ap physics 2: algebra-based

2019

AP®

Physics 2: Algebra-BasedFree-Response Questions

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AP® PHYSICS 2 TABLE OF INFORMATION

CONSTANTS AND CONVERSION FACTORS

Proton mass, 271.67 10 kgpm

Neutron mass, 271.67 10 kgnm

Electron mass, 319.11 10 kgem

Avogadro’s number, 23 10 6.02 10 molN

Universal gas constant, 8.31 J (mol K)R

Boltzmann’s constant, 231.38 10 J KBk

Electron charge magnitude, 191.60 10 Ce

1 electron volt, 191 eV 1.60 10 J

Speed of light, 83.00 10 m sc

Universal gravitational constant,

11 3 26.67 10 m kg sG

Acceleration due to gravity

at Earth’s surface,29.8 m sg

1 unified atomic mass unit, 27 21 u 1.66 10 kg 931 MeV c

Planck’s constant, 34 156.63 10 J s 4.14 10 eV sh25 31.99 10 J m 1.24 10 eV nmhc

Vacuum permittivity, 12 2 20 8.85 10 C N me

Coulomb’s law constant, k 1 4pe 9 2 20 9.0 10 N m C

Vacuum permeability, 70 4 10 (T m)m p A

Magnetic constant, 70 4 1 10 (T m) Ak m p

1 atmosphere pressure, 5 2 51 atm 1.0 10 N m 1.0 10 Pa

UNIT SYMBOLS

meter, m kilogram, kg second, s ampere, A kelvin, K

mole, mol

hertz, Hz newton, N pascal, Pa joule, J

watt, W coulomb, C

volt, V

ohm, Whenry, H

farad, F tesla, T

degree Celsius, Celectron volt, eV

PREFIXES Factor Prefix Symbol

1210 tera T 910 giga G 610 mega M 310 kilo k 210 centi c 310 milli m 610 micro m

910 nano n 1210 pico p

VALUES OF TRIGONOMETRIC FUNCTIONS FOR COMMON ANGLES

q 0 30 37 45 53 60 90

sinq 0 1 2 3 5 2 2 4 5 3 2 1

cosq 1 3 2 4 5 2 2 3 5 1 2 0

tanq 0 3 3 3 4 1 4 3 3

The following conventions are used in this exam. I. The frame of reference of any problem is assumed to be inertial unless

otherwise stated.II. In all situations, positive work is defined as work done on a system.

III. The direction of current is conventional current: the direction in whichpositive charge would drift.

IV. Assume all batteries and meters are ideal unless otherwise stated.V. Assume edge effects for the electric field of a parallel plate capacitor

unless otherwise stated.VI. For any isolated electrically charged object, the electric potential is

defined as zero at infinite distance from the charged object

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AP® PHYSICS 2 EQUATIONS

MECHANICS a = acceleration A = amplitude d = distance E = energy F = force f = frequency I = rotational inertia K = kinetic energy k = spring constant L = angular momentum

= length m = mass P = power p = momentum r = radius or separation

T = period t = time U = potential energy v = speed W = work done on a

system

x = position y = height a = angular acceleration m = coefficient of friction

q = angle t = torque w = angular speed

0x x a tÃ Ã x

2xt0 0

12xx x t aÃ

02 2

0 2x x xa x xÃ Ã

netFFa

m m

f nF Fm

2

carÃ

p mv

p F tD D

212

K mv

cosE W F d Fd qD

EPt

DD

20 0

12

t tq q w a

0 tw w a

cos cos 2x A t A fw tp

i icm

i

m xx

m

net

I Itt

a

sinr F rFt q

L Iw

L ttD D

212

K Iw

sF k x

212sU kx

gU mg yD D

2 1Tf

pw

2smTk

p

2pTg

p

1 22g

m mF G

r

gFg

m

1 2G

Gm mU

r

ELECTRICITY AND MAGNETISM

A = area

B = magnetic field C = capacitance d = distance E = electric field e = emf

F = force I = current

= length

P = power Q = charge q = point charge R = resistance r = separation t = time U = potential (stored)

