Two Sound Sources 0217:04, highSchool, numeric, > 1 min, normal.

Two sources have sound levels of 75 dB and80 dB.

What is their combined intensity?

Chapter 17, section 5, The Doppler Effect 476

Car Horn and Train Whistle 0117:05, highSchool, numeric, > 1 min, normal.

A train is moving parallel and adjacent toa highway with a constant speed of 20 m/s.A car is traveling in the same direction as thetrain at 40 m/s. The train’s whistle sounds at320 Hz.The speed of sound is 343 m/s. When thecar is behind the train what frequency doesan occupant of the car observe for the trainwhistle?

Concept 21 P0517:05, highSchool, numeric, < 1 min, fixed.

A cello string 0.75 m long has a 220 Hzfundamental frequency.

Find the wave speed along the vibratingstring.

Frequency of a Supersonic Jet17:05, highSchool, numeric, > 1 min, normal.

Two jet airplanes are flying due east. Theleading jet is flying at 1.4 times the speed ofsound. The trailing jet is flying at 420 mph(Both relative to the ground). The wind isblowing 150 mph due west. The speed ofsound is 620 mph at this altitude.

If the engine of the leading jet has a fre-quency of 2650 Hz. What frequency is heardby the pilot of the trailing jet?

Frequency Variation17:05, highSchool, multiple choice, > 1 min,wording-variable.

Part 1 of 5A student, standing near a straight road,

records the sound of a car’s horn. Therecorded frequency (as a function of the car’sposition along the road) is plotted in the fig-ure below. The same car made four trial runsalong the road. Each trial was made with thecar traveling at a constant speed. The four re-sults are plotted below, denoted by the curves“K”, “Y ”, “D”, and “G”.

D

D

Y

Y

K

K

G

G

−100−75−50−25 0 25 50 75 100800

850

900

950

1000

Observed

Frequen

cy(H

z)

Car’s position along the road (m)

The car’s lowest speed is in

1. trial G.

2. trial K.

3. trial D.

4. trial Y .

5. undetermined.

Part 2 of 5The car’s speed in trial Y is

1. less than that in trial K.

2. greater than that in trial K.

3. equal to that in trial K.

4. undetermined.

Part 3 of 5The car’s speed in trial D is

1. equal to that in trial Y .

2. greater than that in trial Y .

3. less than that in trial Y .

4. undetermined.

Part 4 of 5A car far away, before it gets to the student,


has a Doppler shifted frequency (as heard bythe student) which is higher than the normalhorn’s frequency. A car far away, after passingthe student, has a Doppler shifted frequencywhich is lower than the normal horn’s fre-quency. The average of these two frequenciesis

1. greater than the horn’s frequency whenthe car is at rest.

2. less than the horn’s frequency when thecar is at rest.

3. equal to the horn’s frequency when thecar is at rest.

4. undetermined

Part 5 of 5In the different trials the distance of the stu-dent from the road (the path of the car) some-times varied.

During which trial did the student standclosest to the road?

1. trial Y

2. trial K

3. trial D

4. trial G

5. undetermined

Horn Sound17:05, highSchool, multiple choice, > 1 min,normal.

John is listening to a horn. He knows thefrequency of the horn is 444 Hz when both heand the horn are at rest.

If John hears the horn’s pitch at 477 Hz,what must be true?A) Both can be moving and have the same

speed.B) Both can be moving and have different

speeds.

C) John is moving towards the horn at rest.D) The distance between John and the horn

is increasing with time.E) Both can be moving in the same direction.F) Both can be moving, but in opposite di-

rections.

1. A, B, C, E, F

2. A, B, C, D, E, F

3. A, C, D, E, F

4. A, B, C, D, F

5. A, B, C, D, E

6. B, C, D, E, F

7. A, B, C, F

8. A, B, C, E

9. B, C, E, F

10. A, C, D, F

Moving Source17:05, highSchool, multiple choice, < 1 min,fixed.

The four figures below represent soundwaves emitted by a moving source. Whichpicture represents a source moving at a speedbigger than zero but less than the speed ofsound?

1.

2.


3.

4.

Police Siren and a Truck 0117:05, highSchool, multiple choice, > 1 min,wording-variable.

Part 1 of 2A police car is traveling at a speed, vc, to

the left. A truck is traveling at a speed, vt, tothe right. The frequency of the siren on thepolice car is fc.

The speed of sound in air is va. Let vt bethe speed of the observer in the truck, andvc be the speed of the source, the police car.

Police

vc vt

Truck

What is the frequency, ft, heard by anobserver in the moving truck?

1. ft =va − vtva + vc

fc

2. ft =va − vtva − vc

fc

3. ft =va + vtva + vc

fc

4. ft =va + vtva − vc

fc

Part 2 of 2A police car is traveling at a speed, vc, tothe right. A truck is traveling at a speed, vt,to the left. A wind is blowing in the samedirection as that of the truck with a speed,vw, to the left. The frequency of the siren onthe police car is fc.

The speed of sound in air is va.

Police

vc vt

Truck

vwwind


1. ft =va + vt − vwva − vc − vw

fc

2. ft =va + vt − vwva + vc + vw

fc

3. ft =va + vt + vwva − vc − vw

fc

4. ft =va + vt + vwva + vc + vw

fc

5. ft =va − vt − vwva − vc − vw

fc

6. ft =va − vt − vwva + vc + vw

fc

7. ft =va − vt + vwva − vc − vw

fc

8. ft =va − vt + vwva + vc + vw

fc


A police car is traveling at a speed, vc, tothe right. A truck is traveling at a speed, vt,


to the right. The frequency of the siren on thepolice car is fc.

The speed of sound in air is va. Let vt bethe speed of the observer in the truck, andvc be the speed of the source, the police car.

Police

vc vt

Truck


1. ft =va − vtva − vc

fc

2. ft =va − vtva + vc

fc

3. ft =va + vtva − vc

fc

4. ft =va + vtva + vc

fc


A police car is traveling at a speed, vc, tothe left. A truck is traveling at a speed, vt,to the right. A wind is blowing in the samedirection as that of the truck with a speed,vw, to the right. The frequency of the sirenon the police car is fc.

The speed of sound in air is va. Let vo bethe speed of the observer in the truck, andvc be the speed of the source, the police car.

Police

vc vt

Truck

vwwind


1. ft =va − vt + vwva + vc + vw

fc

2. ft =va − vt + vwva − vc − vw

fc

3. ft =va − vt − vwva + vc + vw

fc

4. ft =va − vt − vwva − vc − vw

fc

5. ft =va + vt + vwva + vc + vw

fc

6. ft =va + vt + vwva − vc − vw

fc

7. ft =va + vt − vwva + vc + vw

fc

8. ft =va + vt − vwva − vc − vw

fc

Red Shift of Light17:05, highSchool, numeric, > 1 min, normal.

Part 1 of 2The ”red shift” of radiation from a distant

galaxy consists of the light known to have awavelength of 434 nm when observed in thelaboratory, appearing to have a wavelength of462 nm .

What is the speed of galaxy in the line ofsight relative to the Earth?

Part 2 of 2Is it approaching or receding?

1. approaching

2. receding


Wavelength Measurements17:05, highSchool, numeric, > 1 min, normal.

Part 1 of 2The velocity of sound in air is 343 m/s .An ambulance is traveling east at 50 m/s .

Behind it there is a car traveling along thesame direction at 30 m/s . The ambulancedriver hears his siren with a wavelength of0.51 m .


30 m/s

Car

50 m/s

Ambulance

What is the measured wavelength of thesound of the ambulance’s siren when you areholding your measuring device behind the am-bulance?

Part 2 of 2What is the measured wavelength of thesound of the ambulance’s siren when yourmeasuring device is on the car’s hood?

Chapter 17, section 6, Quality of Sound (Noise) 481


On what does the pitch of a note depend?

1. only on loundness

2. only on frequency

3. only on quality of sound

4. only on frequency and quality of sound

4. only on frequency and loudness

4. only on loudness and quality of sound

5. It depends on all of these.


Which of the two musical notes displayedon an oscilloscope screen has the higher pitch?

1. The dashed pattern.

2. The dotted pattern.

3. Both are the same pitch.


In the oscilloscopes shown above, whichscreen shows the louder sound (assuming de-tection by equivalent microphones)?

1. The dashed pattern

2. The dotted pattern

3. Both are the same loudness.


Which is a more objective measurement,sound intensity or loudness, and why?

1. Sound intensity is exactly same as loud-ness.

2. Loudness is a more objective and physi-cal attribute of a sound wave because soundintensity can vary from person to person.

3. Sound intensity is a more objective andphysical attribute of a sound wave becauseloudness can vary from person to person.

4. Sound intensity and loudness are subjec-tive quantities; both can vary from person toperson.


How is an electronic organ able to imitatethe sounds made by various musical instru-ments?

1. An electronic organ plays the recorded


sounds of various musical instruments.

2. An electronic organ duplicates and super-imposes the sine waves that make up the over-all waves produced by these instruments.

3. An electronic organ uses built-in musicalinstruments.

4. An electronic organ mixes the waves ofresonant frequencies of various musical in-struments.


Why does your voice sound fuller in theshower?

1. The frequency of sound gets higher in theshower room.

2. Your ears become more sensitive in theshower.

3. The wavelength of sound gets longer.

4. The small enclosure causes your voice toreverberate as it reflects from wall to wall.


At an outdoor concert, the pitches of musi-cal tones are not affected on a windy day.

Why?

1. Although the speed of sound past a lis-tener on a windy day will change, the wave-length will not change, resulting in no changein pitch.

2. Although the wavelength of sound pasta listener on a windy day will change, thespeed of sound will not change, resulting inno change in pitch.

3. Although the frequency of sound pasta listener on a windy day will change, thewavelength will not change, resulting in nochange in pitch.

4. Although the wavelength of sound past alistener on a windy day will change, the fre-quency will not change, resulting in no changein pitch.


A trumpet has keys and valves that let thetrumpeter change the length of the vibratingair column and the position of the nodes. Abugle has no such keys and valves, yet it cansound different notes.

How does the bugler achieve differentnotes?

1. By controlling how hard he blows andhow he holds his mouth.

2. By controlling how he holds his mouth.

3. By controlling how hard he blows.

4. There is no way to achieve different noteswithout keys or valves.


Do all the people in a group hear the samemusic when they listen to it attentively?

1. Yes; everyone hears the same notes.

2. No; we each perceive what we have beentaught or have learned to perceive.

3. No; those closer hear purer tones.

4. Yes; everyone hears the same quality ofsound.


Concept 21 P0317:06, highSchool, numeric, > 1 min, normal.

Part 1 of 4A certain note has a frequency of 1000 Hz.What is the frequency of a note one octave

above it?

Part 2 of 4Two octaves above it?

Part 3 of 4One octave below it?

Part 4 of 4Two octaves below it?

Chapter 17, section 7, The Ear 484


Part 1 of 2Two speakers are wired to emit identical

sounds in unison. The wavelength in air ofthe sounds is 6 m.

What is the frequency of the sound emit-ted by the speakers? The speed of sound is340 m/s.

Part 2 of 2Is this a low pitch or a high pitch relative tothe range of human hearing?

1. A low pitch.

2. A high pitch.


The human ear is sometimes called aFourier analyzer.

What does this mean and why is it an aptdescription?

1. Our ears can measure the speed ofsound.

2. Our ears can sort out the individual sinewaves from a mixture of two or more sinewaves, so we hear the pure tones that makeup a complex tone.

3. Our ears measure the intensity of sound,which is just what a Fourier analyzer does.

4.Our ears have nothing to do with a Fourieranalyzer.


Why is it a safe prediction that you,presently reading this, will have a significantly

greater loss of hearing in your later years thanyour grandparents experienced?

1. Modern sounds are louder, leading to adecrease in the threshold of hearing.

2. Modern sounds are louder, leading to anincrease in the threshold of hearing.

3. Modern sounds have a higher frequency,leading to an increase in the threshold of hear-ing.

4. Modern sounds have a lower frequency,leading to an increase in the threshold of hear-ing.

Human Ear Sensitivity 0217:07, highSchool, multiple choice, > 1 min,fixed.

The human ear is most sensitive to thesounds in what range?

1. 5000-10000 Hz

2. 100-250 Hz

3. 500-1500 Hz

4. 10000-20000 Hz

5. 2000-3000 Hz

6. 500-1500 s

7. 5000-10000 s

8. 2000-3000 s

9. 4000-5000 Hz

10. 4000-5000 s

Human Ear Sensitivity17:07, highSchool, multiple choice, > 1 min,fixed.

Because the sensitivity of the human ear

Chapter 17, section 7, The Ear 485

varies over the audio spectrum, many soundsystems very high frequencies and

very low frequencies to compensate.

1. do nothing to, amplify

2. dampen, dampen

3. dampen, amplify

4. amplify, dampen

5. amplify, amplify

6. amplify, do nothing to

7. do nothing to, dampen

8. dampen, do nothing to

9. Sound systems do nothing to compen-sate.

Parts of the Ear17:07, highSchool, multiple choice, > 1 min,fixed.

Part 1 of 3The outer ear (meatus and ear flap)

.

1. determines only the direction of sound.

2. determines the intensity and direction ofsound.

3. determines the frequency and intensity ofsound.

4. determines the frequency and direction ofsound.

5. None of these.

6. determines only the intensity of sound.

7. determines only the frequency of sound.

