Study Plan for AP Physics B

7/30/2019 Study Plan for AP Physics B

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Study Plan for AP physics:

1. Rewrite All review guides into document2. Memorize the formulas3. Do some AP workout problems4. Take an official times AP Physics Exam

BEGIN!

AP PHYSICS STUDY GUIDE

I. MechanicsA. Motion

a. Accelerationi. A change in velocity

ii. Acceleration can be speeding up, slowing down, or turningiii. If the sign of the velocity and the sign of the acceleration is the same, the object

speeds up.

iv. If the sign of the velocity and the sign of the acceleration are different, theobject slows down

b. Position VS Time Graphsi. Slope: yf-yi/xf-xi

c. Curved Position

i. At points A and C velocityequals zero

ii. The slope atB is even steeper than at D, so the speed is greatest atBd. Velocity vs Time Graphs

i. As with position vs. time graphs, velocity vs. time graphs may also be curved.Remember that regions with a steep slope indicate rapid acceleration or

deceleration, regions with a gentle slope indicate small acceleration or

deceleration, and the turning points have zero acceleration.

e.f. Free Fall

i. Occurs when an object falls unimpededii. Acceleration of gravity is always down

g. Projectile Motioni. Something if fired, thrown, shot , or hurled near the earths surface


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ii. Horizontal velocity is constantiii. Vertical Velocity is constant

h. Trajectory of Projectilei. Defined by a parabola

ii. RANGE- how far it travels horizontally= 2vcos0tiii. MAXIMUM HEIGHT- occurs halfway through rangeiv. Velocity is tangent to the path for the entire trajectoryv. Vertical velocity changes while horizontal velocity remains constant

i. Horizontal component of Velocityi. Not accelerated/ Not influenced by gravity

ii. Equation: j. Vertical Component of Velocity ( no initial velocity)

i. Use kinematics formulas and adjustk. Projectile Motion in an Angle

i. We must determine the initial velocity and horizontal velocityii. Equations to remember:

1. Horizontal Motion= 2. Vertical Motion=

() ()

()

B. Forcesa. Force= Push or pull of an object

i. Forces cause an object to accelerate (speed up, slow down, change direction)b. Newtons First Law:

i.

The Law of Inertia: A body in motion stays in motion at constant velocityand a body at rest stays at rest unless acted upon by an external force

c. Newtons Second Lawi. F=ma

d. General Procedures for solving second law problemsi. Draw the problem

ii. Free body diagramiii. Setup equationsiv. Substitutev. Solve

e. Newtons third law- For every action there is an equal and opposite reactioni. If A exerts a force F on B then B exerts a force ofF on A

ii. Weight= Mgiii. Normal Force- Force that prevents objects from penetrating each other

1. Reaction to other forces (gravity)iv. This type of reaction can never balance each other out because they act on

different objects.


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f. Drawing free body diagramsi. Fapp= applied force

ii. W= force of gravityiii. Fn- Normal Forceiv. Tension=Tv. Fk or Fs- Kinetic (sliding) friction or Static friction.

g. Friction-the force that opposes a sliding motioni. Static- exists before sliding occur

ii. Kinetic exists after sliding occursiii. iv. Static Friction increases as the force trying to push an object increase

C. Uniform Circular Motiona. Moves at a uniform speed in a circle of constant radiusb. Acceleration in Uniform circular motion

i. Turns object, doesnt speed it up or slow it down. It points toward center ofcircle. Centripetal acceleration

ii.

c. Force in uniform circular motioni. Centripetal force can arise from one force or from a combination of sources

ii.

iii. Speed of object is constant, Kinetic Energy (KE) remains constant, and workis zero.

D. Universal Law of Gravitya. F=-Gm1m2/r^2b. Most orbit problems can be solved by setting the gravitational force equal to the

centripetal force

E. Torquea. A twistb. Equals- Force x distance x sin anglec. Units are Nm

F. Rotational Equilibriuma. If counter clockwise torques equal the clockwise torques, the system is balanced

and no rotation occurs.