energy

V = electric potential v = speed k = dielectric

constant r = resistivity

q = angle F = flux

1 22

0

14E

q qF

rpe

EFE

q

20

14

qE

rpe

EU q VD D

0

14

qV

rpe

VEr

DD

QV

CD

0ACd

ke

0

QE

Ae

21 12 2CU Q V CD VD

QI

tDD

RAr

P I VD

VIRD

s ii

R R

1

p iR

1

iR

p ii

C C

1 1

s iiC C

0

2IBr

mp

MF qv B

sinMF qv Bq

MF I B

sinMF I Bq

B B AF

cosB B AqF

B

te DF

D

B ve

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AP® PHYSICS 2 EQUATIONS

FLUID MECHANICS AND THERMAL PHYSICS

A = area F = force h = depth k = thermal conductivity K = kinetic energy L = thickness m = mass n = number of moles N = number of molecules P = pressure Q = energy transferred to a

system by heating

T = temperature t = time U = internal energy V = volume v = speed W = work done on a system y = height r = density

mV

r

FPA

0P P ghr

bF Vgr

1 1 2 2A v A v

2

2

1 1 1

22 2

12

12

P gy v

P gy v

r r

r r

kA TQt L

DD

BPV nRT Nk T

32 BK k T

W P VD

U Q WD

MODERN PHYSICS

E = energy f = frequency K = kinetic energy m = mass p = momentum l = wavelengthf = work function

E hf

maxK hf f

hp

l

2E mc

WAVES AND OPTICS

d = separation f = frequency or

focal length h = height L = distance M = magnification m = an integer n = index of

refraction s = distance v = speed l = wavelength

q = angle

vf

l

cnÃ

1 1 2sin sinn nq 2q

1 1 1

i os s f

i

o

hM

hi

o

ss

L mlD

sind mq l

GEOMETRY AND TRIGONOMETRY

A = area C = circumference V = volume S = surface area b = base h = height

= length w = width r = radius

Rectangle A bh

Triangle 12

A bh

Circle 2A rp

2C rp

Rectangular solid V wh

Cylinder 2V rp

22 2S r rp p

Sphere 34

3V rp

24S rp

Right triangle 2 2c a 2b

sin ac

q

cos bc

q

tan ab

q

c a

b90°q

2019 AP® PHYSICS 2 FREE-RESPONSE QUESTIONS

GO ON TO THE NEXT PAGE. -5-

PHYSICS 2 Section II

Time—1 hour and 30 minutes 4 Questions

Directions: Questions 1 and 4 are short free-response questions that require about 20 minutes each to answer and are worth 10 points each. Questions 2 and 3 are long free-response questions that require about 25 minutes each to answer and are worth 12 points each. Show your work for each part in the space provided after that part.

1. (10 points, suggested time 20 minutes)

The figure above shows a particle with positive charge +Q traveling with a constant speed 0v to the right and in

the plane of the page. The particle is approaching a region, shown by the dashed box, that contains a constantuniform field. The effects of gravity are negligible.

(a)i. On the figure below, draw a possible path of the particle in the region if the region contains only an

electric field directed toward the bottom of the page.

ii. On the figure below, draw a possible path of the particle in the region if the region contains only amagnetic field directed out of the page.

iii. For which of the previous situations is the motion more similar to that of a projectile in only agravitational field near Earth’s surface, and why?

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(b) Another region of space contains an electric field directed toward the top of the page and a magnetic field directed out of the page. Both fields are constant and uniform. A horizontal beam of protons with a variety of speeds enters the region, as shown above. Protons exit the region at a variety of locations, including points 1 and 2 shown on the figure. In a coherent, paragraph-length response, explain why some protons exit the region at point 1 and others exit at point 2. Use physics principles to explain your reasoning.





The two circuits shown above contain an ideal variable power supply, an ohmic resistor of resistance R, an ammeter A, and two voltmeters PSV and RV . In circuit 1 the ammeter has negligible resistance, and in circuit 2

the ammeter has significant internal ohmic resistance r. The potential difference of the power supply is varied, and measurements of current and potential difference are recorded.

(a) The axes below can be used to graph the current measured by the ammeter as a function of the potential

difference measured across the power supply. On the axes, do the following. • Sketch a possible graph for circuit 1 and label it 1. • Sketch a possible graph for circuit 2 and label it 2.