8. directs sound to the eardrum and helps

determine sound direction.

Part 2 of 3The inner ear (cochlea and auditory nerves)

.

1. determines the frequency and direction ofsound.

2. directs sound to the eardrum and helpsdetermine sound direction.

3. determines the intensity and direction ofsound.

4. determines the frequency and intensity ofsound.

5. None of these.

6. determines only the intensity of sound.

7. determines only the frequency of sound.

8. determines only the direction of sound.

Part 3 of 3The middle ear consists of the .

1. None of these.

2. hammer and anvil only.

3. hammer and stirrup only.

4. stirrup and anvil only.

5. hammer, anvil, and spur.

6. hammer, tooth, and nail.

7. hammer, stirrup, and spur.

8. spur, anvil, and stirrup.

9.meatus, semi-circular canal, and stapes.

10. hammer, anvil, and stirrup.

Chapter 17, section 8, Sources of Musical Sound 486


What does it mean to say that a radiostation is “at 101.1 on your FM dial”?

1. The frequency of the sound signal is 101.1MHz.

2. The carrier frequency of electromagneticwaves emitted by the radio station is 101.1MHz.

3. The radiation power of a radio station is101.1 W.

4. The number 101.1 is a unique numberassigned by the government.

5. The wavelength of the sound signal is101.1 m.


Why do tuning forks with long tines vibrateat a lower frequency than short-tined forks?

1. The longer tines have greater rotationalinertia, so they’ll be more resistant to vibrat-ing.

2. The longer tines have smaller rotationalinertia, so they’ll be more resistant to vibrat-ing.

3. The longer tines have greater mass, sothey’ll have shorter wavelength.

4. The longer tines have greater air friction,so they’ll be more resistant to vibrating.


In a hi-fi speaker system, why is thewoofer (low-frequency speaker) larger thanthe tweeter (high-frequency speaker)?

1. The loudness of sound depends on thefrequency of oscillation, so the woofer has arelatively large surface to produce a greateramplitude of sound.

2. The woofer with a relatively large surfacehas more inertia and is not as responsive tohigher frequencies as a speaker with a smallersurface; the larger speaker pushes the longerwavelengths.

3. A speaker with a smaller surface is moreresponsive to lower frequencies of oscilla-tion.

4. A speaker with a greater mass producesloud sound.


How many octaves does normal humanhearing span, and how many octaves are on acommon piano keyboard?

1. about 100 octaves for both

2. about 100 octaves; about 10 octaves


4. about 1000 octaves for both


Chapter 17, section 9, Digital Sound Recording 487


Whereas a phonograph record rotates at a

constant angular speed, usually 331

3RPM, a

CD rotates at a variable speed so the linearspeed at all radii is a constant.

When will the CD rotate faster, when beingread near the inner part of the disc, or outerpart of the disc?

1. When being read near the outer part ofthe disk

2. When being read near the inner part ofthe disk

3. The rotational speed of the CD is a con-stant.

Chapter 17, section 11, Sonar, Ultrasound, and Ultrasound Imaging 488


Ultrasonic waves have many applicationsin technology and medicine. One advantageis that large intensities can be used withoutdanger to the car.

What is another advantage of their shortwavelength? (Why do microscopists use bluelight rather than white light to see detail?)

1. The short wavelengths of ultrasonic wavesallow the imaging of smaller objects.

2. Ultrasonic waves are good for ourhealth.

3. It is easy to cook food with ultrasonicwaves.

4. Ultrasonic waves are easy to diffract.

Chapter 18, section 1, Superposition of Sinusoidal Waves 489


A special device can transmit sound outof phase from a noisy jackhammer to its op-erator using earphones. Over the noise ofthe jackhammer, the operator can easily hearyour voice while you are unable to hear his.

Why?

1. The operator’s earphones are connectedto your microphone, so he can hear your voiceclearly.

2. These devices reduce jackhammer noiseby using destructive interference to cancelthe noisy sound, so he can hear your voiceclearly.

3. The operator’s earphones change the fre-quencies of your voice, so he can hear yourvoice clearly.

4. The operator’s earphonex amplifies yourvoice, so he can hear your voice clearly.

Concept 21 P0418:01, highSchool, multiple choice, > 1 min,fixed.

Part 1 of 2Starting with a fundamental tone, how

many harmonics are there between the firstand second octaves?

1. one

2. two

3. three

4. four

5. five

Part 2 of 2Between the second and third octaves?

1. one

2. two

3. four

4. five

5. three

Chapter 18, section 2, Interference of Sinusoidal Waves 490

Concept 20 P0718:02, highSchool, multiple choice, > 1 min,fixed.

Part 1 of 3Two speakers are wired to emit identical

sounds in unison. The wavelength in air ofthe sounds is 6 m.

Do the sounds interfere constructively ordestructively at a distance of 12 m from bothspeakers?

1. Constructively

2. Destructively

3. Neither

Part 2 of 3At a distance of 9 m from both speakers?

1. Constructively

2. Destructively

3. Neither

Part 3 of 3At a distance of 9 m from one speaker and 12m from the other?

1. Constructively

2. Destructively

3. Neither


Part 1 of 2A pure tone with frequency 500 Hz is played

through two stereo speaker plugged into thesame jack. As you walk around the room,you notice that the loudness of the soundalternates from loud to soft repeatedly.

What is happening?

1. You are experiencing alternating regionsof constructive and destructive interference.

2. The waves are moving away from you.

3. You are hearing destructive interfer-ence.

4. You are hearing constructive interfer-ence.

5. None of these

Part 2 of 2Would anything be different if a 1000 Hzsound wave were used instead?

I) The wavelength becomes shorterII) the distance between regions of interfer-

ence is smallerIII) the distance between regions of interfer-

ence is largerIV) The wavelength becomes longer

1. I and II only

2. I and IV only

3. II and IV only

4. I and III only

5. None of these

Chapter 18, section 4, Standing Waves in a String Fixed at Both Ends 491


When a guitar string is struck, a standingwave is produced that oscillates with a largesustained amplitude, pushing back and forthagainst the surrounding air to generate sound.

How does the frequency of the resultingsound compare with the frequency of thestanding wave in the string?

1. The frequencies of the resulting soundare half of those of the standing wave in thestring.

2. The frequencies of the resulting sound aretwice of those of the standing wave in thestring.

3. The frequencies of the sound and theoscillating string are the same.

4. The frequencies of the resulting soundhave nothing to do with those of the standingwave in the string.


If a vibrating string is made shorter (i.e.,by holding your finger on it), what effect doesthis have on the frequency of vibration and onthe pitch?

1. The frequency increases; the pitch de-creases.

2. The frequency decreases; the pitch de-creases.

3. Both decrease.

4. Both increase.

5. No effect


A nylon guitar string vibrates in a standingwave pattern shown below.

0.9 m

What is the wavelength of the wave?


Why is the thickness greater for the bassstrings of a guitar than for the treble strings?

1. Thick strings have smaller inertia, so theywill be more resistant to vibrating.

2. Thick strings have greater mass, so theywill have shorter wavelength.

3. Thick strings have greater air friction, sothey will be more resistant to vibrating.

4. Thick strings have greater inertia, so theywill be more resistant to vibrating.


If you very lightly touch a guitar string atits midpoint, you can hear a tone that is oneoctave above the fundamental for that string.(An octave is a factor of two in frequency.)

Why?

1. By touching the midpoint, the string vi-brates in four segments, so the frequency in-creases by a factor of two.

2. By touching the midpoint, the string vi-brates in two segments, so the frequency in-


creases by a factor of two.

3. By touching the midpoint, the tension ofthe string increases, so the frequency increasesby a factor of two.

4. When the string vibrates slightly, thefrequency increases by a factor of two.


A violin string playing the note “A” oscil-lates at 440 Hz.

What is the period of the string’s oscilla-tion?


The string of a cello playing the note “C”oscillates at 264 Hz.

What is the period of the string’s oscilla-tion?


The amplitude of a transverse wave in astretched string is the maxium displacementof the string from its equilibrium position.

To what does the amplitude of a longitudi-nal sound wave in air correspond?

1. the maximum displacement of the air

2. the overpressure of the compression

3. the wavelength of the sound wave

4. the square of the frequency


If the fundamental frequency of a guitarstring is 220 Hz, what is the frequency of the

second harmonic? The third?

1. 221 Hz; 223 Hz

2. 219 Hz; 218 Hz

3. 110 Hz; 55 Hz

4. 440 Hz; 660 Hz

5. 320 Hz; 420 Hz


If the fundamental frequency of a violinstring is 440 Hz, what is the frequency of thesecond harmonic? The third?

1. 442 Hz; 443 Hz

2. 220 Hz; 110 Hz

3. 110 Hz; 55 Hz

4. 440 Hz; 660 Hz

5. 880 Hz; 1320 Hz


Lower-pitched strings on guitars and pianosoften have copper wire wound around them.This wire does not make the string strongeror change the tension of the string.

What purpose does this extra wire serve?

1. Makes the string more massive, giving ita lower pitch.

2. Makes the string more massive, giving ita higher pitch.

3. Strengthens the string, lowering thepitch.


4. Shortens the string, raising the pitch.

5. None of these


When playing a violin, the effect producedwhen the bow is drawn faster across thestrings is

1. a higher pitch.

2. greater wave velocity in the strings.

3. a louder sound.

4. All of these

5. None of these . . . no discernible effect


Part 1 of 3The speed of waves on a guitar string is

115 m/s.What is the fundamental frequency of the

string when the effective string length is 70.0cm?

Part 2 of 3What is the fundamental frequency of thestring when the effective string length is 50.0cm?

Part 3 of 3What is the fundamental frequency of thestring when the effective string length is 40.0cm?


A violin string that is 50.0 cm long has afundamental frequency of 440 Hz.

What is the speed of the waves on thisstring?


Part 1 of 3The note produced on a violin string of

length 31.0 cm produces waves with a speedof 274.4 m/s.

What is the first harmonic of this note?

Part 2 of 3What is the second harmonic?

Part 3 of 3What is the third harmonic?

Standing Waves 0318:04, highSchool, multiple choice, < 1 min,fixed.

A string of length L is clamped at bothends. When it is plucked, it oscillates with a

wavelength that is2L

3. Consider the following

statements:A) There are three points on the string, ex-

cluding the ends, which remain motionlessat all times.

B) There are two points on the string, exclud-ing the ends, which remain motionless atall times.

C) The waves that form are standing waves.D) The waves that form are traveling waves.E) Energy is transferred from the string to

each end clamp.Which statements are correct?

1. A and C

2. B and C

3. A, C, and E

4. B, C, and E

5. A and D


6. B and D

7. A, D, and E

8. B, D, and E

Standing Waves 1518:04, highSchool, numeric,> 1min, wording-variable.

Part 1 of 2The length of a string is 150 cm. The

string is held fixed at each end. The stringvibrates in five sections; i.e., the string has fiveantinodes, and the string vibrates at 120 Hz.

Find the wavelength.

Part 2 of 2What is the fundamental frequency?


Part 1 of 2The length of a string is 180 cm . The ten-

sion in the string is 22 N . The linear densityof the string is 0.0067 kg/m . The string isheld fixed at each end. The string vibrates insix sections; i.e., the string has six antinodes.

Determine the frequency of vibrations inthe string.

Part 2 of 2What is the fundamental frequency; i.e., thelowest frequency the string can sustain?

Standing Waves 2618:04, highSchool, multiple choice, > 1 min,wording-variable.

The figure below represent a wave in astring with both ends held in fixed position.

`

Determine the wave length of the wave inthis string.

1. λ =2 `

7

2. λ = `

3. λ =2 `

3

4. λ =`

2

5. λ =2 `

5

6. λ =`

3

7. λ = 2 `

8. λ =`

4

9. λ =2 `

9

Wavelength 0118:04, highSchool, multiple choice, > 1 min,wording-variable.

The length of a string is 71.4 cm. The stringis held fixed at each end. There is a standingwave on the string with wavelength 20.4 cm.

Which figure schematically represents thestanding wave?

1.

2.


3.

4.

5.

6.

7.

8.

9.

Wavelength 01 A18:04, highSchool, multiple choice, < 1 min,normal.

The diagrams below show different stand-ing waves on a string of length 100 cm.

which wave has a wavelength 50 cm?

1.

2.

3.

4.

5.

6.

7.

8.


9.

Chapter 18, section 5, Forced Vibrations and Resonance 497


Why do soldiers break step in marchingover a bridge?

1. Usually a bridge is too narrow for thesoldiers to march.

2. They do that to avoid making a lot ofnoise.

3. If they do not break step in marching overa bridge, they are likely to expose themselvesto their enemy.

4. The regular step could set the bridge intoa resonance which could destroy the bridge.

5. There is no special reason.


Why is the sound of a harp soft in compar-ison with the sound of a piano?

1. A harp produces relatively softer soundsthan a piano because it is plucked with fin-gers.

2. A harp produces relatively softer soundsthan a piano because its sounding board issmaller and lighter.

3. A harp produces relatively softer soundsthan a piano because its sounding board isbigger and more massive.

4. A harp uses a softer string than a pi-ano.


Apartment dwellers will testify that bassnotes are more distinctly heard from musicplayed in nearby apartments.

Why do lower-frequency sounds getthrough walls, floors, and ceilings more eas-ily?

