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AP Physics C: Mechanics Full-length practice exam 2

35 questions

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Full-length practice exam 2

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Question 1

A motor lifts a 200 kg load at a constant velocity of $2$ m/s. What power does the motor deliver? ( $g = 10$ m/s²)

400

WB.

1000

WC.

4000

WD.

2000

Question 2

A satellite of mass $m$ orbits Earth (mass $M_{E}$ , radius $R_{E}$ ) at altitude $h$ above the surface in a circular orbit. What is the orbital speed?

\frac{G M _{E}}{R _{E}}

\frac{G M _{E}}{R _{E} + h}

\frac{G M _{E}}{R _{E} + h}

\frac{G M _{E} m}{R _{E} + h}

Question 3

Using the integral form of the impulse–momentum theorem, a force $F (t) = F_{0} e^{- t / τ}$ acts on mass $m$ from $t = 0$ to $t = \infty$ starting from rest. Find $v (\infty)$ .

\frac{F _{0}}{m τ}

\frac{F _{0} τ}{m}

\frac{F _{0}}{m}

F_{0} m τ

Question 4

A projectile is launched at angle $θ$ above the horizontal with initial speed $v_{0}$ . Which expression gives the maximum height?

\frac{v _{0}^{2}}{2 g}

\frac{v _{0}^{2} sin θ}{2 g}

\frac{v _{0}^{2} sin ^{2} θ}{2 g}

\frac{v _{0}^{2} cos ^{2} θ}{2 g}

Question 5

A particle moves along the $x$ -axis with velocity $v (t) = 3 t^{2} - 6 t$ m/s. What is the acceleration at $t = 2$ s?

6

m/s²B.

0

m/s²C.

12

m/s²D.

- 6

m/s²

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Question 6

The velocity of a particle is $v (t) = e^{- t}$ m/s for $t \geq 0$ . What is the total distance traveled from $t = 0$ to $t \to \infty$ ?

0

mB.

\frac{1}{e}

mC.

1

mD.

\infty

Question 7

The impulse–momentum theorem in integral form states $\int_{t_{1}}^{t_{2}} F (t) d t = Δ p$ . A force $F (t) = 6 t^{2}$ N acts on a 2 kg object from $t = 0$ to $t = 2$ s starting from rest. Find the final speed.

4

m/sB.

6

m/sC.

8

m/sD.

16

m/s

Question 8

The velocity of a particle is $v (t) = t^{2} - 4 t + 3$ m/s. What is the total distance traveled from $t = 0$ to $t = 4$ s?

(Hint: factor $v$ and identify where it changes sign.)

\frac{4}{3}

mB.

4

mC.

\frac{16}{3}

mD.

6

Question 9

The gravitational potential energy of mass $m$ at distance $r$ from mass $M$ is $U (r) = - \frac{GM m}{r}$ . Why is $U$ negative?

A.Because

G

M

, and

m

are all negative quantities.B.Because we define

U = 0

at infinity, and work must be done on the system to separate the masses.C.Because the force is repulsive at close range.D.Because kinetic energy is always greater than potential energy.

Question 10

Derive the gravitational potential energy by integrating the gravitational force. Starting from $F (r) = - \frac{GM m}{r ^{2}}$ (toward $M$ ), which integral correctly gives $U (r)$ with $U (\infty) = 0$ ?

U (r) = \int_{r}^{\infty} \frac{GM m}{r ^{'2}} d r^{'}

U (r) = - \int_{r}^{\infty} \frac{GM m}{r ^{'2}} d r^{'}

U (r) = \int_{0}^{r} \frac{GM m}{r ^{'2}} d r^{'}

U (r) = \int_{\infty}^{r} \frac{GM m}{r ^{'2}} d r^{'}

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Question 11

A particle of mass $m$ experiences a velocity-dependent drag force $F_{d r a g} = - b v$ , where $b > 0$ . Starting from rest, which expression gives $v (t)$ ?

v (t) = \frac{m g}{b} (1 - e^{- b t / m})

v (t) = \frac{m g}{b} e^{- b t / m}

v (t) = \frac{m g}{b} (1 + e^{- b t / m})

v (t) = \frac{m g}{b} (e^{b t / m} - 1)

Question 12

A figure skater with $I_{1} = 4$ kg·m² spins at $2$ rad/s and pulls in arms to reach $I_{2} = 1$ kg·m². What is the new angular velocity?