G. Periodic Motiona. Repeats itself over a fixed and reproducible period of time (oscillators)b. Simple harmonic Motion- experience a restoring forcec. Restoring Force-

i. F=-kxii. Greatest at maximum displacement and zero at equilibrium

iii. Equilibrium- midpoint of oscillation of a SHO1. Position of minimum PE and highest KE


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d. Amplitude- how far the oscillating mass is from equilibrium at its displacemente. Period (T)- The length of time it takes for one cycle of periodic motion to complete

itself

f. Frequency (f) - How fast the oscillation occurs, is inversely related to period. F=1/Tg. Springs- F=-kx (Hookes Law)h. Period of a spring=

i. PE of a spring- 1/2kx^2j. Pendulum- can be thought of as an oscillator; the displacement needs to be small

for it to work properly. The pendulum forces are gravity and tension

k. Period of a Pendulum=

l. PE of a pendulum- mghH. Work

a.

The bridge between force and energyb. Work is a scalarc. d. Counterintuitive Results

i. There is no work if there is no displacementii. Forces perpendicular to displacement dont work

iii. By doing positive work on an object, a force increases its KE and PE.1. KE=1/2 mv^2 (energy due to motion)

e. The work energy theoremi. When network is positive, the kinetic energy of the object will increase

(speed up)ii. When network is negative, the KE will decrease (slows down)

iii. When there is no network, the KE is unchanged (constant speed)iv. Wnet= KE

f. Work and Graphsi. The area under the curve of a graph of force vs displacement gives the work

done by the force to perform the displacement.

I. Powera. The rate of which work is done

i. P=W/tii. P= (force)(velocity)

iii. When time is little, power is largeiv. When time is large, power is little

b. How we buy energyi. kWh is not power, but energy consumed

ii. 1kWh- 1000 x 3600 JJ. Forces Types


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a.a. Conservative forces

a. Work in moving an object is path independentb. Work in moving along a closed path is zeroc. Work done against conservative forces increases PE, work done by them

decreases it.

b. Non-conservative forcesa. Work is path dependentb. Work along a closed path is not zero

c. Potential Energya. An energy an object possesses by a virtue of its position or configurationb. It is related to work by CONSERVATIVE FORCES only.

d. Spring potential energya. Springs can also possess potential energyb. PE is zero when a spring is in its preferred or equilibrium position where the

spring is neither compressed or extended

e. Law of conservation of Mechanical Energya. U+K= Constantb. U+K=0c. U=-K

K. Momentuma. How hard it is to stop a moving objectb. Impulse- The product of an external force and time which results in a change in

momentum

i. J=delta momentumii. J= (force) (time)

c. Law of conservation of momentumi. If the resultant external force on a system is zero, them the momentum will

remain constant

ii. The sum of momentum before collision is equal to the sum of momentumsafter collision

1. Collision has impulsive forces (high force, short time). Externalforces are ignored

2. Types of collisionsa. Elastic- PE is conserved, KE is conservedb. Inelastic- PE is conserved, KE is NOTc. Perfectly Inelastic- bodies stick together

II. Fluid & Thermodynamica. Simple concepts

i. Density- p=m/vii. Pressure=Force/Areaiii. Gauge pressure ( of a liquid)= pgh


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iv. Absolute Pressure= p+ pghv. Buoyant force= the upward force exerted on a submerged or partially

submerged body. F= pVg

vi. Fluid flow continuity1. Conservation of mass results in continuity of fluid flow2. The volume per unit time of water flowing in a pipe is constant

throughout the pipe.