1. The higher-frequency waves are morelikely to diffract than the lower-frequencywaves.

2. The walls, floors, and ceilings are made ofmaterials that allow low-frequency waves topass.

3. Our ears are more sensitive to the low-frequency waves.

4. The natural frequency of large walls,floors, and ceilings is lower than the natu-ral frequency of smaller surfaces; bass notesmore easily set them into forced vibrationsand resonance.


If the handle of a vibrating tuning fork isheld solidly against a table, the sound fromthe tuning fork becomes louder.

Why, and how will this affect the length oftime the fork keeps vibrating?

1. Because a more massive surface is set intomore lower frequency vibration, the soundbecomes louder. By conservation of energy,this reduces the length of time the fork keepsvibrating.

2. Because a greater surface is set into vi-bration, the sound becomes louder. By con-servation of energy, this reduces the length oftime the fork keeps vibrating.

3. Because a more massive surface is setinto vibration, the sound becomes louder andthe length of time the fork keeps vibratingbecomes longer.


4. Because a greater surface is set into vibra-tion, the sound becomes louder. By conserva-tion of momentum, this reduces the length oftime the fork keeps vibrating.


The sitar, an Indian musical instrument,has a set of strings that vibrate and producemusic, even though they are never pluckedby the player. These “sympathetic strings”are identical to the plucked strings and aremounted below them.

How does this work?

1. The lower strings are resonating with theupper.

2. The upper strings are connected to thelower strings with invisible strings.

3.The lower strings are plucked by a ghost.

4. Scientists are still studying to find thereason.


Why does a dance floor heave only whencertain kinds of dance steps are being per-formed?

1. When certain dance steps have a greaterfrequency than the natural frequency of thefloor, the floor heaves.

2. When certain dance steps have a smallerfrequency than the natural frequency of thefloor, the floor heaves.

3. When certain dance steps resonate withthe natural frequency of the floor, the floorheaves.

4. Very strong dance steps cause the floor toheave.


An object resonates when the frequency ofa vibrating force either matches its naturalfrequency or is a sub-multiple of its naturalfrequency.

Why will it not resonate to multiples of itsnatural frequency? (Think of pushing a childin a swing.)

1. The wave power of a multiple of its nat-ural frequency is too weak to vibrate the ob-ject.

2. The wave power of a multiple of its nat-ural frequency is so strong that the objectwould be broken.

3. If the frequency of the driving force isa multiple of the natural frequency of theobject, the driving force distrupts the motionof the object.

4. If the frequency of the driving force isa multiple of the natural frequency of theobject, the driving force enhances the motionof the object.


Why does a sounding board on a musicalinstrument produce louder sound?

1. A sounding board with large surface hasgreater intertia, so the pitch of the producedsound will increase.

2. A sounding board with large surface isable to set more air vibrating, so the ampli-tude of the produced sound will increase.

3. A sounding board with large surface has


greater intertia, so the pitch of the producedsound will decrease.

4. A sounding board with large surface vi-brates with higher frequency, so the ampli-tude of the produced sound will increase.


Would a plucked guitar string vibrate forlonger or shorter time if the instrument hadno sounding board?

1. A shorter time; the frequency of the pro-duced sound increases.

2. A longer time; its mass is smaller thanthat with a sounding board.

3. A longer time; more air is set into motionper unit of time.

4. A longer time; less air is set into motionper unit of time.

Chapter 18, section 6, Standing Waves in Air Columns 500


As you pour water into a glass, you repeat-edly tap the glass with a spoon. (The soundis not being generated by the cavity of the aircolumn.)

As the tapped glass is being filled, which ofthe following is true?

1. Decrease in the pitch of the sound

2. No change in the pitch of the sound

3. Increase in the pitch of the sound

4. Increase in the volume of the sound

5. Decrease in the volume of the sound


Calculate the fundamental frequency of a4 meter organ pipe that is open at both ends.Assume that the temperature is 20◦C and thespeed of the sound is 344 m/s.


What is the fundamental frequency of a0.2 m long organ pipe that is closed at oneend, when the speed of sound in the pipe is352 m/s?


Part 1 of 3A flute is essentially a pipe open at both

ends. The length of a flute is approximately66 cm.

The speed of sound in the flute is 340 m/s.What is the first harmonic of a flute when

all keys are closed, making the vibrating air

column approximately equal to the length ofthe flute?




The human ear canal is about 2.8 cm longand can be regarded as a tube open at oneend and closed at the eardrum.

What is the fundamental frequency aroundwhich we would expect hearing to be bestwhen the speed of sound in air is 340 m/s?


Part 1 of 4A pipe that is open at both ends has a

fundamental frequency of 320 Hz when thespeed of sound in air is 331 m/s.

What is the length of this pipe?



Part 4 of 4What is the fundamental frequency of thispipe when the speed of sound in air is in-creased to 367 m/s due to a rise in the tem-perature of the air?


Part 1 of 3The frequency of a tuning fork can be found

by the method shown in the figure. A longtube open at both ends is submerged in abeaker of water, and the vibrating tuning forkis placed near the top of the tube. The length


L of the air column is adjusted by moving thetube vertically. The sound waves generatedby the fork are reinforced when the lengthof the air column corresponds to one of theresonant frequencies of the tube. The smallestvalue for L for which a peak occurs in soundintensity is 9 cm.

The speed of sound in air is 345 m/s.

L

What is the frequency of the tuning fork?

Part 2 of 3What is the value of L for the second resonantposition?

Part 3 of 3What is the value of L for the third resonantposition?


Part 1 of 2An open organ pipe is 2.46 m long, and the

speed of sound in the pipe is 345 m/s.What is the fundamental frequency of this

pipe?

Part 2 of 2How many harmonics are possible in a per-son’s hearing range of 21 Hz to 20000 Hz?

Holt SF 13Rev 49


If you blow across the open end of a sodabottle and produce a tone of 250 Hz, what willbe the frequency of the next harmonic heardif you blow much harder?


The fundamental frequency of an open or-gan pipe corresponds to the note middle C(with frequency 261.6 Hz on the chromaticmusical scale). The third harmonic f3 of an-other organ pipe that is closed at one end hasthe same frequency.

Compare the lengths of these two pipes by

findingLclosed

Lopen.

Open Tube Resonance18:06, highSchool, multiple choice, < 1 min,fixed.

This picture shows the displacements s ofthe air molecules in a traveling sound wave asa function of distance x.

l1 l2

Which of the following tubes, open at bothends, is closest to the right length so as toresonate at its fundamental frequency whenplaced in this sound wave?

1.l1/4

2.l1/2

3.l1

4.l2/4


5.l2/2

6.l2


Part 1 of 2The length of a hollow pipe is 120 cm. The

air column in the pipe is vibrating and hasfour nodes.


Find the frequency of the sound wave in thehollow pipe.

Part 2 of 2What is the fundamental frequency; i.e., thelowest frequency the pipe can sustain?

Standing Waves 2518:06, highSchool, multiple choice, > 1 min,wording-variable.

Part 1 of 2The figure below represents a sound wave

in a hollow pipe with both ends open.

`

Determine the wavelength of the soundwave in this hollow pipe.

1. λ =2 `

7

2. λ = `

3. λ =2 `

3

4. λ =`

2

5. λ =2 `

5

6. λ =`

3

7. λ = 2 `

8. λ =`

4

9. λ =2 `

9

Part 2 of 2Consider another organ pipe which has oneend open and one end closed.

`

Determine the wave length of the soundwave in this hollow pipe.

1. λ =4 `

7

2. λ =4 `

3

3. λ =4 `

5

4. λ = 4 `

5. λ =4 `

9

6. λ =4 `

11

7. λ =4 `

13

8. λ =4 `

15

9. λ =4 `

17



Part 1 of 3An open vertical tube has water in it. A

tuning fork vibrates over its mouth. As thewater level is lowered in the tube, the fourthresonance is heard when the water level is19.25 cm below the top of the tube.


19.25cm

What is the wave length of the sound wave?

Part 2 of 3What is the frequency of the sound wave; i.e.,the tuning fork?

Part 3 of 3The water continues to leak out the bottomof the tube.

When the open vertical tube next resonateswith the tuning fork, what is its length.

Tuning Fork Frequency 0118:06, highSchool, multiple choice, > 1 min,fixed.

Part 1 of 2An open vertical tube is filled with water

and a tuning fork vibrates over the top near

the open end. As the water level is lowered inthe tube, the first resonance is heard when thewater level is at L from the top of the tube.

The speed of sound in air is vs .

L

What is the frequency f0 of the tuning fork?

1. f0 =vs4L

2. f0 =vs2L

3. f0 =3 vs4L

4. f0 =vsL

5. f0 =5 vs4L

6. f0 =3 vs2L

7. f0 =7 vs4L

8. f0 =2 vsL

9. none of these

Part 2 of 2


As we continue to lower the water level inthe tube, the second f1 and the third f2 reso-nances are heard when the heights h1 and h2

of the air column in the tube are

1. h1 = 3L and h2 = 5L .

2. h1 = 2L and h2 = 5L .

3. h1 = 2L and h2 =3

2L .

4. h1 =5

2L and h2 = 3L .

5. h1 = 2L and h2 = 3L .

6. h1 = 3L and h2 = 4L .

7. h1 =5

2L and h2 =

7

2L .

8. h1 = 2L and h2 =7

2L .

9. h1 = 2L and h2 =5

2L .

10. h1 = 3L and h2 =5

2L .

Tuning Fork Frequency 0218:06, highSchool, numeric, > 1 min, normal.

Part 1 of 2An open vertical tube is filled with water

and a tuning fork vibrates over the top nearthe open end. As the water level is loweredin the tube, the first resonance is heard whenthe water level is at 17 cm from the top of thetube.


17cm

What is the frequency of the tuning fork?

Part 2 of 2As we continue to lower the water level inthe tube, the second f1 and the third f2 reso-nances are heard when the heights are h1 andh2 in the air column.

What is the height h2 ?


The length of a hollow pipe is 66.3 cm. Thepipe has one end open. There is a standingwave in the pipe with wavelength 20.4 cm.

Which figure schematically represents thisstanding wave?

1.


2.

3.

4.

5.

6.

7.

8.

9.


The length of a hollow pipe is 71.4 cm. Thepipe is open at both ends. There is a standingwave in the pipe with wavelength 20.4 cm.

Which figure schematically represents thisstanding wave?

1.

2.

3.

4.

5.

6.

7.

8.

9.

Wavelength 0518:06, highSchool, multiple choice, < 1 min,wording-variable.

The length of a hollow pipe is 11.5 cm .There is a standing wave in the pipe with


wavelength 9.2 cm.Which figure schematically represents the

standing wave?

1.

L

2.

L

3.

L

4.

L

5.

L

6.

L

7.

L

8.

L

9.

L

10.

L

Chapter 18, section 9, Beats: Interference in Time 507


A mosquito flaps its wings 600 times persecond, which produces the annoying 600 Hzbuzz. The speed of sound in air is 340 m/s.

How far does the sound travel between wingbeats?


Two sound waves of the same frequencycan interfere, but to create beats, two soundwaves have to have different frequencies.

Why?

1. To alternate between constructive anddestructive interfrence requires different fre-quencies.

2. Two waves of different frequencies inter-fere destructively, independent of their phasedifference.

3. Two waves of different frequencies inter-fere constructively, independent of their phasedifference.

4. Waves of the same frequency interfereconstructively, independent of their relativephase.

5. Waves of the same frequency interferedestructively, independent of their relativephase.


Walking beside you, your friend takes 50strides per minute while you take 48 stridesper minute.

If you start in step, when will you be in stepagain?

Concept 20 39


Suppose a piano tuner hears 3 beats persecond when listening to the combined soundfrom his tuning fork and the piano note beingtuned. After slightly tightening the string, hehears 5 beats per second.

Should the string be loosened or tightened?

1. The string should be loosened becausethe frequency of the string is 5 Hz above thecorrect frequency.

2. The string should be loosened becausethe frequency of the string is 5 Hz below thecorrect frequency.

3. The string should be tightened becausethe frequency of the string is 5 Hz above thecorrect frequency.

4. The string should be tightened becausethe frequency of the string is 5 Hz below thecorrect freguency.

5. The string should be loosen to increase itsfrequency.


A human cannot hear sound at a frequencyof 100 kHz, or sound at 102 kHz. But ifyou walk into a room in which two sourcesare emitting sound waves at 100 kHz and 102kHz, you’ll hear sound. Why?

1. The superposition of two sounds makes alouder sound.

2. The two sounds interfere constructively.

3. The two sounds interfere destructively.

4. You can hear a “beat” representing al-ternate constructive and destructive interfer-ence.

Chapter 18, section 9, Beats: Interference in Time 508

Concept 20 P1018:09, highSchool, multiple choice, < 1 min,fixed.

What beat frequencies are possible withtuning forks of frequencies 256, 259, and 261Hz?

1. 3 possible: 256 Hz, 259 Hz, and 261 Hz.



4. 2 possible: 2 Hz and 3 Hz.

5. 4 possible: 2 Hz, 3 Hz, 5 Hz, and 7 Hz.


When a tuning fork of frequency 256 Hz vi-brates beside a piano string, beats are heard.The string is tightened slightly and the beatsgo away.

What was the original frequency of thestring?

1. less than 256 Hz

2. greater than 256 Hz

3. 256 Hz


When two tuning forks of 132 Hz and 137Hz, respectively, are sounded simultaneously,how many beats per second are heard?