2

rad/sB.

4

rad/sC.

8

rad/sD.

0.5

rad/s

Question 13

A wheel starts from rest and reaches an angular velocity of $10$ rad/s in $5$ s under constant angular acceleration. What is the angular acceleration?

0.5

rad/s²B.

2

rad/s²C.

50

rad/s²D.

5

rad/s²

Question 14

A uniform solid disk of mass $M$ and radius $R$ has moment of inertia about its central axis $I = \frac{1}{2} M R^{2}$ . A net torque $τ = 4$ N·m is applied to a disk with $M = 2$ kg and $R = 1$ m. What is the angular acceleration?

2

rad/s²B.

4

rad/s²C.

8

rad/s²D.

1

rad/s²

Question 15

A particle of mass $m = 0.5$ kg moves in a circle of radius $r = 2$ m at speed $v = 4$ m/s. What is its angular momentum about the center?

2

kg·m²/sB.

4

kg·m²/sC.

8

kg·m²/sD.

0.5

kg·m²/s

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Question 16

A particle's position is $x (t) = A sin (ω t)$ . Using calculus, find $a (t)$ and identify the relationship between $a$ and $x$ .

a (t) = A ω cos (ω t)

;

a = ω x

a (t) = - A ω sin (ω t)

;

a = - x

a (t) = - A ω^{2} sin (ω t)

;

a = - ω^{2} x

a (t) = A ω^{2} cos (ω t)

;

a = ω^{2} x

Question 17

A uniform disk ( $I_{c m} = \frac{1}{2} M R^{2}$ ) has a small bolt of mass $m$ attached at its rim. Using the parallel-axis theorem, what is the total moment of inertia about the disk's center?

\frac{1}{2} M R^{2}

\frac{1}{2} (M + m) R^{2}

\frac{1}{2} M R^{2} + m R^{2}

\frac{1}{2} M R^{2} + \frac{1}{2} m R^{2}

Question 18

A 0.4 kg mass on a spring ( $k = 160$ N/m) is released from rest at $x = 0.05$ m from equilibrium. Find the total mechanical energy.

0.1

JB.

0.2

JC.

0.4

JD.

0.01

Question 19

Using Kepler's third law $T^{2} \propto r^{3}$ , if Earth's orbital radius is $1$ AU and period is $1$ yr, what is the orbital period of a planet at $4$ AU?

4

yrB.

8

yrC.

16

yrD.

64

Question 20

A particle has position $r (t) = t^{2} \hat{i} + 2 t^{3} \hat{j}$ m. What is $∣ a ∣$ at $t = 1$ s?

12

m/s²B.

14

m/s²C.

237

m/s²D.

40

m/s²

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Question 21

A mass $m$ is attached to two identical springs (each constant $k$ ) in parallel (both springs pull on the mass simultaneously). What is the effective spring constant and resulting oscillation frequency?

k_{e f f} = k /2

ω = k / (2 m)

k_{e f f} = 2 k

ω = 2 k / m

k_{e f f} = k

ω = k / m

k_{e f f} = 2 k

ω = k / (2 m)

Question 22

A damped oscillator has equation $m \overset{x}{¨} + b \overset{x}{˙} + k x = 0$ with $b^{2} < 4 mk$ . Which statement correctly describes the motion?

A.The system oscillates at the same frequency as the undamped case.B.The amplitude decays exponentially while the system oscillates at

ω_{d} < ω_{0}

.C.The system returns to equilibrium without oscillating.D.The energy grows exponentially due to damping.

