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AP Physics 2 Full-length practice exam 3

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Full-length practice exam 3

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Question 1

A heat engine operates between a hot reservoir at $T_{H} = 600 K$ and a cold reservoir at $T_{C} = 300 K$ . What is the maximum (Carnot) efficiency of this engine?

25%

50%

75%

100%

Question 2

A fish is $1.0 m$ below the surface of water ( $n_{w} = 1.33$ ). A person looks straight down at the fish from air ( $n_{air} = 1.0$ ). Due to refraction, the fish appears to be at what depth below the surface?

d_{apparent} \approx 0.75 m

d_{apparent} \approx 1.33 m

d_{apparent} = 1.0 m

(no distortion)D.

d_{apparent} \approx 0.50 m

Question 3

An electron is fired horizontally into a uniform electric field directed vertically downward with magnitude $E = 500 N/C$ . The electron has initial speed $v_{0} = 2.0 \times 1 0^{6} m/s$ . What is the magnitude of the electron's acceleration? ( $m_{e} = 9.11 \times 1 0^{- 31} kg$ , $e = 1.6 \times 1 0^{- 19} C$ )

a \approx 8.8 \times 1 0^{13} m/ s^{2}

a \approx 4.4 \times 1 0^{13} m/ s^{2}

a \approx 8.8 \times 1 0^{10} m/ s^{2}

a \approx 5.5 \times 1 0^{14} m/ s^{2}

Question 4

A circuit has a $9 V$ battery with internal resistance $r = 1 Ω$ connected to an external resistance $R = 8 Ω$ . What is the terminal voltage of the battery?

V_{terminal} = 9 V

V_{terminal} = 8 V

V_{terminal} = 1 V

V_{terminal} = 9.1 V

Question 5

A long straight wire carries current $I$ to the right. A proton (positive charge) is located directly above the wire and is moving to the right (same direction as $I$ ). What is the direction of the magnetic force on the proton?

A.Upward, away from the wireB.Downward, toward the wireC.To the left, opposing the proton's motionD.Out of the page

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Question 6

Kirchhoff's voltage law (KVL) states that the sum of all voltage drops around any closed loop in a circuit equals zero. This law is a consequence of which fundamental principle?

A.Conservation of chargeB.Conservation of energyC.Newton's third lawD.Ohm's law

Question 7

A $P V$ diagram shows a gas undergoing a rectangular cycle (two isobaric and two isochoric processes). In which segment does the gas do the most positive work?

A.The isochoric (constant volume) expansion at high pressure.B.The isobaric compression at low pressure.C.The isobaric expansion at high pressure.D.The isochoric compression at low volume.

Question 8

A fully charged capacitor ( $C = 100 μ F$ , $V_{0} = 10 V$ ) is connected in series with a resistor $R = 2 k Ω$ with no battery. After the switch is closed, what is the current through the resistor at $t = 0$ (immediately after closing)?

I_{0} = 0

I_{0} = 5 mA

I_{0} = 50 mA

I_{0} = 1 A

Question 9

A square loop of side $s = 0.2 m$ and resistance $R = 4 Ω$ is in a magnetic field that is increasing at $d B / d t = 50 T/s$ perpendicular to the loop. What is the power dissipated in the loop?

P = 0.25 W

P = 1.0 W

P = 16 W

P = 0.5 W

Question 10

One mole of an ideal monatomic gas undergoes an isobaric expansion from volume $V_{1}$ to $2 V_{1}$ at pressure $P$ . Which expression correctly gives the heat $Q$ added to the gas? (Use $R$ for the ideal gas constant.)

Q = P V_{1}

Q = \frac{3}{2} P V_{1}

Q = \frac{5}{2} P V_{1}

Q = 2 P V_{1}

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Question 11

A parallel-plate capacitor has plate area $A$ and plate separation $d$ . If the separation is doubled while the charge on the plates remains constant, how does the voltage across the capacitor change?