Chapter 19, section 2, The Zeroth Law of Thermodynamics: Thermal Equilibrium 509


If the air in your room is in thermal equi-librium, which of following is wrong?

1. The molecules of the air have the sameaverage kinetic energy.

2. The molecules of the air exchange energywith each other at all times.

3. Different parts of your room have thesame average temperature.

4. The molecules of the air have the sameaverage speed.


In your room there are things such as tables,chairs, other people, and so forth.

Which of these has a temperature greaterthan the temperature of the air?

1. people

2. tables

3. chairs

4. tables, chairs and other people

5. All are wrong.


How does the temperature of a thermome-ter outdoors on a sunny day compare with thetemperature of the air?

1. A little higher

2. A little lower

3. The same

4. Much lower

5. All are wrong.


At what common temperature will a blockof wood and a block of metal both feel neitherhot nor cold to the touch?

1. When the temperature of the blocks isthe same as the temperature of your hand

2. At room temperature

3. At the freezing point

4. When the temperature of the blocks ishigher than the temperature of your hand

5. When the temperature of the blocks islower than the temperature of your hand

Chapter 19, section 3, Celsius and Fahrenheit Temperature Scales 510

Celsius vs Fahrenheit19:03, highSchool, multiple choice, < 1 min,fixed.

The coldest temperature possible is −273degrees Celsius, which is called absolute zero.

What is this temperature in degreesFahrenheit?

1. −459.4 ◦F

2. −491.4 ◦F

3. −523.4 ◦F

4. +459.4 ◦F

5. +491.4 ◦F

6. +523.4 ◦F

7. 0 ◦F

8. 32 ◦F

9. −32 ◦F

10. −119.667 ◦F


Convert 300◦C to Fahrenheit.


At what temperature is the Celsius andFahrenheit value the same?

1. −40◦C

2. −22◦C

3. −50◦C

4. 40◦C

5. 20◦C

6. 0◦C

7. −26◦C

8. −18◦C

Holt SF 10A 0119:03, highSchool, numeric, < 1 min, fixed.

Part 1 of 2The lowest outdoor temperature ever

recorded on Earth is −128.6◦F, recorded atVostok Station, Antarctica, in 1983.

a) What is this temperature on the Celsiusscale?

Part 2 of 2b) What is this temperature on the Kelvinscale?


Part 1 of 2The normal human body temperature is

98.6◦F. A person with a fever may record102◦F.

a) What is the lower temperature on theCelsius scale?

Part 2 of 2b) What is the higher temperature on theCelsius scale?


Part 1 of 2The freezing and boiling points of water on

the imaginary “Too Hot” temperature scaleare selected to be exactly T freezing

TH= 51◦ TH

and T boilingTH

= 197◦ TH.a) Derive an equation relating the Too Hot

scale to the Celsius scale.

Chapter 19, section 3, Celsius and Fahrenheit Temperature Scales 511

1. TC=

50

73(T

TH− 51)

2. TC=

50

73T

TH+ 51

3. TC=

73

50(T

TH− 51)

4. TC=

73

50T

TH+ 51

5. TC= T

TH+ 51

6. TC= T

TH− 51

7. None of these

Part 2 of 2b) Calculate absolute zero in degrees TH.


At what Fahrenheit temperature are theCelsius and Fahrenheit temperatures numeri-cally equal?

New Thermometric Scale19:03, highSchool, numeric, > 1 min, normal.

We introduce the X thermometric scale.Given: The melting point 316 ◦C of a par-

ticular alloy is 212 ◦X and the freezing point−54 ◦C of a particular liquid is 32 ◦X.

At what temperature does water boil on theX scale?

Chapter 19, section 4, The Constant-Volume Gas Thermometer and the Kelvin Scale 512


Convert 120◦F to Kelvin.


Convert 80 K to Celsius.


Part 1 of 4The temperatures of one northeastern state

range from 105◦F in the summer to −25◦F inwinter.

a) What is the lower temperature on theCelsius scale?

Part 2 of 4b) What is the lower temperature on theKelvin scale?

Part 3 of 4c) What is the higher temperature on theCelsius scale?

Part 4 of 4d) What is the higher temperature on theKelvin scale?


Part 1 of 2A pan of water is heated from 23◦C to 78◦C.a) What is the change in temperature on

the Kelvin scale?

Part 2 of 2b) What is the change in temperature on theFahrenheit scale?

Holt SF 10A 0519:04, highSchool, numeric, > 1 min, fixed.

Part 1 of 2

Liquid nitrogen is used to cool substancesto very low temperatures. The boiling pointof liquid nitrogen (at 1 atm of pressure) is77.34 K.

a) What is this temperature on the Celsiusscale?

Part 2 of 2b)What is this temperature on the Fahrenheitscale?


Part 1 of 2The highest recorded temperature on Earth

was 136◦F, at Azizia, Libya, in 1922.a) What is this temperature on the Celsius

scale?



Part 1 of 2The melting point of gold is 1947◦F.a) What is this temperature on the Celsius

scale?


Holt SF 10Rev 4119:04, highSchool, multiple choice, > 1 min,fixed.

Part 1 of 2Absolute zero on the Rankine temperature

scale is TR = 0◦R, and the scale’s unit is thesame size as the Fahrenheit degree.

a) Write a formula that relates the Rankinescale to the Fahrenheit scale.

Chapter 19, section 4, The Constant-Volume Gas Thermometer and the Kelvin Scale 513

1. TF = TR − 459.67

2. TF = TF − 459.67

3. TF = TR + 459.67

4. TF = TR + 20

5. None of these

Part 2 of 2b) Write a formula that relates the Rankinescale to the Kelvin scale.

1. TR =9

5T

2. TR =9

5TF

3. None of these

4. TR =5

9TF

5. TR =5

9T


Part 1 of 4The boiling point of liquid hydrogen is

−252.87◦C.a) What is this temperature in degrees

Fahrenheit?

Part 2 of 4b) What is this temperature in Kelvin?

Part 3 of 4Consider the temperature of a room at20.5◦C.

c) What is this temperature in degreesFahrenheit?

Part 4 of 4d) What is this temperature in Kelvin?


At what Fahrenheit temperature are theKelvin and Fahrenheit temperatures numeri-cally equal?

Chapter 19, section 5, Thermal Expansion of Solids and Liquids 514


The coefficient of linear expansion for asilver strip is 1.9× 10−5 /◦C.

What is its length on a hot day when thetemperature is 37◦C if the strip is 0.2 m longwhen it is −10◦C?


If a 50 m steel footbridge experiencesextreme temperatures between −15 ◦C and45 ◦C, what is the range in size of thisbridge if it measures exactly 50 m at 20◦C?(Steel has a coefficient of linear expansion of1.1× 10−5 /◦C)


A square hole is cut out of a piece of sheetmetal. When the temperature of the metal israised, the metal expands.

What happens to the size of the squarehole? Hint: Break up the piece of metal intoeight smaller square pieces of sheet metal,then raise the temperature, then put thenback together.

1. The hole becomes bigger.

2. The hole becomes smaller.

3. The hole remains the same.


Suppose your gold wedding ring becamestuck on your finger. Some home remediessuggest soaking your finger in ice water andthen trying to remove the ring.

If this remedy relies on thermal expansioneffects, what does this tell you about the rel-ative expansion coefficients of gold and yourfinger?

1. The expansion coefficient of gold ishigher.

2. The expansion coefficient of your finger ishigher.



Two pieces of copper pipe are stuck to-gether, as shown.

One way to separate them is to run waterinside the inner pipe and over the outer pipe.

Which method is applicable to separatethem?

1. Run cold water inside the inner pipe andpour hot water over the outer pipe.

2. Run hot water inside the inner pipe andpour cold water over the outer pipe.

3. Run hot water inside the inner pipe andpour hot water over the outer pipe.


4. Run cold water inside the inner pipe andpour cold water over the outer pipe.


Two thin strips of metal (A and B) areglued together at 0◦C as shown in the figure.

A

B

At 20◦C they bend upward because themetals expand differently.

A

B

Which metal, A or B, has a higher thermalexpansion coefficient?

1. B

2. A

3. They have the same coefficient.


A mercury thermometer consists of amercury-filled glass bulb that is connectedto a narrow glass tube. Mercury thermome-ters are based on the thermal expansion ofmercury: as the mercury expands, it rises upthe tube.

Which has the higher thermal expansioncoefficient?

1. mercury

2. glass


Hewitt CP9 12 E0419:05, highSchool, multiple choice, < 1 min,

fixed.

When water freezes, it expands.What does this say about the density of ice

relative to the density of water?

1. Ice is denser than water.

2. Ice is as dense as water.

3. Ice is less dense than water.


Which strip bends when heated?

1. an aluminum strip

2. a copper strip

3. a lead strip

4. a bimetallic strip

5. None of these


Why do boulders break when first placed infire for an extended period of time and thendoused with cold water?

1. The change of temperature causes vibra-tion.

2. Heat makes them expand, while suddencooling causes them to contract quickly.

3. The inner and outer parts of the boulderhave different temperatures.

4. Heat melts them, causing the material tochange it’s properties.

Hewitt CP9 15 E27



What is correct?

1.Grandfather’s pendulum clock runs fasteron a hot day.

2. On a hot day the pendulum lengthensslightly.

3. Both are correct.

4. Neither is corrent.


Imagine two drinking glasses that stick to-gether when put one into the other.

Which of the following advice will help sep-arate them?

1. Fill the inner glass with hot water andrun hot water over the surface of the outerglass.

2. Fill the inner glass with cold water andrun cold water over the surface of the outerglass.

3. Fill the inner glass with hot water andrun cold water over the surface of the outerglass.

4. Fill the inner glass with cold water andrun hot water over the surface of the outerglass.

5. There is no easy way to separate them.


One end of the bridge is fixed, while the endshown rides on a rocker to allow for thermalexpansion.

When would it be most reasonable to seethe top of the rocker slightly tipped to theright?

1. during the hottest part of the year

2. during the coldest part of the year

4. The rocker will shift up and down, notright and left.

5. The rocker will neither tilt nor shift.


A metal ball is just able to pass through ametal ring.

What is correct?

1. When the ball is heated, it will not passthrough the ring.

2. When the ball is heated, it will still passthrough the ring.

3. When the ring is heated, the size of thehole does not change.

4. When the ring is heated, the size of thehole decreases.

5. When the ring is cooled, the size of thehole increases.


Suppose you cut a small gap in a metal ring,


What is correct?

1. The gap in the ring will become widerwhen the ring is heated.

2. The gap in the ring will become narrowerwhen the ring is heated.

3. The gap in the ring will not change whenthe ring is heated.

4. The gap in the ring will become widerwhen the ring is cooled.

5. The gap in the ring will not change whenthe ring is cooled.


What was the precise temperature at thebottom of Lake Superior at 12 a.m. on Octo-ber 31, 1894?

1. 0 ◦C

2. 2 ◦C

3. 4 ◦C

4. 100 ◦C

5. All are wrong.


Consider water pipes in winter.What is wrong?

1. When the temperature is below freezing,water contracts.

2.Water pipes freeze before water does.

3. When the temperature is below freezing,water expands.

4. When the temperature is below freezing,pipes contract.

5. Metal pipes will fracture if water in themfreezes.

Chapter 19, section 6, Macroscopic Description of an Ideal Gas 518


What change in pressure occurs in a partyballoon that is squeezed to one third of itsoriginal volume with no change in tempera-ture?

1. The pressure decreases three times.

2. The pressure increases three times.

3. The pressure decreases to two thirds of itsoriginal value.

4. The pressure increases one and a halftimes.

5. There is no change in pressure.

Concept 14 5319:06, highSchool, multiple choice, > 1 min,wording-variable.

Air in a cylinder is compressed to one tenthof its original value with no change in temper-ature. Then a valve is opened to let enoughair out to bring the pressure back to its origi-nal value.

What percent of molecules escape?

1. 90%

2. 9%

3. 0.9%

4. 0.09%

5. 10%

6. 1%

7. 0.1%

8. 0.01%


Consider two equal-sized rooms connectedby an open door. One room is maintained ata higher temperature than the other.

Which room contains more air molecules?

1. the cooler room

2. the hotter room

3. Both rooms contain the same number ofair molecules.

4. It’s impossible to determine.


A 1-liter tank contains 1,000,000,000 oxy-gen (O2) molecules and 1,000,000,000 he-lium (He) atoms. Another tank contains1,000,000,000 helium (He) atoms. The gasesin the tanks have the same pressure and tem-perature.

What is the volume of the tank that con-tains only helium?

1. 1 liter

2. 2 liter

3. 0.5 liter

4. 0.25 liter

5. 4 liter


Part 1 of 2Two gas-filled tanks have the same volume,

temperature, and pressure. They are identicalin every way except that one is filled with


oxygen (O2) gas and the other is filled withnitrogen (N2) gas.

Which container has more gas molecules?

1. The container of oxygen

2. The container of nitrogen

3. They have the same number ofmolecules.

Part 2 of 2Two gas-filled tanks have the same volume,temperature, and pressure. They are identicalin every way except that one is filled withoxygen (O2) gas and the other is filled withnitrogen (N2) gas.

Which container weighs more?



3. They have the same weight.

Conceptual 09 Q9 short19:06, highSchool, multiple choice, < 1 min,fixed.

