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AP Physics C: Mechanics Medium practice

15 questions

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Medium practice

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Question 1

Using the gravitational field $g = - \frac{GM}{r ^{2}} \overset{r}{^}$ , find the work done by gravity on mass $m$ moving from $r_{1} = 2 R_{E}$ to $r_{2} = 4 R_{E}$ .

W = \frac{G M _{E} m}{4 R _{E}}

W = - \frac{G M _{E} m}{4 R _{E}}

W = \frac{G M _{E} m}{2 R _{E}}

W = 0

Question 2

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 3

An Atwood machine has masses $m_{1} = 4$ kg and $m_{2} = 6$ kg connected by a massless rope over a frictionless pulley. What is the acceleration of the system? ( $g = 10$ m/s²)

1

m/s²B.

2

m/s²C.

5

m/s²D.

4

m/s²

Question 4

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 5

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)

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Question 6

A rocket launches from Earth's surface (mass $M_{E}$ , radius $R_{E}$ ). What is the minimum launch speed needed to escape Earth's gravity entirely?

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

\frac{2 G M _{E}}{R _{E}}

\frac{2 G M _{E}}{R _{E}}

\frac{G M _{E}}{2 R _{E}}

Question 7

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 8

A variable force $F (x) = 3 x^{2}$ N acts on a particle along the $x$ -axis. What is the work done from $x = 0$ to $x = 2$ m?

6

JB.

8

JC.

12

JD.

4

Question 9

Two particles with masses $m_{1} = 4$ kg at $x = 0$ and $m_{2} = 2$ kg at $x = 6$ m. Where is the center of mass?

3

mB.

2

mC.

4

mD.

1

Question 10

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}

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Question 11

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 12

Three particles have masses and positions: $m_{1} = 2$ kg at $x_{1} = 0$ m, $m_{2} = 3$ kg at $x_{2} = 4$ m, and $m_{3} = 1$ kg at $x_{3} = 6$ m. Find the center of mass.

\frac{10}{3} \approx 3.33

mB.

3

mC.

2

mD.

4

Question 13

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

Question 14

A 2 kg ball moving at $5$ m/s to the right collides elastically with a 2 kg ball at rest. What are their velocities after the collision?

A.Both move at

2.5

m/sB.First stops; second moves at

5

m/sC.First moves at

5

m/s; second stopsD.First moves at

- 2.5

m/s; second at

7.5

m/s

Question 15

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

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