A.The voltage is halved.B.The voltage is unchanged.C.The voltage doubles.D.The voltage quadruples.

Question 12

A converging (convex) lens with focal length $f = 20 cm$ has an object placed $10 cm$ from it (inside the focal length). What type of image does the lens produce?

A.Real, inverted, and magnifiedB.Virtual, upright, and magnifiedC.Real, upright, and diminishedD.No image is formed when the object is inside the focal length.

Question 13

Two resistors, $R_{1} = 6 Ω$ and $R_{2} = 3 Ω$ , are connected in parallel across a battery. What is the equivalent resistance of the combination?

R_{eq} = 9 Ω

R_{eq} = 4.5 Ω

R_{eq} = 2 Ω

R_{eq} = 1 Ω

Question 14

In the Compton effect, an X-ray photon of wavelength $λ_{0}$ scatters off a free electron and the scattered photon has a longer wavelength $λ^{'}$ . The Compton shift $Δ λ = λ^{'} - λ_{0}$ depends on:

A.The initial wavelength

λ_{0}

of the photon onlyB.The scattering angle

θ

only (and fundamental constants)C.Both the initial wavelength and the scattering angleD.The mass of the photon and the electron mass

Question 15

According to the Heisenberg uncertainty principle, the minimum uncertainty in the momentum of an electron confined to a region of length $Δ x = 1.0 \times 1 0^{- 10} m$ (atomic scale) is approximately: ( $h = 6.63 \times 1 0^{- 34} J \cdot s$ )

Δ p \approx 6.63 \times 1 0^{- 24} kg \cdot m/s

Δ p \approx 5.3 \times 1 0^{- 25} kg \cdot m/s

Δ p \approx 1.0 \times 1 0^{- 10} kg \cdot m/s

Δ p \approx 6.63 \times 1 0^{- 44} kg \cdot m/s

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Question 16

A circular loop of radius $r = 0.1 m$ has resistance $R = 5 Ω$ . It is placed in a magnetic field perpendicular to the loop. The field changes at a rate of $\frac{d B}{d t} = 200 T/s$ . What is the induced current in the loop?

I \approx 0.04 A

I \approx 1.26 A

I \approx 6.28 A

I \approx 0.4 A

Question 17

A thin film of soap ( $n = 1.35$ ) in air has a thickness $t = 350 nm$ . For what wavelength of visible light (in air) does the film appear brightest (constructive interference in reflection)?

λ = 945 nm

(infrared — not visible)B.

λ = 630 nm

(orange-red)C.

λ = 472.5 nm

(blue-violet)D.

λ = 315 nm

(ultraviolet — not visible)

Question 18

Snell's law describes refraction at the interface between two media. If a ray travels from medium 1 (index $n_{1}$ ) into medium 2 (index $n_{2} > n_{1}$ ), what happens to the angle of refraction $θ_{2}$ compared to the angle of incidence $θ_{1}$ ?

θ_{2} > θ_{1}

(ray bends away from the normal)B.

θ_{2} < θ_{1}

(ray bends toward the normal)C.

θ_{2} = θ_{1}

(no bending occurs)D.

θ_{2} = 90°

(total internal reflection occurs)

Question 19

Light travels from glass ( $n_{g} = 1.5$ ) into water ( $n_{w} = 1.33$ ) at an angle of incidence of $60°$ . What is the angle of refraction in water? ( $sin 60° \approx 0.866$ )

θ_{2} \approx 40.6°

(ray bends toward the normal)B.Total internal reflection occurs; no transmitted ray.C.

θ_{2} \approx 77.8°

(ray bends away from the normal)D.

θ_{2} = 60°

(no bending at the glass-water interface)

Question 20

Three point charges are placed along a line: $+ Q$ at $x = 0$ , $- Q$ at $x = d$ , and $+ Q$ at $x = 2 d$ . At the point $x = d$ (the location of the $- Q$ charge), the net electric field due to the other two charges points in which direction?