Two gas-filled tanks have the same volume,temperature, and pressure. They are identicalin every way except that one is filled withoxygen (O2) gas and the other is filled withnitrogen (N2) gas.

Which container weighs more?



3. They have the same weight.


Part 1 of 2If the pressure on a gas in a flexible closed

container is increased and the temperature re-

mains constant, what happens to the volumeof gas?

1. increases

2. decreases

3. remains the same



Part 2 of 2Tom says that it is impossible to maintainconstant temperature while the container isbeing compressed.

Do you agree with his statement?

1. Yes; the average kinetic energy of themolecules increases because the the externalforce does positive work.

2. No; the average kinetic energy of themolecules could remain the same if some heatwere removed from the gas.

3. Yes; the temperature will always de-crease.


Under constant pressure and with a con-stant amount of gas present, what happensto the volume of the gas if the temperatureincreases?

1. increases

2. decreases

3. remains the same





A fixed amount of helium gas is held insidea l-liter container at a temperature of 25 ◦Cand atmospheric pressure.

If the container expands to 2 liters withoutany change in temperature or amount of gas,what is the pressure?

1. 0.5 atm

2. 1 atm

3. 2 atm

4. 0.25 atm


The pressure on the walls of the containeris due to the collisions of the gas moleculeswith the container wall. If you increase thetemperature of a closed container of gas thathas a fixed volume, the pressure inside willincrease because the molecules exert a greaterforce on the walls.

Why could the molecules exert a greaterforce?

1. The molecules move faster.

2. The volume increases.

3. The mass decreases.

4. The molecules move slower.

Chapter 19, section 7, Problem Solving: Ideal Gas Law 521


What is wrong?

1.When the air inside a house is heated, thevolume of the air does not change.

2.When a gas is heated, it expands.

3. One can heat the air without increasingthe volume of the house.

4. When air is heated inside a house, someof the air leaks to the outside.

5.When you cool the house, air is drawn infrom outside.


A cylinder with a movable piston containsgas at a temperature of 27 ◦C, with a volumeof 15 m3 and a pressure of 0.200× 105 Pa.

What will be the final temperature of thegas if it is compressed to 0.700 m3 and itspressure is increased to 0.800× 105 Pa?


Gas is confined in a tank at a pressure of1.00×108 Pa and a temperature of 15◦C. Halfof the gas is withdrawn and the temperatureis raised to 65◦C.

Find the new pressure in the tank.

Holt SF 09E 0319:07, highSchool, numeric, > 1 min, normal.

A gas bubble with a volume of 0.1 cm3

is formed at the bottom of a 10 cm deepcontainer of mercury. The temperature is27 ◦C at the bottom of the container and

37◦C at the top of the container.The acceleration of gravity is 9.81 m/s2 .What is the volume of the bubble just be-

neath the surface of the mercury? Assumethat the surface is at atmospheric pressure.


An ideal gas is contained in a vessel offixed volume at a temperature of 325 K and apressure of 1.22× 105 Pa.

If the pressure is increased to 1.78×105 Pa,what is the final temperature of the gas?


The pressure in a constant-volume gas ther-mometer is 7.09 × 104 Pa at 100.0 ◦C and5.19× 104 Pa at 0.0 ◦C.

What is the temperature when the pressureis 4.05× 103 Pa?


A swimmer has 8.20× 10−4 m3 of air in hislungs when he dives into a lake.

The acceleration of gravity is 9.81 m/s2 .Assuming the pressure of the air is 95 per-

cent of the external pressure at all times, whatis the volume of the air at a depth of 10.0 m?Assume that the atmospheric pressure at thesurface is 1.013 × 105 Pa, the density of thelake water is 1.00 × 103 kg/m3, and the tem-perature is constant.


An air bubble has a volume of 1.50 cm3

when it is released by a submarine 100.0 mbelow the surface of the sea.


Chapter 19, section 7, Problem Solving: Ideal Gas Law 522

What is the volume of the bubble when itreaches the surface? Assume that the temper-ature of the air in the bubble remains constantduring ascent.


The density of helium gas at 0.0 ◦C is0.179 kg/m3. The temperature is then raisedto 100.0 ◦C, but the pressure is kept constant.

Assuming that helium is an ideal gas, cal-culate the new density of the gas.


A weather balloon is designed to expandto a maximum radius of 20.0 m when the airpressure is 3.0 × 103 Pa and the temperatureof the air surrounding it is 200.0 K.

If the balloon is filled at a pressure of 1.01×105 Pa and 300.0 K, what is the radius of theballoon at the time of liftoff?


Part 1 of 2Before beginning a long trip on a hot day,

a driver inflates an automobile tire to a gaugepressure of 1.8 atm at 293 K. At the end ofthe trip, the gauge pressure in the tire hasincreased to 2.1 atm.

a) Assuming the volume of the air insidethe tire has remained constant, what is itstemperature at the end of the trip?

Part 2 of 2Air is released from the tire during a shorttime interval, so that the temperature remainsat the value found in part a). Assume thatthe amount of air released is small enough forthe tire’s volume to be treated as constant.

b) What quantity of air (as a fraction ofthe initial number of particles, Ni) must be

released from the tire so that the pressurereturns to its initial value?


A cylindrical diving bell 3.0 m in diame-ter and 4.0 m tall with an open bottom issubmerged to a depth of 220 m in the ocean.The temperature of the air at the surface is25◦C, and the air’s temperature 220 m down is5.0◦C. The density of sea water is 1025 kg/m3.

The acceleration of gravity is 9.81 m/s2 .How high does the sea water rise in the bell

when the bell is submerged?


Part 1 of 2An air bubble originating from a deep-sea

diver has a radius of 2.0 mm at the depthof the diver. When the bubble reaches thesurface of the water, it has a radius of 3.0 mm.Assume that the temperature of the air in thebubble remains constant.

The acceleration of gravity is 9.81 m/s2 .a) Determine the depth of the diver.

Part 2 of 2b) Determine the absolute pressure at thisdepth.


A sealed glass bottle at 27◦C contains air ata pressure of 1.01× 105 Pa and has a volumeof 30.0 cm3. The bottle is tossed into an openfire.

When the temperature of the air in thebottle reaches 225◦C, what is the pressureinside the bottle? Assume the volume of thebottle is constant.

Chapter 20, section 1, Heat and Thermal Energy 523


A glass of water sits on a table. The tem-perature of the water is the same as that ofthe glass.

Which are moving faster, the silicon dioxidemolecules (SiO2) that make up the glass or thewater molecules (H2O)?

1. water molecules

2. silicon dioxide molecules

3. They move at the same speed.


Part 1 of 3Two glasses of water contain different vol-

umes of water at the same temperature.

A B

In which glass are the water molecules mov-ing faster?

1. A

2. B

3. Same speed in both


Part 2 of 3Which glass contains more thermal energy?

1. A

2. B

3. Same in both


Part 3 of 3Which glass requires more heat to increase itstemperature by 1◦C ?

1. A

2. B

3. Either



Part 1 of 2A wooden block is released from rest at the

top of a frictionless inclined plane and slidesdown to the bottom.

What conversions of energy are taking placeas the block slides down the inclined plane?

1. Gravitational potential energy is con-verted into kinetic energy.

2. Gravitational potential energy is con-verted into kinetic energy and thermal en-ergy.

3. Kinetic energy is converted into thermalenergy.

4. No energy conversion takes place.

Chapter 20, section 1, Heat and Thermal Energy 524

Part 2 of 2What would be your answer if there werefriction between the block and the plane?

1. Gravitational potential energy is con-verted into kinetic energy.

2. Gravitational potential energy is con-verted into kinetic energy and thermal en-ergy.

3. Kinetic energy is converted into thermalenergy.

4. No energy conversion of energy takesplace.


You use energy to heat your home.What ultimately happens to the energy

that you pay for in your heating bill?

1. The energy heats your home.

2. The energy escapes your home and heatsthe outside.

3. The energy changes to mass.

4. The energy disappears as it never ex-ists.

Chapter 20, section 2, Internal Energy 525

Figuring Physics 1820:02, highSchool, multiple choice, < 1 min,normal.

Helium has the special property that itsinternal energy is directly proportional to itsabsolute temperature. Consider a flask ofhelium with a temperature of 2◦C.

If it is heated to twice its internal energy,what will its temperature be?

1. 277◦C

2. 4◦C

3. 275 K

4. 277 K

5. 275◦C

6. None of these


Which of the following has the greatestamount of internal energy?

1. an iceberg

2. a cup of hot coffee

3. a cup of cold water

4. a pencil

5. a laptop


A vessel contains water. Paddles that arepropelled by falling masses turn in the wa-ter, causing the water’s internal energy to in-crease. The temperature of the water is then

measured, giving an indication of the water’sinternal energy increase.

The acceleration of gravity is 9.81 m/s2 .If a total mass of 11.5 kg falls 6.69 m and

all of the mechanical energy is converted tointernal energy, by how much will the internalenergy of the water increase? (Assume noenergy is transferred as heat out of the vesselto the surroundings or from the surroundingsto the vessel’s interior.)


A worker drives a 0.500 kg spike into arail tie with a 2.50 kg sledgehammer. Thehammer hits the spike with a speed of 65.0m/s.

If one third of the hammer’s kinetic en-ergy is converted to the internal energy of thehammer and spike, how much does the totalinternal energy increase?


A 3.0 × 10−3 kg copper penny drops a dis-tance of 50.0 m to the ground.

The acceleration of gravity is 9.81 m/s2 .If 65 percent of the initial potential energy

goes into increasing the internal energy of thepenny, find the magnitude of that increase.


A 2.5 kg block of ice at a temperature of0.0◦C and an initial speed of 5.7 m/s slidesacross a level floor.

If 3.3 × 105 J are required to melt 1.0 kgof ice, how much ice melts, assuming that theinitial kinetic energy of the ice block is entirelyconverted to the ice’s internal energy?

Holt SF 10B 0520:02, highSchool, numeric,< 1min, wording-

Chapter 20, section 2, Internal Energy 526

variable.

The amount of internal energy needed toraise the temperature of 0.25 kg of water by0.2◦C is 209.3 J.

How fast must a 0.25 kg baseball travelin order for its kinetic energy to equal thisinternal energy?


A 0.75 kg spike is hammered into a railroadtie. The initial speed of the spike is equal to3.0 m/s.

If the tie and spike together absorb 85 per-cent of the spike’s initial kinetic energy asinternal energy, calculate the increase in in-ternal energy of the tie and spike.


Part 1 of 2A gas expands when 606 J of energy is

added to it by heat. The expanding gas does418 J of work on its surroundings.

a) What is the overall change in the internalenergy of the gas?

Part 2 of 2b) If the work done by the gas equals 1212 J,how much energy must have been added asheat in order for the change in internal energyat the end of the process to equal the initialchange in internal energy?

Chapter 20, section 3, Heat Capacity and Specific Heat 527


A power station with an efficiency of 0.4generates 1 × 108 W of electric power anddissipates 1.5 × 108 J/s of thermal energy tothe cooling water that flows through it. Thespecific heat of water is 4184 J/kg ·◦C.

How much water flows through the planteach second if the water is heated through3◦C?


Suppose a new liquid were discovered thatis identical to water in every way except thatit has a lower specific heat. Consider taking ashower with this liquid.

Would insulating the pipes from the hotwater heater to the shower head be more orless important with this new liquid?

1. More important; the lower specific heatmakes it easier to cool the liquid flowing fromthe pipes to the shower head.

2. Less important; the lower specific heatmakes it harder to cool the liquid flowingfrom the pipes to the shower head.

3. No significant difference in importance.


One hundred grams of liquid A is at a tem-perature of 100◦C. One hundred grams of liq-uid B is at a temperature of 0◦C. When thetwo liquids are mixed, the final temperatureis 50◦C.

What can you say about the specific heatsof the two liquids?

1. The specific heat of A is greater than thatof B.

2. The specific heat of B is greater than thatof A.

3. The specific heats of A and B are equal.


Two hundred grams of liquid A is at atemperature of 100◦C. One hundred grams ofliquid B is at a temperature of 0◦C. When thetwo liquids are mixed, the final temperatureis 50◦C.

Which material has a higher specific heat?

1. The specific heat of A is greater than thatof B.

2. The specific heat of B is greater than thatof A.

3. The specific heats of A and B are equal.


Which statement is wrong?

1. Adding the same amount of heat to twodifferent objects will produce the same in-crease in temperature.

2. Different substances have different ther-mal properties due to differences in the wayenergy is stored internally in the substances.

3.When the same amount of heat producesdifferent changes in temperature in two sub-stances of the same mass, we say that theyhave different specific heat capacities.

4. Each substance has its own characteristicspecific heat capacity.

5. Temperature measures the average ki-netic energy of random motion, but not other


kinds of energy.


Consider the following statement:Water has a high specific heat capacity.

1. It’s not true.

2. It’s true only if water is not mixed withother substances; for example, milk wouldhave low specific heat.

3. It’s always true. A watermelon stays coolfor a longer time than sandwiches when bothare removed from a cooler on a hot day.


Iceland, so named to discourage conquestby expanding empires, is not at all ice-coveredlike Greenland and parts of Siberia, eventhough it is close to the Arctic Circle. Theaverage winter temperature of Iceland is con-siderably higher than in the regions at thesame latitude in eastern Greenland and cen-tral Siberia.

What explains this?