a. Av=AVb. V=Avt

vii. Bernoullis theorem1. The faster the fluid moves, the lower the pressure it exerts on surfaces

parallel to velocity

a. Pressure+ (density)(gravity)(height)+ (density)(velocity)^2viii. Total energy= U+K+E

ix. Temperature1. Measure of KE in individual molecules2. Difference in temp causes heat energy to be exchanged between bodies

in contact

x. Thermal Equilibrium1. Occurs when two bodies are the same temperature2. NO heat is transferred between the bodies

xi. Ideal Gas Law= PV/T=PV/T1. PV=nRT2. PV=nKT3. R=NK

xii. Kinetic Theory of Gases1. Gases consist of a large number of molecules that make elastic collisions

with each other and the walls of the container

2. Molecules are separated, on average, by large distances and exert noforces on each other except when they collide

3. No preferred position for a molecule in the container and no preferreddirection for velocity

xiii. Average KE of Molecules1. 3/2 Kb T2. 3/2 (Boltzmann constant 1.38E-23) (temp)

b. First law of thermodynamicsi. U=Q+W

ii. U is always zero if there is no temperature changeiii. Gas processes

1. Isobaric- constant pressure ( work is zero)a. During isobaric heating/cooling, and n is constant we have

Charles's Law: Vi /Ti=Vf/Tf


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c. Work done BY gasesi. Area under the curve of PV graph

ii. Positive area for expansions; negative area for compression.iii. Arrow pointing right is positive work done by gas (and W is negative)iv. Arrow pointing left is negative work done by gas (and W is positive)

d. Work done ON gasesi. Also the area under the curve on PV graph; but after finding the work done by

the gas, you need to take the negative of that number.

ii. Arrow pointing right is negative work done by environment (and W is negative)iii. Arrow pointing left is positive work done by environment (and W is positive)

e. Work at constant pressurei. W = pDV

f. Work for a full cyclei. Start and end at the same spot

ii. Work is area inside the shape defined by the steps of the cycleg. Clockwise cycles

i. Work done by gas is positiveii. Work done by environment is negativeiii. W is therefore negative

h. Counterclockwise cyclesi. Work done by gas is positive

ii. Work done by environment is negativeiii. W is therefore positive

i. Second Law of Thermodynamicsi. No process is possible whose sole result is the

ii. Complete conversion of heat from a hot reservoir into mechanical work.iii. No process is possible whose sole result is the transfer of heat from a cooler to a

hotter body.

j. Heat Enginesi. As heat is transferred from a hot reservoir to a cold reservoir, the heat engine

converts some of this heat into mechanical work. It can never convert 100% to

mechanical work however.

k. Efficiency of Heat Enginei. Efficiency = W/QH = (QH - QC)/QH

l. Carnot Enginei. The most efficient heat engine theoretically possible. No one has built a Carnot

engine. In addition to the efficiency equations shown above, Carnot efficiency

can be calculated from the temperatures of the hot and cold reservoirs.

m. Carnot Efficiencyi. Efficiency = (TH - TC)/TH


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III. Electricitya. Charge (Q or q, unit: Coulomb)

i. Comes in + andii. The proton has a charge of e.iii. The electron has a charge ofe.iv. e = 1.602 10^-19 Coulombs.

b. Charge distributioni. Positively charged objects have too few electrons; negatively charged objects

have too many.

ii. If the charged object is an insulator, the excess charge is usually distributedevenly throughout; if it is a conductor, the excess charge will accumulate on the

surface.

c. Electric Fields (E, unit: N/C or V/m)i. Start on + charges and terminate on charges.

ii. Electric field lines indicate direction force would be on a tiny + test charge put inthe field.

iii. Electric field lines are not vectors. The field vectors are tangent to the field lines.iv. Electric field vector gives direction of electric force on a + charge placed in the

field.

d. The electric field inside a conductor is always zero, whether or not the conductor ischarged or near some external charges.

e. Principle of Superpositioni. The electric field at a given point in space is the vector sum of the electric fields

due to all charges in the vicinity.

ii. The resulting vector gives the direction of the electric force on a positive chargeplaced in the field.

f. Electric Polarizationi. Electric fields cause polarization (redistribution of charge) on neutral objects

ii. Conductors are especially vulnerable to this effect.iii. When placed in an electric field, the charges redistribute themselves so that the

electric field inside the conductor is zero.

iv. Remember our electroscope experiments? The electroscope is a conductor.When a charged rod is brought near, the charges on the electroscope move.