A.In the

+ x

directionB.In the

- x

directionC.The net electric field at

x = d

from the two

+ Q

charges is zero.D.Perpendicular to the line (in the

y

-direction)

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Question 21

Two long parallel wires carry equal currents $I$ in opposite directions and are separated by distance $d$ . What is the nature of the magnetic force between them?

A.Attractive, because opposite currents create fields that reinforce between the wires.B.Repulsive, because the magnetic fields between the wires push outward.C.Attractive, same as for parallel currents in the same direction.D.There is no magnetic force because the fields cancel between the wires.

Question 22

A long solenoid has $n$ turns per unit length and carries current $I$ . Which expression gives the magnetic field inside the solenoid?

B = μ_{0} I / (2 π r)

B = μ_{0} n I

B = μ_{0} N I / r

where

N

is total turns and

r

is radiusD.

B = μ_{0} n I^{2}

Question 23

A photon has a wavelength of $λ = 400 nm$ . What is its energy in electron-volts? ( $h = 6.63 \times 1 0^{- 34} J \cdot s$ , $c = 3 \times 1 0^{8} m/s$ , $1 eV = 1.6 \times 1 0^{- 19} J$ )

E \approx 1.24 eV

E \approx 3.1 eV

E \approx 6.2 eV

E \approx 0.31 eV

Question 24

In the photoelectric effect, which property of light determines the maximum kinetic energy of the ejected electrons?

A.The intensity (brightness) of the lightB.The frequency (or wavelength) of the lightC.The angle of incidence of the light on the metalD.The total duration of illumination

Question 25

In a double-slit interference experiment, the slits are separated by $d = 0.5 mm$ and a screen is $L = 2.0 m$ away. For light of wavelength $λ = 500 nm$ , what is the distance between adjacent bright fringes?

Δ y = 1.0 mm

Δ y = 2.0 mm

Δ y = 0.5 mm

Δ y = 4.0 mm

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Question 26

A rectangular loop of wire is placed in a uniform magnetic field $B$ pointing into the page. The loop lies in the plane of the page. If the magnetic flux through the loop is $Φ_{B} = B A$ where $A$ is the loop area, what is the induced EMF when the loop is stationary?

E = B A

E = B / A

E = 0

E = B^{2} A

Question 27

An object is placed $15 cm$ to the left of a converging lens with $f_{1} = 10 cm$ . A second converging lens with $f_{2} = 20 cm$ is placed $40 cm$ to the right of the first lens. Where is the final image formed relative to the second lens?

20 cm

to the right of lens 2 (real image)B.

20 cm

to the left of lens 2 (virtual image)C.

13.3 cm

to the right of lens 2 (real image)D.No image is formed — the object is at

f_{2}

Question 28

A convex (diverging) mirror always produces what type of image for a real object?

A.Real, inverted, diminishedB.Real, upright, magnifiedC.Virtual, inverted, diminishedD.Virtual, upright, diminished

Question 29

Three resistors are connected between nodes A, B, and C: $R_{A B} = 3 Ω$ (directly between A and B), $R_{B C} = 3 Ω$ (between B and C), and $R_{A C} = 6 Ω$ (between A and C). A $12 V$ battery is connected between A and B. What is the total current delivered by the battery?

I = 4 A

I = 5.33 A

I = 1 A

I = 2.67 A

Question 30

A nuclear reaction fuses two deuterium nuclei to produce helium-3 and a neutron:
$_{1}^{2} H +_{1}^{2} H \to_{2}^{3} He +_{0}^{1} n$
Given that the mass defect is $Δ m = 3.3 \times 1 0^{- 30} kg$ , how much energy is released? ( $c = 3 \times 1 0^{8} m/s$ )

E \approx 2.97 \times 1 0^{- 13} J

E \approx 9.9 \times 1 0^{- 22} J

E \approx 3.0 \times 1 0^{- 13} J

E \approx 9.9 \times 1 0^{- 13} J

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Question 31

A gas undergoes an isothermal process. Which of the following is true about the change in internal energy $Δ U$ of an ideal gas during this process?

