Final Review Lecture

Remember: Final is at 9 am

Monday, December 7

Chapter 1 Units and densityThe three basic units are meters, kilograms and secondsDensity is mass/volume: ρ=m/V

Chapter 2 One-dimensional motionThe three basic measures of motion are displacement, velocity and

accelerationFor constant acceleration, position (s) vs. time is a parabola: s-s0=v0t-½at2

Chapter 3 Vector mathThe three basic vector operations are addition, dot products and cross productsaddition→vector in plane, dot→scalar, cross→vector perpendicular to plane

Chapter 4 Three-dimensional motionProjectile trajectory depends on angle and velocity: y=(tanθ)x-gx2/2(v0cosθ)2

Uniform circular motion causes centripetal acceleration: a=v2/r

Chapter 5a Frictionless free-body diagramsAlong each axis, net force is mass×acceleration: ∑Fx=max, ∑Fy=may

Action-reaction force pairs act on different bodies (Newton’s Third Law)

Chapter 5b and 6 Free-body diagrams with frictionNormal force→perpendicular to surface; friction→parallel (surface area no effect)

Friction force is normal force×coefficient of friction (static or kinetic): fs,k=s,kn

Chapter 7a Kinetic energy (K)Kinetic energy quantifies an object’s translational state: K=½mv2; Power: P=FvPositive work done by an object (hand) transfers energy to system (brick+earth)

Chapter 7b Potential energy (U)Potential energy quantifies an object’s configurational state: U=mgh or U=½kx2

Total energy is conserved: W=ΔE=(K+U+Ethermal+Einternal)f-(K+U+Eth+Eint)i

Chapter 9 Linear momentum and collisionsAlong each axis the center of mass is mass(fraction)×distance, e.g.

xcom=1/M∑mixi

Linear momentum is mass×velocity: p=mv, and is conservedCollisions conserve momentum, elastic collisions also conserve energyImpulse, J, is the momentum change, or the area under a force vs. time curve

Chapter 10 Simple rotations and torqueTransfer all concepts from linear frame to rotational frame, e.g. force→torques=θr, v=ωr, a=αr=ω2r; I=∑mir

2i , K=½Iω2, τ=r×F =Iα, W=∫τdθ, P=τω,

I=Icom+Mh2

Chapter 11 Rolling rotations and angular momentumRolling is “perfect” combination of rotation and translationAngular momentum, l=r×p or L=Iω, is conserved; τ=dL/dt (Newton’s 2nd

law)

Chapter 12 Free-body diagrams with torqueIn equilibrium, net force and net torque equal zeroThe three elastic moduli (Young’s, shear, and bulk) equal stress÷strain

Chapter 13 GravityGravitational force follows the inverse square law: F=GMm/r2 and U=-GMm/r

Kepler’s Laws: planet move in ellipses, sweep equal areas/time, T2=(42/GM)r3

Chapter 14 Fluid statics and dynamicsPressure, P, is force÷area (increases with depth by ρgh), Fbuoyant=m(fluid displaced)g

Dynamic flow follows continuity and Bernoulli equations: Av, p+½ρv2+ρgh=cnst.

Chapter 15 Time-dependant oscillationsPeriod, T, is (frequency)-1 or 2ω; f(t)=Acos(ωt+φ), solves differential equationPendulums: T=2(L/g) -½ or 2(I/mgh) -½ for simple and physical, respectively

Chapter 16 Time and distance dependant wavesTransverse and longitudinal sine waves (can be both: water), f(x,t)=Asin(kx-ωt+φ)

Chapter 17 Sound waves in elastic mediumResonance occurs at frequencies=nv/2L (n integer) for (anti)nodes at both endsDoppler effect reduces/increases frequencies for departing/approaching sources

Chapter 18 Superposition and standing wavesStanding wave: 2Asin(kx)cosωt; any wave’s velocity is (elasticity÷inertia) -½

A)1B)2C)3D)4E)1, 2, or 3

The uniform rod shown below is held in place by the rope and wall. Suppose you know the weight of the rod and all dimensions. Then you can solve a single equation for the force exerted by the rope, provided you write expressions for the torques about the point:

3)The ideal mechanical advantage (i.e. the ratio of the weight W to the pull P for equilibrium) of the combination of pulleys shown is:

A) 1 B) 2 C) 3 D) 4 E) 5

2)The pull P is just sufficient to keep the 14-N block and the weightless pulleys in equilibrium as shown. The tension T in the upper cable is:

A) 14 N B) 28 N C) 16 N D) 9.33 N E) 18.7 N

4) To shear a cube-shaped object, forces of equal magnitude and opposite directions might be applied:

A) to opposite faces, perpendicular to the faces B) to opposite faces, parallel to the faces C) to adjacent faces, perpendicular to the faces D) to adjacent faces, neither parallel or perpendicular to the

faces E) to a single face, in any direction

5) A projectile is fired straight upward from Earth's surface with a speed that is half the escape speed. If R is the radius of Earth, the highest altitude reached, measured from the surface, is:

A) R/4 B) R/3 C) R/2 D) R E) 2R

6) A planet is in circular orbit around the Sun. Its distance from the Sun is four times the average distance of Earth from the Sun. The period of this planet, in Earth years, is:

A) 4 B) 8 C) 16 D) 64 E) 2.52

1 10 s

10 s

7) The period of a simple pendulum is 1 s on Earth. When brought to a planet where g is one-tenth that on Earth, its period becomes:

A) 1 s B) C) 1/10 sD) E) 10 s

8) Five hoops are each pivoted at a point on the rim and allowed to swing as physical pendulums. The masses and radii are

hoop 1: M = 150g and R = 50 cmhoop 2: M = 200g and R = 40 cmhoop 3: M = 250g and R = 30 cmhoop 4: M = 300g and R = 20 cmhoop 5: M = 350g and R = 10 cm

Order the hoops according to the periods of their motions, smallest to largest.

A) 1, 2, 3, 4, 5B) 5, 4, 3, 2, 1C) 1, 2, 3, 5, 4D) 1, 2, 5, 4, 3E) 5, 4, 1, 2, 3

9) A certain spring elongates 9 mm when it is suspended vertically and a block of mass M is hung on it. The natural frequency of this mass-spring system is:

A) 0.014 B) 5.3 Hz C) 31.8 Hz D) 181.7 Hz E) need to know M

10) The mathematical forms for the three sinusoidal traveling waves are gives by

wave 1: y(x,t) = (2 cm) sin (3x – 6t)wave 2: y(x,t) = (3 cm) sin (4x – 12t)wave 3: y(x,t) = (4 cm) sin (5x – 11t)

where x is in meters and t is in seconds. Of these waves:A) wave 1 has the greatest wave speed and the greatest

maximum transverse string speedB) wave 2 has the greatest wave speed and wave 1 has the

greatest maxmium transverse string speedC) wave 3 has the greatest wave speed and the greatest

maximum transverse string speedD) wave 2 has the greatest wave speed and wave 3 has the

greatest maximum transverse string speedE) wave 3 has the greatest wave speed and wave 2 has the

greatest maximum transverse string speed

11) A 40-cm long string, with one end clamped and the other free to move transversely, is vibrating in its fundamental standing wave mode. The wavelength of the constituent traveling waves is:

A) 10 cm B) 20 cm C) 40 cm D) 80 cm E) 160 cm

A sinusoidal wave is traveling toward the right as shown. Which letter correctly labels the wavelength of the wave?

A) A B) B C) C D) D E) E

A standing wave pattern is established in a string as shown. The wavelength of one of the component traveling waves is:

A) 0.25 m B) 0.5 m C) 1 m D) 2 m E) 4 m

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2

14) Two notes are an "octave" apart. The ratio of their frequencies is:

A) 8B) 10C) D) 2E)

15) A stationary source emits a sound wave of frequency f. If it were possible for a man to travel toward the source at the speed of sound, he would observe the emitted sound to have a frequency of:

A) zero B) f/2 C) 2f/3 D) 2f E) infinity

16) The "A" on a trumpet and a clarinet have the same pitch, but the two are clearly distinguishable. Which property is most important in enabling one to distinguish between these two instruments?

A) intensity B) fundamental frequency C) displacement amplitude D) pressure amplitude E) harmonic content

17) The pressure exerted on the ground by a man is greatest when:

A) he stands with both feet flat on the ground B) he stands flat on one foot C) he stands on the toes of one foot D) he lies down on the ground E) all of the above yield the same pressure

Take the speed of sound to be 340 m/s. A thunder clap is heard about 3 s after the lightning is seen. The source of both light and sound is:

A)moving overhead faster than the speed of sound

B)emitting a much higher frequency than is heard

C)emitting a much lower frequency than is heard

D)about 1000 m away E)much more than 1000 m away