That makes the vanes separate, since they assume the same charge.

v. The electric field inside the electroscopes metal parts will be zerog. Electrical Potential (V, unit: Volt, V)

i. The electric potential is a scalar value related to potential energy, which is also ascalar. Potential gets more positive as you approach positive charges. Mobile

positive charges therefore like to move to positions of lower potential

ii. Potential gets more negative as you near negative charges. Mobile negativecharges therefore like to move to positions of higher potential

iii. Potential difference, DV, is usually more usefulthan absolute potential, V.


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iv. Potential difference, DV, is necessary for current to flow.h. Electrical Potential: uniform field calculation (that is, and electric field that is like the

one you drew in the capacitor above)

i. DV = -Edf. Capacitor

a. Consists of two plates (or conductors) in close proximity. When the capacitoris charged, there is a voltage across the plates, and they are equal and

opposite charges.

g. Capacitance (C, unit: Farad)a. The ability of a capacitor to hold charge.

i. C = q / DVh. Equivalent capacitance

a. The capacitance that a group of capacitors together possesses.i. For capacitors in series:

a. 1/Ceq = S(1/Ci)j. For capacitors in parallel:

a. Ceq = SCik. UE = C (DV)^2 is Energy of a capacitorl. Capacitance of parallel plate capacitor

a. Capacitance is related linearly with plate area, and inversely with spacingbetween the plates

b. C = kee0A/di. C: capacitance (F)ii. Ke : dielectric constant of filling

iii. e0 : electrical permittivity (8.85 x 10 -12 F/m)iv. A: plate areav. d: distance between plates (m)

L. Current (I, unit: Ampere, A)a. Flow of positive charge I = Q/t

M. Conductorsa. Conduct electricity easily; i.e., metals.b. Have low resistivity.

N. Insulatorsa. Dont conduct electricity easily; i.e. rubber.b. Have high resistivity.

O. Resistivity (r)a. Depends on the identity of the material, not its shape, size, or configuration.

P. Resistors (R, unit: ohm, W)a. Devices put in circuits to reduce the current: The more a resistor reduces current,

the higher the resistance it provides to the circuit.

Q. Calculating resistance (R) from resistivity (r) R = rL/A


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R. Ohmmeter & Voltmeter & Ammetera. Placed across resistor or other circuit element to measure resistance when no

current is flowing.

b. Voltmeter- Placed across resistor or other circuit element to measure potentialchange when current is flowing.

c. Ammeter- Placed in a circuit in place of a wire to measure the current flowing inthat part of the circuit.

S. Power in Electrical Circuits (P, unit: Watt, W)a. P = I DV

T. Energy in Electrical Circuits (unit: Joule, J)a. E = (P)(t)

U. Kirchhoffs 1st Rule (Junction rule)a. The sum of the currents entering a junction equals the sum of the currents leaving

the junction. Conservation of charge.

V. Kirchhoffs 2nd Rule (Loop rule)a. The net change in electrical potential in going around one complete loop in a circuit

is equal to zero. Conservation of energy.

W. Magnetic Dipolea. Magnetic field lines are complete loops that exit the magnet at the North Pole and

re-enter at the South Pole.

X. Magnetic Field (B-field)-Units- Tesla (SI)a. Magnetic Force on Charged Particle

F = qvBsinq

b. direction: Right Hand RuleY. Magnetic Fields are formed by moving charges. They may exert a force on moving charges,

provided a portion of the velocity is perpendicular to the field.