(b) Let D PSV be the potential difference measured by voltmeter PSV across the power supply, and let I be the

current measured by the ammeter A. For each circuit, write an equation that satisfies conservation of energy, in terms of D PSV , I, R, and r, as appropriate.

Circuit 1 Circuit 2




(c) Explain how your equations in part (b) account for any differences between graphs 1 and 2 in part (a). (d) In circuit 2, W= 40 R . When voltmeter PSV reads 3.0 V, voltmeter RV reads 2.5 V. Calculate the internal

resistance r of the ammeter. (e) Voltmeter RV in circuit 2 is replaced by a resistor with resistance W120 to create circuit 3 shown below.

Voltmeter PSV still reads 3.0 V.

i. Calculate the equivalent resistance eqR of the circuit.

ii. Calculate the current in each of the resistors that are in parallel.





A group of students use the apparatus shown above to determine the thermal conductivity of a certain type ofplastic. A hot plate is used to keep water in a container boiling at a temperature of ∞100 C . They place a slab of

the plastic with area 20.025 m and thickness 0.010 m above the container so that the bottom surface of the slabis at a temperature of ∞100 C . They put a large block of ice with temperature ∞0 C on top of the plastic slab.Some of the ice melts, and the students measure the amount of water collected during a time tD . The studentscorrectly calculate the amount of energy Q delivered to the ice and thus determine Q Dt . They repeat thisexperiment several times, each time adding an identical slab to increase the total thickness L of plastic. Theirresults are shown in the table below.

Energy flow rate Q tD ( )J s 97 53 31 27 18

Total thickness of plastic L (m) 0.010 0.020 0.030 0.040 0.050

(a) The students want to create a graph to yield a straight line whose slope could be used to calculate thethermal conductivity of the plastic.




i. Label the axes below to indicate a pair of quantities that could be graphed to yield a straight line. Include units for the quantities.

ii. On the grid on the previous page, create a linear graph using the values for the quantities indicated in part (a)(i). Be sure to do the following. • Add to the data table the values of any quantities to be plotted that are not already given. • Scale the axes. • Plot the data from the table. • Draw a line that best represents the data.

iii. Use the graph to calculate the thermal conductivity of the plastic.

(b) Indicate one potential problem with the setup that could lead to an experimental value for the thermal conductivity that is different from the actual value. Use physics principles to explain the effect this problem could have on the experimental value.

(c) The rectangle below represents a side view of the plastic slab. Draw a single arrow on the diagram

representing the direction of the net flow of energy through the plastic.




(d) Describe what occurs in the plastic at the microscopic level that explains the energy flow you indicated in part (c).

(e) An extra plastic slab sits on a wood surface, with both the plastic slab and the wood surface at room

temperature. A student touches each and finds that the plastic slab feels cooler than the wood surface. Explain what causes this observation.



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A student notices many air bubbles rising through the water in a large fish tank at an aquarium.

(a) In the figure below, the circle represents one such air bubble, and two incoming rays of light, A and B, are shown. Ray B points toward the center of the circle. On the diagram, draw the paths of rays A and B as they go through the bubble and back into the water. Your diagram should clearly show what happens to the rays at each interface.

(b) The bubble has a volume 1V , the air inside it has density Ar , and the water around it has density Wr . The

bubble starts at rest and has a speed fv when it has risen a height h. Assume that the change in the bubble’s

volume is negligible. Derive an expression for the mechanical energy dissipated by drag forces as the bubble rises this distance. Express your answer in terms of the given quantities and fundamental constants, as appropriate.

(c) At a particular instant, one bubble is 4.5 m below the water’s surface. The surface of the water is at sea level, and the density of the water is 31000 kg m .

i. Determine the absolute pressure in the bubble at this location. ii. The bubble has a volume 1V when it is 4.5 m below the water’s surface. Assume that the temperature of

the air in the bubble remains constant as it rises. In terms of 1V , calculate the volume of the bubble when it is just below the surface of the water.

iii. If the air in the bubble cooled as it rose, the volume of the bubble would be less than the value calculated in part (c)(ii). Use physics principles to briefly explain why.

STOP

END OF EXAM


ap physics 2: algebra-based

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