1. The climate of Iceland is moderated bythe surrounding water.

2. Iceland is below sea level.

3. Both are true.

4. Neither is true.


What is the explanation for the fact thatthe desert sand is very hot in the day and verycool at night?

1. Sand reflects light very well.

2. Sand has a low specific heat compared toair.

3. Sand is a bad heat conductor.


What would be wrong if water had a lowerspecific heat?

1. Ponds would be less likely to freeze.

2. The temperature would decrease morerapidly when water gives up energy.

3. Water would readily be cooled to thefreezing point.

4. Making tea would be much faster.


Milk with a mass of 0.032 kg and a temper-ature of 11◦C is added to 0.16 kg of coffee at91◦C.

What is the final temperature? Assume thespecific heat capacities of the two liquids arethe same as water, and disregard any energytransfer to the liquids’ surroundings.


When a driver brakes an automobile, fric-tion between the brake disks and the brakepads converts part of the car’s translationalkinetic energy to internal energy.

If a 1500 kg automobile traveling at 32 m/scomes to a halt after its brakes are applied,how much can the temperature rise in eachof the four 3.5 kg steel brake disks? Assume


the disks are made of iron (cp = 448 J/kg ·◦ C)and that all of the kinetic energy is distributedin equal parts to the internal energy of thebrakes.


A 3.0 kg rock is initially at rest at the topof a cliff. Assume that the rock falls into thesea at the foot of the cliff and that its kineticenergy is transferred entirely to the water.The specific heat of water is 4186 J/kg ·◦ C

The acceleration of gravity is 9.81 m/s2 .How high is the cliff if the temperature of

1.0 kg of water is raised 0.10 ◦C?


Given: specific heat of water =4186 J/kg ·◦C and density of water =1000 kg/m3.

A hot-water heater is operated by solarpower.

If the solar collector has an area of6.0 m2 and the power delivered by sunlightis 550 W/m2, how long will it take to increasethe temperature of 1.0 m3 of water from 21◦Cto 61◦C?

Holt SF 10Rev 4920:03, highSchool, multiple choice, < 1 min,normal.

Given: specific heat of water =4186 J/kg ·◦ C

A 250 g aluminum cup holds and is in ther-mal equilibrium with 850 g of water at 83◦C.The combination of cup and water is cooleduniformly so that the temperature decreasesby 1.5◦C/min.

At what rate is energy being removed?Assume the specific heat of aluminum is899 J/kg ·◦ C.

Chapter 20, section 4, Heat Capacity of Gases 530


Given: specific heat of water =4186 J/kg ·◦C

The air temperature above coastal areasis profoundly influenced by the large specificheat capacity of water.

How large of a volume of air can be cooledby 1.0◦C if energy is transferred as heat fromthe air to the water, thus increasing the tem-perature of 1.0 kg of water by 1.0◦C? Thespecific heat capacity of air is approximately1000.0 J/kg·◦C, and the density of air is ap-proximately 1.29 kg/m3.

Chapter 20, section 6, Latent Heat 531


Why does blowing over hot soup cool thesoup?

1. Air temperature is much lower than thesoup.

2. Air temperature lowers as you blow.

3. The air becomes dryer when you blow.

4. Net evaporation increases as does its cool-ing effect.


Why are icebergs often surrounded by fog?

1. The evaporation from an iceberg con-denses into droplets (fog).

2. An iceberg attracts vapor from the sur-rounding air.

3. The air is dryer near an iceberg.

4. The chilled air in the vicinity of an icebergresults in condensation of water vapor in theair (fog).


Consider the changes of state for a simplewater molecule that goes from a solid to aliquid to a gas from the perspective of theforces that it experiences from its neighbour-ing molecules.


1. As the ice melts, the force holding a watermolecule to its neighbouring molecules gets

weaker.

2. As the water becomes a gas, there are vir-tually no forces between the water moleculesexcept during collisions.

3. Change of state has no effect on forcesholding the molecules together.


Consider the changes of state for a simplewater molecule that goes from a solid to aliquid to a gas from the perspective of itsaverage kinetic energy.

What statement is true?

1. As the ice melts, the kinetic energy in-creases.

2. As the water becomes a gas, the kineticenergy decreases.

3. As the ice melts and becomes a gas, thekinetic energy decreases.


Consider the influence of pressure on thephase change of a material under this pres-sure.

What statement is false?

1. Pressure has the tendency to lower theboiling temperature of a liquid.

2. Pressure has the effect of lowering themelting temperature of a solid.

3. Pressure has the tendency to increase thecondensation temperature of a gas.



Suppose a new liquid were discovered thatis identical to water in every way except thatit has a lower latent heat of vaporization.

Which would be better for cooking pasta?

1. Ordinary water

2. This new liquid

3. Either will be fine.


Suppose a new liquid were discovered thatis identical to water in every way except thatit has a lower latent heat of fusion.

Would it take a longer or shorter time tomake ice out of this liquid in your freezer?

1. Longer

2. Shorter

3. It depends on other factors, also.


How would you determine wind directionafter wetting your finger and holding it up inthe air?

1. If a finger feels cold the wind must beblowing from North. If it feels warm, it’sSouth wind.

2. If a finger dries up quickly then it’s atropical South wind. If it takes a while forit to dry it must be a wind from the nearestocean, full of evaporation, and depends onwhere you are on the continent.

3. The side of your finger that feels coldshows where the wind is blowing from.

4. It’s not a scientific way to determine thewind direction, but rather a silly supersti-tion.


When you step out of a swimming pool ona hot, dry day in the southwest, why do youfeel quite chilly?

1. The temperature outside the swimmingpool is much lower.

2. The temperature drops dramaticallywhen you finish swimming.

3. The water evaporates rapidly in the dryair, gaining its energy from your skin, whichis cooled.

4. The temperature doesn’t change at all; itis all in your mind.


If all the molecules in a liquid had thesame speed, and some were able to evapo-rate, would the remaining liquid be cooled?

1. No; the energy of exiting molecules wouldbe no different than the energy of moleculesleft behind.

2. Yes; there is lower energy left.

3. Yes; evaporation can reduce the speed ofthe remaining molecules.

4. No; energy is conserved in the whole sys-tem.



Double-pane windows have nitrogen gas orvery dry air between the panes.

Why is ordinary air a poor idea?

1. There would be a great number of oxygenmolecules that would react chemically withthe window.

2. Ordinary air has a greater pressure thatcould crack the window glass.

3. Ordinary air is not physically stable.

4. Visibility is impaired if there is anycondensation of water between the panes ofglass.


A great amount of water vapor changesphase to become water in the clouds thatform a thunderstorm.

Does this release thermal energy or absorbit?

1. Absorb energy; water is heavier than wa-ter vapor.

2. Absorb energy; water vapor cools to be-come water.

3. Release energy; water vapor undergoescondensation.

4. Release energy; some of the watermolecules lose their energies.


Why does the temperature of boiling waterremain the same as long as the heating andboiling continue?

1. The water and the stove have the sametemperature.

2. When water boils, it is being cooled bythe boiling process as fast as it is being heatedby the stove.

3. The stove stops working when the wateris boiling.

4. The cold air around the water takes awaythe heat given by the stove.


Given:

cp,ice = 2090 J/kg ·◦Ccp,water = 4186 J/kg ·◦Ccp,steam = 2010 J/kg ·◦C

Lf = 3.33× 105 J/kg

Lv = 2.26× 106 J/kg

How much energy is required to change a42 g ice cube from ice at −11◦C to steam at111◦C?


Liquid nitrogen, which has a boiling pointof 77 K, is commonly used to cool substancesto low temperatures.

How much energy must be removed from1.0 kg of gaseous nitrogen at 77 K for it tocompletely liquefy? Assume the latent heatof liquid nitrogen is 2.01× 105 J/kg


A sample of lead used to make a lead sinkerfor fishing has an initial temperature of 27.3◦Cand is poured into a mold immediately afterit has melted.

How much energy is needed to melt 0.225kg of lead? Assume the specific heat, thelatent heat and the melting point of lead are


128 J/kg ·◦C, 2.45 × 104 J/kg and 327.3 ◦Crespectively.


You have collected exactly 1000 aluminumcans for recycling, each with a mass of 14.0 g.

How much energy is needed to melt them iftheir initial temperature is 26.4◦C? Assumethe specific heat, the latent heat and themelting point of aluminum are 899 J/kg ·◦C,3.97× 105 J/kg and 660.4 ◦C respectively.


Given: specific heat of water =4186 J/kg ·◦C and water’s latent heat of fu-sion = 3.33× 105 J/kg.

A 0.011 kg cube of ice at 0.0◦C is added to0.450 kg of soup at 80.0◦C.

Assuming that the soup has the same spe-cific heat capacity as water, find the final tem-perature of the soup after the ice has melted.


Given: specific heat of aluminum =899 J/kg ·◦C and latent heat of fusion of alu-minum = 3.97× 105 J/kg.

At a foundry, 25 kg of molten aluminumwith a temperature of 660.4◦C is poured intoa mold.

If this is carried out in a room containing130 kg of air at 25◦C, what is the temperatureof the air after the aluminum is completelysolidified? Assume that the specific heat ca-pacity of air is 1.0× 103 J/kg ·◦C.


A plastic-foam container used as a picniccooler contains a block of ice at 0.0◦ C.

If 225 g of ice melts, how much heat

passes through the walls of the container?Assume the latent heat of plastic-foam is333000 J/kg.


Given: specific heat of water =4186 J/kg ·◦C and latent heat of fusion ofwater = 3.33× 105 J/kg.

The largest of the Great Lakes, Lake Supe-rior, contains about 1.20× 1016 kg of water.

If the lake had a temperature of 12.0◦C,how much energy would have to be removedto freeze the whole lake at 0◦C?


Given: The specific heat of water is4186 J/kg ·◦ C .

A jar of tea is placed in sunlight until itreaches an equilibrium temperature of 32◦C .In an attempt to cool the liquid, which has amass of 180 g , 112 g of ice at 0.0◦C is added.

Assume the specific heat capacity of the teato be that of pure liquid water.

At the time at which the temperature of thetea is 31.7◦C , find the mass of the remainingice in the jar.

Chapter 20, section 8, Calorimetry 535


A 3.0 kg gold bar at 99◦C is dropped into0.22 kg of water at 25◦C.

What is the final temperature? Assume thespecific heat of gold is 129 J/kg ·◦C.


A 0.225 kg sample of tin initially at 97.5◦Cis dropped into 0.115 kg of water initially at10.0◦C.

If the specific heat capacity of tin is230 J/kg ·◦C, what is the final equilibriumtemperature of the tin-water mixture? Thespecific heat of water is 4186 J/kg ·◦C.


A cup is made of an experimental materialthat can hold hot liquids without significantlyincreasing its own temperature. The 0.75 kgcup has an initial temperature of 36.5◦C whenit is submerged in 1.25 kg of water with aninitial temperature of 20.0◦C.

What is the cup’s specific heat capacity ifthe final temperature is 24.4◦C? The specificheat of water is 4186 J/kg ·◦C.


Brass is an alloy made from copper andzinc. A 0.59 kg brass sample at 98.0◦C isdropped into 2.80 kg of water at 5.0◦C.

If the equilibrium temperature is 6.8◦C,what is the specific heat capacity of brass?The specific heat of water is 4186 J/kg ·◦C.

Holt SF 10C 0720:08, highSchool, numeric,> 1min, wording-

variable.

A hot, just-minted copper coin is placed in101 g of water to cool. The water temperaturechanges by 8.39◦C and the temperature of thecoin changes by 83.8◦C.

What is the mass of the coin? Disregardany energy transfer to the water’s surround-ings and assume the specific heat of copperis 387 J/kg ·◦C. The specific heat of water is4186 J/kg ·◦C.


A 25.5 g silver ring (cp = 234 J/kg·◦ C) isheated to a temperature of 84.0 ◦C and thenplaced in a calorimeter containing 5.00×10−2

kg of water at 24.0 ◦C. The calorimeter isnot perfectly insulated, however, and 0.140 kJof energy is transferred to the surroundingsbefore a final temperature is reached.

What is the final temperature? The specificheat of water is 4186 J/kg ·◦C.


A student drops two metallic objects into a120 g steel container holding 150 g of waterat 25◦C. One object is a 253 g cube of copperthat is initially at 85◦C, and the other is achunk of aluminum that is initially at 5 ◦C.To the students’s surprise, the water reachesa final temperature of 25◦C, precisely whereit started.

What is the mass of the aluminum chunk?Assume the specific heat of copper and alu-minum are 387 J/kg ·◦ C and 899 J/kg ·◦ C.

Chapter 20, section 9, Work and Heat in Thermodynamic Processes 536


If you throw a Wham-O SuperBall againsta wall, it will rebound with approximately thesame speed with which you threw it. If youthrow it at a wall that’s moving toward you,the ball will rebound with a faster speed. Ifthe wall is moving away from you, the ballwill rebound with a slower speed.

Using the SuperBall example as an analogy,what happens to the energy of gas moleculeswhen the gas is compressed?

1. The container wall moves toward the gasmolecules, so the molecules gain energy.

2. The container wall moves toward the gasmolecules, so the molecules lose energy.

3. The container wall moves away from thegas molecules, so the molecules gain energy.

4. The container wall moves away from thegas molecules, so the molecules lose energy.


What do you say about the temperature ofwater at the bottom of Niagara Falls?