Z. Magnetic Forces can accelerate charged particles by changing their direction, causingcharged particles to move in circular or helical paths

AA.Magnetic Forces cannot change the speed or kinetic energy of charged particles, or do workon charged particles

BB.The magnetic force is centripetala. qvBsinq = mv^2/ r qB = mv/r

CC.Hand Rule for magnetic force on moving positive chargea. Place fingers in direction of velocity. Then rotate your wrist so that your fingers can

bend into the direction of the field. Your thumb gives direction of the force.

DD.Hand Rule for magnetic force on moving negative charge. Uses the method described above,and then flip your thumb 180. Alternately, you may use your left hand.

EE.Hand Rule for magnetic force on current in wire. Place fingers in direction of current. Thenrotate your wrist so that your fingers can bend into the direction of the field. Your thumb

will be pointing in the direction of the force.

FF. Hand Rule for fields where current is straight. Curve your fingers. Place thumb in direction ofcurrent. Your curved fingers point in direction of curved magnetic field.


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GG.Hand Rule for fields where current is circular. Curve your fingers. Place curved fingers indirection of current. Your thumb points in direction of magnetic field in center of circular

current.

HH.Magnetic Flux (FB, unit Webber, Wb)a. The product of magnetic field and area.b. FB = BAcosq

II. Induced Currenta. A system will respond to oppose changes in magnetic flux. Changing the magnetic

flux can generate electrical current.

JJ. Faradays Law of Inductiona. e = -NDFB/Dt

i. To generate voltageii. e = -DFB/Dt

iii. e = -D(BAcosq)/DtKK.Lenzs Law

a. Induced current will flow in a direction so as to oppose the change in flux.IV. Optics

a. Naming optical imagesi. Nature: real (converging rays) or virtual (diverging rays)

ii. Orientation: upright or invertediii. Size: true, enlarged or reduced

b. Law of Reflectioni. Angle of incidence equals angle of reflection.

c. Plane Mirrori. Produces virtual, upright, and true sized images.

V. Wavesa. Light is a wave

i. c = lf (speed is wavelength times frequency)b. Light is a particle

i. A particle of light is called a photonii. This is a quantum of light energy (quantum means smallest indivisible quantity)

c. Energy of a photoni. E = hf

VI. Modern Physicsa. The electron-volt (eV)

i. An energy unit useful on the atomic level.ii. If a moving electron or proton is stopped by 1 Volt of electric potential, we say it

has 1 electron-volt (or 1 eV) of kinetic energy!

iii. 1 eV = 1.60210^ -19 Jb. Absorption Spectrum

i. Photon is absorbed and excites atom to higher energy state.ii. Absorption indicated by upward arrows on energy-level diagrams.


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iii. Creates dark bands, since the light disappears and goes into the atom.c. Emission Spectrum

i. Photon is emitted and atom drops to lower energy state.ii. Emission indicated by downward arrows on energy-level diagrams.iii. Creates bright bands of color, since the light is emitted and goes into the atom.

d. Energy Level diagrami. Horizontal lines indicate allowed atomic energies.

ii. Atom cannot exist at in between energies.iii. Upward arrows are absorptionsiv. Downward arrows are emissionsv. Photon energies are calculated by examining the diagramvi. Photon frequencies are calculated from Plancks equation

e. Nuclear Reactionsi. Energy released an element changes from one to another. Lots of energy is

released due to mass being destroyed. E = mc^2

ii. Mass + energy are conserved. Charge is conserved.iii. Nucleons

1. Proton: Charge: +e2. Neutron: Charge: 0

iv. Nuclear reactions1. Nuclear Decay

a. Alpha decay: He^ 2+ . Released from heavy nucleusb. Beta decay

i. Beta Minus: e-1. released from nucleus

ii. Positron: e+1. released from nucleus

v. Fission: Heavy nucleus splits.vi. Fusion: Small nuclei combine

f. Wave-Particle Dualityi. Waves are particles and particles are waves

ii. Energy1. Particle: E = K + U2. Photon: E = hf

iii. Momentum1. Particle: p = mv2. Photon: p = h/

iv. Wavelength1. Photon: c/f2. Particle: = h/p

g. Compton Scattering


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i. Proof of the momentum of photons. High-energy photons collided withelectrons. Conservation of momentum. Scattered photons examined to

determine loss of momentum.

h. Davisson-Germer Experimenti. Verified that electrons have wave properties by proving that they diffract.