Δ U > 0

because work is done on the gas.B.

Δ U < 0

because the gas must release heat to maintain constant temperature.C.

Δ U = 0

because internal energy of an ideal gas depends only on temperature.D.

Δ U = Q

because no work is done during an isothermal process.

Question 32

A positive test charge $+ q$ is placed in an electric field $E$ . The electric force on the test charge is:

F = E / q

F = q E

, directed opposite to

E

since the charge is positive.C.

F = q E

, directed in the same direction as

E

.D.

F = q^{2} E

Question 33

In single-slit diffraction, the first minimum occurs at angle $θ$ given by $a sin θ = λ$ , where $a$ is the slit width. If the slit width is doubled while keeping the wavelength constant, the central diffraction maximum becomes:

A.Twice as wide and half as brightB.Half as wide and more brightC.The same width but twice as brightD.Half as wide and half as bright

Question 34

An RC circuit has a capacitor $C = 200 μ F$ in series with a resistor $R = 5 k Ω$ and a $12 V$ battery. The capacitor is initially uncharged. Approximately how long after the switch is closed does the voltage across the capacitor reach $7.6 V$ ? (Use $e \approx 2.718$ , so $1 - e^{- 1} \approx 0.632$ .)

t \approx 0.5 s

t \approx 1.0 s

t \approx 2.0 s

t \approx 0.1 s

Question 35

Total internal reflection can occur when light travels from:

A.Air into glass, at any angle of incidenceB.Glass into air, at angles exceeding the critical angleC.Glass into air, at angles smaller than the critical angleD.Air into water, when the beam is nearly parallel to the surface

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Question 36

A $60 W$ lightbulb is designed to operate at $120 V$ . What is its operating resistance?

R = 0.5 Ω

R = 240 Ω

R = 2 Ω

R = 7200 Ω

Question 37

In nuclear physics, a nucleus with mass number $A = 235$ and atomic number $Z = 92$ (uranium-235) undergoes alpha decay. What are the mass number and atomic number of the daughter nucleus?

A = 231

Z = 90

A = 233

Z = 90

A = 231

Z = 91

A = 235

Z = 90

Question 38

An electron enters a region with both a uniform electric field $E = 1000 V/m$ pointing upward and a uniform magnetic field $B = 0.02 T$ pointing out of the page. The electron moves horizontally to the right without deflection. What must be the speed of the electron?

v = 5 \times 1 0^{4} m/s

v = 2 \times 1 0^{- 5} m/s

v = 5 \times 1 0^{4} m/s

in a specific direction onlyD.

v = 2 \times 1 0^{7} m/s

Question 39

Light of frequency $f = 1.5 \times 1 0^{15} Hz$ illuminates a metal with work function $ϕ = 3.6 eV$ . What is the maximum kinetic energy of the emitted electrons in eV? ( $h = 4.14 \times 1 0^{- 15} eV \cdot s$ )

K_{max} = 2.61 eV

K_{max} = 6.21 eV

K_{max} = 3.6 eV

K_{max} = 9.81 eV

Question 40

A heat engine absorbs $Q_{H} = 800 J$ from a hot reservoir and does $W = 200 J$ of work per cycle. What is the change in entropy of the cold reservoir per cycle if it is at $T_{C} = 400 K$ ?