Question 23

A 3 kg object moving at $8$ m/s to the right undergoes a perfectly inelastic collision with a 5 kg object moving at $4$ m/s to the left. Find their common velocity after the collision.

6

m/s to the rightB.

2

m/s to the rightC.

0.5

m/s to the rightD.

1

m/s to the left

Question 24

A 2 kg block slides 4 m down a frictionless incline inclined at 30°. Using the work–energy theorem, what is the final kinetic energy? ( $g = 10$ m/s²)

20

JB.

40

JC.

69

JD.

80

Question 25

A car rounds a banked curve of radius $R$ at angle $θ$ (no friction). What is the speed $v$ at which no friction is needed?

R g sin θ

R g cos θ

R g tan θ

R g tan θ

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Question 26

A particle's position components are $x (t) = v_{0 x} t$ and $y (t) = v_{0 y} t - \frac{1}{2} g t^{2}$ . Which expression correctly gives $y$ as a function of $x$ (the trajectory equation)?

y = \frac{v _{0 y}}{v _{0 x}} x - \frac{g}{v _{0 x}^{2}} x^{2}

y = \frac{v _{0 y}}{v _{0 x}} x - \frac{g}{2 v _{0 x}^{2}} x^{2}

y = \frac{v _{0 x}}{v _{0 y}} x - \frac{g}{2 v _{0 y}^{2}} x^{2}

y = \frac{v _{0 y}}{v _{0 x}} x + \frac{g}{2 v _{0 x}^{2}} x^{2}

Question 27

A block of mass $m$ is pushed against a vertical wall by a horizontal force $F$ (with $F > μ_{s} m g$ ). What is the minimum $F$ needed to prevent sliding?

F_{min} = m g

F_{min} = μ_{s} m g

F_{min} = \frac{m g}{μ _{s}}

F_{min} = \frac{μ _{s}}{m g}

Question 28

A constant force $F = 8$ N acts on a 2 kg object for 3 s. What is the change in velocity?

4

m/sB.

12

m/sC.

24

m/sD.

3

m/s

Question 29

Using the integral definition $I = \int r^{2} d m$ , find the moment of inertia of a thin uniform rod of mass $M$ and length $L$ about one end.

\frac{1}{12} M L^{2}

\frac{1}{2} M L^{2}

\frac{1}{3} M L^{2}

M L^{2}

Question 30

A constant force $F = 10$ N is applied at $0°$ to a block that moves 5 m along a frictionless surface. How much work is done by $F$ ?

0

JB.

2

JC.

50

JD.

500

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Question 31

A student derives the moment of inertia of a thin spherical shell of mass $M$ and radius $R$ about a diameter. Which result is correct?

\frac{1}{2} M R^{2}

\frac{2}{5} M R^{2}

\frac{2}{3} M R^{2}

M R^{2}

Question 32

A ball is launched horizontally from a cliff 80 m high with speed $20$ m/s. Using $g = 10$ m/s², how far from the base of the cliff does it land?

40

mB.

80

mC.

160

mD.

20

Question 33

Two ice skaters (60 kg and 40 kg) push off each other from rest. If the 40 kg skater moves at $3$ m/s to the right, what is the velocity of the 60 kg skater?

3

m/s to the leftB.

2

m/s to the leftC.

4.5

m/s to the leftD.

2

m/s to the right

Question 34

Apply energy conservation to derive the orbital speed of a satellite in a circular orbit of radius $r$ around a planet of mass $M$ . What is $v$ ?

v = \frac{2 π r}{T}

onlyB.

v = \frac{GM}{2 r}

v = \frac{GM}{r}

v = \frac{GM}{r ^{2}}

Question 35

A 0.1 kg bullet traveling at $400$ m/s embeds in a 4.9 kg stationary block on a frictionless surface. A spring ( $k = 1000$ N/m) is in front of the block. What is the maximum spring compression?

0.2

mB.

0.4

mC.

0.8

mD.

0.566

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