Shone electrons onto a metal strip; they diffracted like light to form a diffraction

pattern.

i. Rutherford Scatteringi. Collided alpha particles onto a gold foil strip. Unexpectedly large back-scattering

indicated elastic collision of the alpha particles with nuclei in the atoms.

Evidence of a nuclear atom with a dense positive nucleus.

j. Milliken Oil Drop Experimenti. Suspended charged oil drops in electric field. Proved that the charge on an

electron was the smallest possible charge (or quantum of charge).

k. Photoelectric effecti. Showed that the energy of photons depended upon the frequency of incident

light, and not on its intensity. Showed that Plancks equation E = hfwas correct.

Evidence of the particle nature of light.

VII.Wavesa. Mechanical Wave

i. A disturbance that propagates through a medium with little or no netdisplacement of the particles of the medium.

b. Parts of a Wavei. Crest: high point; Trough: low point

ii. Equilibrium: mid-pointiii. Amplitude: distance from equilibrium to crest or troughiv. Wavelength: distance between adjacent crests

c. Speed of a wavei. Distance traveled by a given point on the wave (such as a crest) in a given

interval of time. v = d/t and v = l

d. Period of a wavei. T = 1/(reciprocal of frequency)

e. Wave typesi. A transverse wave: particles of the medium oscillate perpendicular to direction

of wave propagation. Example: waves on a string

ii. A longitudinal wave (also called a compression wave): particles of the mediumoscillate parallel to direction of wave propagation. Example: sound

iii. Light A transverse electromagnetic wave that requires no medium throughwhich to travel

f. Reflection of wavesi. A wave strikes a medium boundary and bounces back into original medium.


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ii. Fixed-end reflection: inverted phase. Occurs when reflecting medium hasgreater density.

iii. Open-end reflection: Same phase. Occurs when reflecting medium has lesserdensity.

g. Refraction of wavesi. Transmission of wave from one medium to another. Refracted waves may

change speed and wavelength. Refracted waves do not change frequency.

h. Principle of Superpositioni. When two or more waves pass a particular point in a medium simultaneously,

the resulting displacement at that point in the medium is the sum of the

displacements due to each individual wave. The waves interfere with each other.

i. Types of interference.i. If the waves are in phase (crests and troughs aligned) the amplitudes are

summed. This is called constructive interference.

ii. If the waves are out of phase (crests and troughs are completely misaligned)the amplitudes are subtracted. This is called destructive interference.

j. Sounds in the Real Worldi. Because of superposition and interference, real world waveforms may not

appear to be pure sine or cosine functions. That is because most real world

sounds are composed of multiple frequencies.

k. Standing Wavei. A standing wave is a wave that is reflected back and forth between fixed ends

(of a string or pipe, for example). Reflection may be fixed or open ended.

Superposition of the wave upon itself results in constructive interference and an

enhanced wave.

l. Resonancei. Occurs when a vibration from one oscillator occurs at a natural frequency for

another oscillator. The first oscillator causes the second to vibrate.

m. Doppler Effecti. The raising or lowering of perceived pitch of a sound based on the relative

motion of the observer and the source of the sound. When an ambulance is

racing toward you, the sound of its siren appears to be higher in pitch. When

the ambulance is racing away from you, the sound of its siren appears to be

lower in pitch.

n. Diffractioni. The bending of a wave around a barrier. Diffraction of light combined with

interference of diffracted waves causes diffraction patterns.

o. Double-slit or multi-slit diffractioni. nl = d sinq

1. d: spacing between slits (m)2. n: bright band number


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Study Plan for AP Physics B