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AP Physics C: Mechanics Hard practice

15 questions

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Hard practice

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Question 1

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 2

A torsional pendulum has restoring torque $τ = - κ θ$ where $κ$ is the torsion constant and $I$ is the moment of inertia. What is the period of oscillation?

T = 2 π \frac{κ}{I}

T = 2 π \frac{I}{κ}

T = \frac{1}{2 π} \frac{I}{κ}

T = 2 π I κ

Question 3

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 4

A rocket of initial mass $M_{0}$ expels exhaust at speed $u$ relative to the rocket. Applying Newton's second law to variable mass, what is the thrust force?

F_{t h r u s t} = u \frac{d M}{d t}

(positive)B.

F_{t h r u s t} = - u \frac{d M}{d t}

F_{t h r u s t} = u M_{0}

F_{t h r u s t} = \frac{u}{d M / d t}

Question 5

A particle of mass $m$ on a frictionless horizontal surface is attached to a spring (constant $k$ ) and experiences a drag force $F_{d} = - b v$ . Which differential equation governs its motion?

m \overset{x}{¨} + k x = 0

m \overset{x}{¨} - b \overset{x}{˙} + k x = 0

m \overset{x}{¨} + b \overset{x}{˙} + k x = 0

m \overset{x}{¨} + b \overset{x}{˙} - k x = 0

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Question 6

A conservative force on a particle is $F (x) = - \frac{d U}{d x}$ where $U (x) = 2 x^{3} - x^{2}$ J. Find the force at $x = 1$ m.

- 4

NB.

4

NC.

- 2

ND.

1

J (wrong unit)

Question 7

A spring–mass system ( $k$ , $m$ ) undergoes SHM. At $t = 0$ , $x_{0} = 0.06$ m and $v_{0} = 0.8$ m/s. Given $ω = 10$ rad/s, find the amplitude.

0.06

mB.

0.08

mC.

0.1

mD.

0.14

Question 8

Derive Kepler's third law ( $T^{2} \propto r^{3}$ ) for a circular orbit from Newton's law of gravitation and the definition of circular motion.

T^{2} = \frac{4 π ^{2} r ^{3}}{GM}

T^{2} = \frac{2 π r ^{3}}{GM}

T^{2} = \frac{4 π ^{2} r ^{2}}{GM}

T = \frac{2 π r}{GM / r}

Question 9

A disk ( $I_{1} = 2$ kg·m², $ω_{1} = 6$ rad/s) drops onto a stationary disk ( $I_{2} = 3$ kg·m²) on the same frictionless axle. They reach a common angular velocity $ω_{f}$ . How much kinetic energy is lost?

0

JB.

14.4

JC.

21.6

JD.

36

Question 10

A particle moves in the $x y$ -plane from $(0, 0)$ to $(2, 4)$ m under the force $F = (3 x^{2}) \hat{i} + (2 y) \hat{j}$ N along the straight-line path $y = 2 x$ . What is the total work done?

8

JB.

16

JC.

24

JD.

32

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Question 11

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

Question 12

Using the work integral, derive the work done by a spring force $F_{s} = - k x$ as a block is displaced from $x = 0$ to $x = A$ .

W = - k A

W = - \frac{1}{2} k A^{2}

W = \frac{1}{2} k A^{2}

W = k A^{2}

Question 13

A net torque $τ_{n e t} = 10$ N·m acts on a solid sphere ( $I = \frac{2}{5} M R^{2}$ , $M = 5$ kg, $R = 0.2$ m). Find $α$ .

50

rad/s²B.

125

rad/s²C.

250

rad/s²D.

10

rad/s²

Question 14

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 15

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}

AP Physics C: Mechanics Hard practice — Free with Answer Explanations | Test Practice Hub