AP physics 2: algebra based 2019 free response questions

AP Physics 2 Algebra Based 2019 Free Response Questions 2019 AP ® Physics 2 Algebra Based Free Response Questions © 2019 The College Board College Board, Advanced Placement, AP, AP Central, and the ac[.]

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2019

Physics 2:

Algebra-Based

Free-Response Questions

AP Central is the official online home for the AP Program: apcentral.collegeboard.org

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CONSTANTS AND CONVERSION FACTORS Proton mass, m p 1.671027 kg

Neutron mass, m n 1.671027 kg

Electron mass, m e 9.111031 kg

Avogadro’s number, N0 6.0210 mol23 1

Universal gas constant, R 8.31 J (mol K)<

Boltzmann’s constant, k B 1.381023J K

Electron charge magnitude, e 1.601019 C

1 electron volt, 1 eV 1.601019 J Speed of light, c 3.0010 m s8 Universal gravitational

constant,

6.67 10 m kg s

Acceleration due to gravity

at Earth’s surface,

2

9.8 m s

g

1 unified atomic mass unit, 1 u 1.661027 kg 931 MeV c2

Planck’s constant, h 6.631034 J s< 4.141015 eV s<

1.99 10 J m 1.24 10 eV nm

Vacuum permittivity, e0 8.851012C2 N m< 2

Coulomb’s law constant, k 1 4pe0 9.0 10 N9 <m2 C2 Vacuum permeability, m0 4p10 7 (T m)< A

Magnetic constant, k m0 4p 1 107 (T m) A<

1 atmosphere pressure, 1 atm 1.0 10 N m5 2 1.010 Pa5

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

henry, H

farad, F tesla, T degree Celsius, C electron volt, eV

PREFIXES

Factor Prefix Symbol

12

9

6

3

2

10 centi c

3

10 milli m

6

10 micro m

9

10 nano n

12

10 pico p

VALUES OF TRIGONOMETRIC FUNCTIONS FOR COMMON ANGLES

30D 37D 45D 53D 60D 90D

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 which positive 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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-3-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

A = 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

0

x x a t

Ã Ã x

2

x t

1 2

x

x x Ã t a

0

x x a x x x

net

F

a

Ç G G

G

FG m FG

2

c

a

r

Ã

pG mvG

p F t

DG GD

2

1

2

cos

E W F d Fd q

E

P

t

D

2

1 2

q q w a

w w a

cos cos 2

i i

cm

i

m x

x

m

Ç

net

t

a G ÇG G

sin

r F rF

D D

2

1

2

s

FG k xG

2

1 2

s

g

U mg y

T

f

p w

2

T

k p

2

p

T

g

p A

1 2 2

g

m m

r

G

g F g m

G G

1 2

G

Gm m U

r

ELECTRICITY AND MAGNETISM

A = area

B = magnetic field

C = capacitance

d = distance

E = electric field

e = emf

F = force

I = current

A = 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 2 2 0

1 4

E

q q F

r pe

G

E F E q

K K

2 0

1 4

q E

r pe

G

E

D D

0

1 4

q V

r pe

V E

r

D D G

Q V C

D

0

A C

d ke

0

Q E

A e

2

C

U Q VD C DV

Q I t

D D

R A

rA

P I VD

V I R

D

i

R ÇR

1

i R

i

C ÇC

0

2

I B

r

m p

M

FG qvG BG

sin

M

FG qvG q BG

M

FG IGA BG

sin

M

FG IGA q BG

B B A

F G<G

cos

B B q A

F G G

B

t

e DF

D

B v

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-4-AP® PHYSICS 2 EQUATIONS FLUID MECHANICS AND THERMAL PHYSICS

A = area

F = force

h = depth

k = thermal conductivity

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

m

V

r

F

P

A

0

P P r gh

b

F r Vg

A v A v

2

1

2

1 2

kA T

Q

D

B

3

2 B

K k T

W P VD

MODERN PHYSICS

E = energy

f = frequency

m = mass

p = momentum

l= wavelength

f = work function

max

K hf f

h

p

l

2

E 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

v f

l

c n Ã

s s f

i o

h M h

i o

s s

D sin

GEOMETRY AND TRIGONOMETRY

A = area

C = circumference

V = volume

S = surface area

b = base

h = height

A= length

w = width

r = radius

Rectangle

Triangle

1 2

A bh

Circle

2

A p r

C 2p r

Rectangular solid

Cylinder

2

V p r A

2

S p rA p r

Sphere

3

4 3

V p r

2

4

S p r

Right triangle

c a b2

sin a

c

q

cos b

c

q

tan a

b

q

c a

b

90°

q

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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 v to the right and in0 the plane of the page The particle is approaching a region, shown by the dashed box, that contains a constant uniform 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 a magnetic 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 a

gravitational field near Earth’s surface, and why?

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GO ON TO THE NEXT PAGE -6-

(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

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The two circuits shown above contain an ideal variable power supply, an ohmic resistor of resistance R, an

ammeter A, and two voltmeters VPS and VR 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 DV be the potential difference measured by voltmeter PS VPS 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 DV , I, R, and r, as appropriate PS

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

resistance r of the ammeter

(e) Voltmeter VR in circuit 2 is replaced by a resistor with resistance 120 W to create circuit 3 shown below Voltmeter VPS still reads 3.0 V

i Calculate the equivalent resistance R eq of the circuit

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

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-9-3 (12 points, suggested time 25 minutes)

A group of students use the apparatus shown above to determine the thermal conductivity of a certain type of plastic 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 0.025 m and thickness 0.010 m above the container so that the bottom surface of the slab2

is 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 Dt The students

correctly calculate the amount of energy Q delivered to the ice and thus determine Q Dt They repeat this experiment several times, each time adding an identical slab to increase the total thickness L of plastic Their

results are shown in the table below

Energy flow rate Q D t ( )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 the thermal conductivity of the plastic

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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

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(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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-12-

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 V , the air inside it has density 1 r , and the water around it has density A r The W

bubble starts at rest and has a speed v f 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 1000 kg m3

i Determine the absolute pressure in the bubble at this location

ii The bubble has a volume V1 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 V1, 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

2019 AP< /b>® PHYSICS FREE- RESPONSE QUESTIONS

-5 -PHYSICS

Section...

4 Questions

Directions: Questions and are short free- response questions that require about 20 minutes each to answer and are

worth 10 points each Questions. .. class="text_page_counter">Trang 6

2019 AP< /b>® PHYSICS FREE- RESPONSE QUESTIONS

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