1. a little higher than the temperature atthe top

2. a little lower than the temperature at thetop

3. much higher than the temperature at thetop

4. much lower than the temperature at thetop

5. the same as the temperature at the top

6. It’s impossible to predict without a mea-surement.


A force of 315 N is applied horizontally toa wooden crate in order to displace it 35.0 macross a level floor at a constant velocity. As aresult of this work the crate’s internal energyis increased by an amount equal to 14 percentof the crate’s initial internal energy.

Calculate the initial internal energy of thecrate.


Part 1 of 2Gas in a container is at a pressure of 1.6 ×

105 Pa and a volume of 4.0 m3.a) What is the work done by the gas if

it expands at constant pressure to twice itsinitial volume?

Part 2 of 2b) What is the work done by the gas if itis compressed at constant pressure to one-quarter of its initial volume?


A gas is enclosed in a container fitted with apiston. The applied pressure is maintained at599.5 kPa as the piston moves inward, whichchanges the volume of the gas from 5.317 ×10−4 m3 to 2.523× 10−4 m3.

How much work is done?


A toy balloon is inflated with helium at aconstant pressure that is 430000 Pa in excessof atmospheric pressure.

Chapter 20, section 9, Work and Heat in Thermodynamic Processes 537

If the balloon inflates from a volume of0.00018 m3 to 0.00095 m3 , how much work isdone by the balloon on the surrounding air?Atmospheric pressure is 101000 Pa .


Steam moves into the cylinder of a steamengine at a constant pressure and does 0.84J of work on a piston. The diameter of thepiston is 1.6 cm, and the piston travels 2.1 cmin one stroke.

What is the pressure of the steam?


How much work is done when a tire’s vol-ume increases from 0.03525 m3 to 0.03947 m3

at a pressure of 255000 Pa in excess of atmo-spheric pressure?


Helium in a toy balloon does work on itssurroundings as it expands with a constantpressure of 2.52 × 105 Pa in excess of atmo-spheric pressure. The balloon’s initial vol-ume is 1.1 × 10−4 m3, and its final volume is1.50× 10−3 m3.

Find the amount of work done by the gasin the balloon.

Chapter 20, section 10, The First Law of Thermodynamics 538


During a certain thermodynamic process asample of gas expands and cools, reducing itsinternal energy by 3000 J, while no heat isadded or taken away.

Howmuch work is done during this process?


What happens on a hot summer day whenthe energy demand on your local power plantexceeds its energy output?

1. Nothing happens.

2. Brownouts are experienced.

3. The power plant stops working.

4. The output will be increased simultane-ously.


A cylinder with a movable piston containsa gas as shown below. A weight is placed ontop of the piston. When 100 Joules of heat isadded to the gas, the internal energy of thegas increases by 50 Joules and the piston rises,doing 75 Joules of work.

Mass

Heat HeatHeat

Does this process violate any law ofphysics?

1. No

2. Yes; the first law of thermodynamics.

3. Yes; the second law of thermodynamics.

4. Yes; conservation of energy.


Part 1 of 3A closed, rigid container contains an ice-

water mixture at 0 ◦C. Heat is added slowlyand some, but not all, of the ice melts.

How much work did the system do?

1. > 0

2. < 0

3. No work.


Part 2 of 3Did the internal energy increase or decrease?

1. It increased.

2. It decreased.

3. It remained the same.


Part 3 of 3Did the temperature increase?

1. Yes; the internal energy increased.

2. No; the internal energy didn’t change.

3. No; not all of the ice melted.




Suppose you compress a gas, doing 100Joules of work on the gas.

If 100 Joules of heat are allowed to escapeduring the compression, what is the change ininternal energy?

1. ∆E > 0

2. ∆E < 0

3. ∆E = 0



A metal spoon is dropped into a shallow potof boiling water and its temperature increasesto 100◦ C. Assume the heat added to thespoon is exactly equal to the increase in thespoon’s internal energy.

How much work does the spoon do in theprocess?

1. > 0

2. < 0

3. No work



Part 1 of 2Two pieces of metal (A and B) are identical

in every way, except that A has a much largerthermal expansion coefficient.

If equal amounts of heat are added to both

pieces of metal, which metal does more workon its surroundings?

1. A

2. B

3. They do the same work.


Part 2 of 2Which metal’s temperature increases more?

1. A

2. B

3. Same in both



Part 1 of 3Three identical blocks exchange heat in the

following way: A transfers 500 Joules of heatto B and B transfer 200 Joules of heat toC. Suppose the blocks do not expand norcontract, so no work is done.

B

A

C

500 J200 J

Which block’s internal energy increased themost?

1. A

2. B

3. C


4. B and C have the same internal energyincrease.

Part 2 of 3Which block’s internal energy decreased?

1. A

2. B

3. C


Part 3 of 3Is it possible for block C to transfer heat toblock A?

1. Yes.

2. No.



Suppose you squeeze an air-filled hollowrubber ball in your hand.

Assuming no heat escapes, what happensto the internal energy of the air inside?

1. It decreases.

2. It increases.

3. It doesn’t change.



A system’s initial internal energy is 27 J.Then heat is added to the system.

If the final internal energy is 34 J and thesystem does 26 J of work, how much heat is

added to the system?


The internal energy of the gas in a gasolineengine’s cylinder decreases by 195 J.

If 52.0 J of work is done by the gas, howmuch energy is transferred as heat?


A 2.0 kg quantity of water is held at con-stant volume in a pressure cooker and heatedby a range element. The system’s internal en-ergy increases by 8.0 × 103 J. However, thepressure cooker is not well insulated, and2.0 × 103 J of energy is transferred to thesurrounding air.

How much energy is transferred from therange element to the pressure cooker asheat?


Part 1 of 2The internal energy of a gas decreases by

344 J.a) If the process is adiabatic, how much

energy is transferred as heat?

Part 2 of 2b) How much work is done on or by the gas?


A steam engine’s boiler completely converts155 kg of water to steam. This process in-volves the transfer of 3.50× 108 J as heat.

If steam escaping through a safety valvedoes 1.76×108 of work expanding against theoutside atmosphere, what is the net changein the internal energy of the water-steam sys-


tem?


Heat is added to an open pan of waterat 100.0◦C, vaporizing the water. The ex-panding steam that results does 43.0 kJ ofwork, and the internal energy of the systemincreases by 604 kJ.

How much energy is transferred to the sys-tem as heat?


The lid of a pressure cooker forms a nearlyairtight seal. Steam builds up pressure andincreases temperature within the pressurecooker so that food cooks faster than it doesin an ordinary pot. The system is defined asthe pressure cooker and the water and steamwithin it.

If 2.0 g of water is sealed in a pressurecooker and then vaporized by heating, and5175 J must be added as heat to completelyvaporize the water, what is the change in thesystem’s internal energy?

Chapter 20, section 11, Work and the PV Diagram for a Gas 542

Ideal Gas Path20:11, highSchool, multiple choice, < 1 min,fixed.

Identify the parameter paths for an idealgas that are isovolumetric / isobaric / isother-mal.

P

V

A

C

B

T1T2

T3

T1 > T2 > T3

1. A / B / C

2. A / C / B

3. C / B / A

4. C / A / B

5. B / A / C

6. B / C / A

Chapter 20, section 12, Some Applications of the First Law of Thermodynamics 543


Part 1 of 3A 150 kg steel rod in a building under con-

struction supports a load of 6050 kg. Duringthe day the rod’s temperature increases from22◦C to 47◦C, causing the rod to thermallyexpand and raise the load 5.5 mm.

The acceleration of gravity is 9.81 m/s2 .The specific heat of iron is 448 J/kg ·◦C .

a) Find the energy transferred as heat toor from the rod. (Assume the specific heatcapacity of steel is the same as for iron.)

Part 2 of 3b) Find the work done by or on the rod in thisprocess.

Part 3 of 3c) How great is the change in the rod’s internalenergy?

Chapter 20, section 13, Heat and Energy Transfer 544


If you hold one end of a metal nail againsta piece of ice, the end in your hand soonbecomes cold.

Which description is right?

1.The cold flows from the ice to your hand.

2. Energy flows from your hand to the ice.

3. Temperature flows from the ice to yourhand.

4. Heat flows from the ice to your hand.


You can bring water in a paper cup to aboil by placing it over a hot flame.

Why doesn’t the paper cup burn?

1. Paper cup is better conductor than wa-ter.

2. The temperature of the flame is below theignition temperature of the paper cup.

3.Water is better conductor than paper.

4. The water absorbs the energy that wouldotherwise raise the temperature of the pa-per.


You can comfortably hold your fingers closebeside a candle flame, but cannot put yourfingers very close above the flame.

Which of the following options is wrong?

1. You can hold your fingers quite close to

the side of a candle flame without harm be-cause the air between is a good insulator.

2. You will burn your fingers if you holdthem above the flame because of the convec-tion of hot gases in the flame.

3. Heat transfer by radiation is not impor-tant when you hold your fingers beside a can-dle flame.

4. Heat transfer by radiation becomes moreimportant than convection if you put yourfingers above the flame.


You can safely hold you bare hand in a hotpizza oven for a few seconds, but if you mo-mentarily touch the metal inside you’ll burnyourself.

Which option below is wrong about thisphenomenon?

1. The temperature of the air in the oven isin fact near the temperature of your hand.

2. Air is a poor conductor, so very little heatis conducted by the air to your hand in a shorttime.

3. The metal in the oven is a good conduc-tor.

4. Heat will be readily conducted to yourhand if you touch the metal inside theoven.


Consider a hot object placed in contactwith a cooler object.

What statement is correct?

1. Cold will flow from the cooler object to


the hot one.

2. The hot object will lose as much temper-ature as the cooler one gains.

3. The hot object will lose as much heat asthe cooler one gains.

4. If the cooler object is bigger, it can gainmore heat than the hot one loses.


What does the high specific heat of waterhave to do with convection currents in the airat the seashore?

1. Sunshine warms water much less than itwarms land; the air is warmed over the landand rises, causing the convection currents inthe air.

2. Sunshine warms water much more thanit warms land; the air is warmed over the seaand rises, causing the convection currents inthe air.

3. Sunshine warms water much less than itwarms land; the air is warmed over the landand descends, causing the convection currentsin the air.

4. Sunshine warms water much more thanit warms land; the air is warmed over the seaand descends, causing the convection currentsin the air.


Interestingly, a steam radiator warms aroom more by convection than by radiation.

Nevertheless, with respect to its radiatingproperties, what is the most efficient color fora steam radiator?

1. white

2. red

3. blue

4. black


William burns 0.6 g of peanuts beneath1000 g of water, which increases in tempera-ture from 22◦C to 50◦C.

Assuming 40% efficiency, what is the foodvalue of the peanut?


Water will boil spontaneously in a vacuum(on the moon, for example).

Could you cook an egg in this boiling water?Why?

1.Yes; the bubbing of the surrounding watercooks the egg.

2. Yes; water that boils will always cook theegg.

3. No; the boiling of water in this conditionis not very intense.

4. No; the water temperature is low.


An inventor proposes a design of cookwarethat will allow boiling to take place at a tem-perature much lower than 100◦C so that foodcan be cooked with less energy consumption.

What is your opinion about this proposal?

1. It’s a good idea; food can be cookedquicker in this new cookware.


2. It’s a good idea; water boiling at lowertemperatures saves energy.

3. Not a good idea; the boiling water in thiscondition is not very intense.

4. Not a good idea; the temperature of thefood is not high enough to cook.


Why do some animals roll up into a ballwhen they are cold?

1. Rolling into a ball reduces their exposedarea, thus reducing heat loss through conduc-tion and radiation.

2. Rolling into a ball reduces the energyconsumed by the animals.

3. Rolling into a ball increases theirmetabolism, making it easier to generateheat.


Why are feather beds warm and why isgoose down considered the best filling for aparka?

1. Goose down and feathers trap a lot of air,which is a good insulator.

2. Goose down and feathers have high spe-cific heat.

3. Goose down and feathers have a highernatural temperature than other materials.


Imagine lying on a hot beach on a sunnysummer day.

In what different ways is heat transferredto your body?

1.Radiation from the Sun heats your body.

2. Conduction from the hot sand heats yourbody.

3. Convection moves heated air away fromyour body.

4. All of these


A golf ball is dropped onto hard groundand, after a few bounces, comes to rest.

Why is the golf ball’s temperature slightlyhigher after it comes to rest?

1. The ball acquired energy from frictionwith the air molecules.

2. Each collision with the ground gives asmall kinetic energy to the atoms in the ball.

3. The air temperature is higher than thatof the ball.


Three identical potatoes are taken out ofa hot oven to cool. The first is placed onthe countertop. The second is wrapped inaluminum foil and placed inside a jar, andthen the air is removed from the air. Thethird potato is wrapped in aluminum foil andthen placed on the countertop alongside thefirst.

Place the potatoes in order of which willcool fastest.

1. First, second, third


2. First, third, second

3. Second, first, third

4. Third, first, second

5. Third, second, first

6. Second, third, first


A certain amount of heat is added to somewater so that its temperature rises. The sameamount of heat is added to a piece of alu-minum with the same mass as the water.

Which has the higher temperature change?

1. aluminum

2. water

3. They have equal temperature changes.


If water had a lower specific heat, wouldyour chances of enjoying a long, hot bath begreater or less?

1. Greater

2. Less



Plants and animals are still dying and end-ing up at the ocean bottom today.

Should fossil fuels be classified as renewableresources?