Δ S_{C} = 0.5 J/K

Δ S_{C} = 1.5 J/K

Δ S_{C} = 2.0 J/K

Δ S_{C} = - 1.5 J/K

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Question 41

A proton moves in a circle of radius $r$ when it enters a region with a uniform magnetic field $B$ perpendicular to its velocity. Which of the following expressions gives the speed of the proton? ( $m_{p}$ = proton mass, $e$ = proton charge)

v = \frac{e B}{m _{p} r}

v = \frac{e B r}{m _{p}}

v = \frac{m _{p} r}{e B}

v = e B r m_{p}

Question 42

A particle is accelerated through a potential difference of $V = 50 kV$ . Using the de Broglie relation $λ = h / p$ and energy conservation (non-relativistic), what is the de Broglie wavelength of a proton accelerated through this potential? ( $m_{p} = 1.67 \times 1 0^{- 27} kg$ , $e = 1.6 \times 1 0^{- 19} C$ , $h = 6.63 \times 1 0^{- 34} J \cdot s$ )

λ \approx 1.28 \times 1 0^{- 13} m

λ \approx 5.5 \times 1 0^{- 12} m

λ \approx 1.28 \times 1 0^{- 10} m

λ \approx 6.63 \times 1 0^{- 34} m

Question 43

According to special relativity, a muon traveling at $v = 0.99 c$ relative to Earth has a lifetime measured in Earth's frame that is longer than its proper lifetime. This phenomenon is called:

A.Length contractionB.Time dilationC.The twin paradoxD.Mass-energy equivalence

Question 44

An electron (charge $- e$ ) is released from rest at a point where the electric potential is $V = - 50 V$ and moves to a point where $V = + 50 V$ . By how much does the electron's kinetic energy increase?

Δ K E = - 1.6 \times 1 0^{- 17} J

(electron loses energy)B.

Δ K E = + 8.0 \times 1 0^{- 18} J

Δ K E = + 1.6 \times 1 0^{- 17} J

Δ K E = 0

(electron starts from rest so gains no energy)

Question 45

An object is placed $30 cm$ in front of a concave mirror with focal length $f = 10 cm$ . Using the mirror equation $\frac{1}{f} = \frac{1}{d _{o}} + \frac{1}{d _{i}}$ , what is the image distance $d_{i}$ ?

d_{i} = - 15 cm

d_{i} = 15 cm

d_{i} = 20 cm

d_{i} = 40 cm

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Question 46

A $12 Ω$ resistor and an $8 Ω$ resistor are connected in series to a $20 V$ battery with negligible internal resistance. What is the voltage across the $8 Ω$ resistor?

V_{8} = 12 V

V_{8} = 8 V

V_{8} = 10 V

V_{8} = 20 V

Question 47

A $6 Ω$ resistor and a $3 Ω$ resistor are connected in parallel. This parallel combination is in series with a $2 Ω$ resistor, and the whole circuit is powered by a $12 V$ battery. What is the current through the $6 Ω$ resistor?

I_{6} = 3 A

I_{6} = 1 A

I_{6} = 2 A

I_{6} = 4 A

Question 48

An ideal gas is held at constant volume while heat $Q$ is added to it. Which expression correctly gives the change in internal energy $Δ U$ ?

Δ U = Q - W

, where

W = P Δ V > 0

Δ U = Q

Δ U = - Q

Δ U = 0

, because temperature does not change at constant volume.

Question 49

A charge $q = + 2 μ C$ is moved from point A to point B in an electric field. The potential at A is $V_{A} = 100 V$ and at B is $V_{B} = 40 V$ . What is the work done by the electric field on the charge?

W = + 1.2 \times 1 0^{- 4} J

W = - 1.2 \times 1 0^{- 4} J

W = + 2.8 \times 1 0^{- 4} J

W = + 8.0 \times 1 0^{- 5} J

Question 50

A rectangular conducting loop is pulled out of a uniform magnetic field $B$ pointing into the page at constant velocity $v$ . The loop has width $L$ (the side perpendicular to $v$ ). Which expression gives the magnitude of the induced EMF while the loop is being pulled out?

E = B L^{2} v

E = B Lv

E = B v / L

E = B^{2} Lv

AP Physics 2 Full-length practice exam 3 — Free with Answer Explanations | Test Practice Hub