1. Yes

2. No

3. Oil should be; coal should not.

4. Coal should be; oil should not.


Some people say that you lose more Caloriesby eating celery than you gain.

Is that possible?

1. Yes; chewing uses more energy than iscontained in the celery.

2. Yes; the celery doesn’t contain any en-ergy.

3. No; eating helps you get energy.

4. No; you won’t lose or gain any Calo-ries.


One kind of energy can be converted intoanother.

Identify an example of the conversion ofthermal energy into chemical potential en-ergy.

1. smelting iron

2. a flashlight

3. a remote controlled car

4. fusion in the sun

5. charging of a battery

6. None of these



A system can be classified as either open orclosed with respect to matter and with respectto energy.

How would you classify the Earth and theSun?

1. open with respect to energy; closed withrespect to matter.

2. open with respect to energy; open withrespect to matter.

3. closed with respect to energy; closed withrespect to matter.

4. closed with respect to energy; open withrespect to matter.


Consider the following statements.A. Heat flows from an object in liquid state

to an object in solid state;B. Heat flows from an object with higher

thermal energy to one with lower ther-mal energy;

C. Heat flows from an object at higher tem-perature to an object at lower tempera-ture.

Which statements are true?

1. C only

2. A and B only

3. A and C only

4. B and C only

5. All are true.

6. None is true.

7. A only

8. B only


Two systems contain vastly differentamounts of internal energy. For the sake ofdefiniteness, assume that system A contains1000000 J of internal energy and system Bcontains 100 J of internal energy.

In which direction will heat flow if thesetwo systems are placed in thermal contact?

1. A→B

2. B→A

3. No heat flow.



A cube of aluminum metal is placed in con-tact with a cube of copper metal. The averagespeed of the atoms in each metal is the same.

Which way does heat flow?

1. from copper to the aluminum

2. from aluminum to copper

3. No heat flows.


A piece of metal and a piece of wood ofequal mass and equal temperature are re-moved from a hot oven and dropped ontoblocks of ice.


Which will melt more ice before cooling tothe ice temperature?

1. The metal.

2. The wood.

3. Both will melt equal amounts of ice.


Hot water/steam radiators are common fix-tures that nicely warm the interiors of build-ings.

These radiators warm a room primarily via

1. conduction.

2. convection.

3. radiation.

4. All about equally


When you step from the shade into thesunlight the Sun’s heat is evident like the heatfrom hot coals in a fireplace in an otherwisecold room.

Which of the following is the correct state-ment?

1. The Sun is only twice as far from theEarth as the Moon is.

2. The Sun’s radius is nearly twice the dis-tance between the Earth and the Moon.

3. The Sun is almost twice as hot as thecoals in a fireplace.

4. The strength of the heat we feel has noth-ing to do with either the distance, or the size,or the temerature of the Sun.


Which statement is wrong?

1. When no more energy can be extractedfrom a material, it is at absolute zero.

2. There is no limit to how much energy canbe added to a material.

3. Kinetic energy has a minimum (zero) butno maximum.

4. There is no maximum temperature.

5. There is no minimum temperature.


In the winds at the latitude of San Franciscoand Washington D.C. were mainly from theeast rather than from the west, what wouldbe wrong?

1. As the Atlantic ocean near WashingtonD.C. cooled in the winter, the heat it lostwould warm the atmosphere.

2. The climate of San Francisco would bechilled by winter winds from dry and coldNevada.

3. Both are wrong.

4. Neither is wrong.


Wrap a fur coat around a thermometer.How does the temperature change?

1. It does not change.


2. It rises.

3. It drops.

4. It rises at first, then drops back to theoriginal.

5. It depends on the material of the ther-mometer.


Why is there a layer of copper and alu-minum at the bottom of stainless steel cook-ware?

1. Stainless steel transfers heat more quicklyto the cookware’s interior.

2.Copper and aluminum are bad conductorsof electricity.

3. Copper and aluminum are better conduc-tors of heat than stainless steel.

4. There is no reason behind it.


Many have injured their tongues by lickinga piece of metal on a very cold day.

Which of the following is true?I) Heat transfers quickly to the metal.II) Metal is a good heat conductor.III) Saliva freezes as soon as the tongue

touches the metal surface.IV) Licking a piece of wood would result in

the same injury.

1. I and II only

2. I and III only

3. I and IV only

4. II and III only

5. II and IV only

6. III and IV only

7. I,II and III only

8. II,III and IV only

9. I,II and IV only

10. All of them

Chapter 21, section 1, Molecular Model of an Ideal Gas 551


Hint: Some physics problems are just hotair.

A short and a long candle burnin an open jar as shown below.

When the jar is covered the candle to goout first will be the

1. short candle.

2. tall candle.

3. 50-50, a toss up.

Chapter 21, section 7, Distribution of Molecular Speeds 552


In a mixture of hydrogen and oxygen gasesat the same temperature, which moleculesmove faster and why?

1.Hydrogen molecules will move faster; theyhave a larger average kinetic energy.

2. Hydrogen molecules will move faster; themass of hydrogen is less than that of oxygen.

3. Oxygen molecules will move faster; theyhave a larger average kinetic energy.

4. They have the same average speed be-cause they have the same average kinetic en-ergy.


In a gas of U-235 and U-238 in thermalequilibrium, which molecules move faster andwhy?

1. U-235 molecules will move faster; theyhave a larger average kinetic energy.

2. U-235 molecules will move faster; themass of U-235 is less than U-238.

3. U-238 molecules will move faster; theyhave a larger average kinetic energy.

4. They have the same average speed be-cause they have the same average kinetic en-ergy.


When a container of gas is heated, whathappens to the average speed of its molecules?

1. decreases

2. increases

3. doesn’t change

4. Additional information is needed.


What is correct?

1. Gas molecules move at random speed.

2. Gas molecules move at the same speed.

3. The kinetic energy of gas moleculesdoesn’t change.

4. Temperature affects random speeds.

5. It would be statistically possible for anylarge number of molecules to have the samespeed.

Chapter 22, section 1, The Second Law of Thermodynamics 553


Why don’t all the atoms in the room you’resitting in move to one side, leaving you in avacuum?

1. That would violate the first law of ther-modynamics.

2. That would violate the second law ofthermodynamics

3. That would violate Newton’s third law ofmotion.

4. That would violate Newton’s first law ofmotion.


Why do they install big cooling stacksaround nuclear reactors and coal-fired gen-erating plants?

1. to absorb particle radiation

2. to remove heat that does not go into usefulwork

3. to remove gases formed during the pro-cess


“Cogeneration” is a term used to describesystems in which waste heat from electric gen-erating plants is used to heat nearby homes.Such systems achieve efficiencies much greaterthan 50%.

Does cogeneration violate the second law ofthermodynamics?

1. Yes, waste heat can’t be converted intomechanical work.

2. Yes, the second law forbids high effi-ciency.

3. No, the second law only forbids efficiencyequal to 100%.

4. No, but it violates the first law of thermo-dynamics.


Is a perpetual motion machine possible?Why?

1. Yes, it’s theoretically possible, but toocomplicated to build.

2. No, it would violate either the first orsecond laws of thermodynamics.

3. No, it would violate the first law of ther-modynamics.


Seawater is full of moving molecules thatpossess kinetic energy.

Could we extract this energy from seawa-ter?

1. Yes, by putting the seawater into contactwith something hotter.

2. Yes, by putting the seawater into contactwith something cooler.

3. No, the kinetic energy is unusable.


Chapter 22, section 1, The Second Law of Thermodynamics 554

When ice freezes, water goes from a stateof larger disorder to one with more order.

Does this violate the second law of thermo-dynamics?

1. Yes, the second law does not hold inseveral rare cases.

2. No, the ice is not a isolated system.

3. No, the entropy of ice increased eventhough it’s in a state with more order.


A power plant has a power output of1055 MW and operates with an efficiency of33.0 percent. Excess energy is carried awayas heat from the plant to a nearby river thathas a flow rate of 1.1× 106 kg/s.

How much energy is transferred as heat tothe river each second?


The energy provided each hour by heat tothe turbine in an electric power plant is 9.5×1012 J.

If 6.5 × 1012 J of energy is exhausted eachhour from the engine as heat, what is theefficiency of this heat engine?

Chapter 22, section 2, Heat Engines 555


Part 1 of 2During a complete cycle of an engine, the

net internal energy change is 0. During thatcycle, an amount of heat Qin enters the en-gine, an amount Qout leaves the engine, andan amount of work W is done. The follow-ing table lists these quantities for a variety ofengines.

Engine Qin Qout WA 100 J 100 J 0 JB 100 J 50 J 50 JC 100 J 0 J 100 JD 100 J 20 J 60 JE 100 J 100 J 50 J

Which of these engines violates the first lawof thermodynamics?

1. D and E

2. only D

3. only C

4. C and E

5. A, B and C

Part 2 of 2Which of these engines violates the secondlaw of thermodynamics?

1. D and E

2. only D

3. only C

4. C and E

5. A, B and C

Conceptual 13 Q11


Imagine that it were possible to constructa reservoir at −5 K (below absolute zero).Suppose you ran an engine and used the −5K reservoir as the cold reservoir.

Would such an engine violate the secondlaw of thermodynamics?

1. No, the engine efficiency would be high,but reasonable.

2.Yes; the engine efficiency would be greaterthan 100%.


If a steam engine takes in 2.254 × 104 kJfrom the boiler and gives up 1.915× 104 kJ inexhaust during one cycle, what is the engine’sefficiency?


Part 1 of 2A steam engine absorbs 1.98 × 105 J and

expels 1.49×105 J in each cycle. Assume thatall of the remaining energy is used to do work.

a) What is the engine’s efficiency?

Part 2 of 2b) How much work is done in each cycle?


If the energy removed from an engine asheat during one cycle is 6.0×102 J, how muchenergy must be added to the engine duringone cycle in order for it to operate at 31percent efficiency?

Holt SF 11Rev 28

Chapter 22, section 2, Heat Engines 556


In one cycle, an engine burning a mixtureof air and methanol (methyl alcohol) absorbs525 J and expels 415 J.

What is the engine’s efficiency?


A heat engine absorbs 850 J of energy percycle from a high-temperature source.

The engine does 350 J of work during eachcycle, expelling 500 J as heat.


Chapter 22, section 4, The Carnot Engine 557


What is the Carnot efficiency of an OTECpower plant that operates on the temperaturedifference between deep 4◦C water and 25◦Csurface water?


An engine has a hot reservoir of 600 K anda low-temperature reservoir of 300 K.

What is the theoretical efficiency of thisengine?


A steam engine has a high-temperaturereservoir of 100 ◦C and a low-temperatureof 10 ◦C.

What is its maximum possible efficiency?


Part 1 of 2A power plant burns natural gas at a tem-

perature of 600 K, with low-temperature sur-roundings at 300 K.

What is its maximum possible efficiency?

Part 2 of 2How much more efficient would the plant beif it were built in the Arctic, where the low-temperature reservoir is at 250 t2?


Part 1 of 2The Ocean Thermal Electric Conversion

system (OTEC) is an example of a high-techelectric generator. It takes advantage of thefact that in the tropics, deep ocean water isat a temperature of 4 ◦C, while the surface

is at a temperature around 25◦C. The ideais to find a material that boils between thesetemperatures. The material in the fluid formis brought up through a large pipe from thedepths, and the expansion associated with itsboiling is used to drive an electrical turbine.The gas is then pumped back to the depths,where is condenses back into a liquid and thewhole process repeats.

What is the maximum efficiency with whichOTEC can produce electricity?

1. 7.0%

2. 84%

3. 7.6%

4. 93%

5. 1.3%

Part 2 of 2What is the ultimate source of the energygenerated by OTEC?

1. the Earth’s internal energy

2. the Sun

3. water

Chapter 22, section 5, Gasoline and Deisel Engines 558


What is the ideal efficiency of an automo-bile engine where fuel is heated to 2700 K andthe outdoor air is at 270 K?

Holt SF 11C 0222:05, highSchool, numeric, < 1 min, normal.

A test model for an experimental gasolineengine does 45 J of work in one cycle and givesup 31 J as heat.


Holt SF 11C 0422:05, highSchool, numeric, < 1 min, normal.

If a gasoline engine has an efficiency of 21percent and loses 780 J to the cooling systemand exhaust during each cycle, how muchwork is done by the engine?


A certain diesel engine performs 372 J ofwork in each cycle with an efficiency of 33.0percent.

How much energy is transferred from theengine to the exhaust and cooling system asheat?

Chapter 22, section 7, Entropy 559


A large parking lot contains 50 identicalcars.

Which is a higher entropy situation?

1. When the cars are allowed to park any-where

2.When the cars are forced to park betweenthe lines in designated spaces

3. Either


Chapter 22, section 8, Entropy Changes in Irreversible Processes 560


An ice cube melts on the warm sidewalkon a hot summer day. Let the entropies ofthe ice cube, of the pavement and of the icecube-sidewalk system be Sice, Ssw and Ssys.

What happens to these entropies?

1. Sice increases, Ssw decreases, Ssys in-creases

2. Sice increases, Ssw increases, Ssys in-creases

3. Sice decreases, Ssw increases, Ssys de-creases

4. Sice increases, Ssw decreases, Ssys doesnot change.

Chapter 22, section 9, Entropy on a Microscopic Scale 561


Which state is more disordered?

1. liquid

2. solid

3. Either


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