AP Physics C: Mechanics Unit 2 Practice Test & Exam | 28 Questions

Questions 1-3 refer to the following information.

1. What is the magnitude of the acceleration of the system?

(A)$1.0 \text{ m/s}^2$(B)$2.8 \text{ m/s}^2$(C)$4.0 \text{ m/s}^2$(D)$5.2 \text{ m/s}^2$

2. If the tabletop were frictionless, how would the tension $T$ in the string compare to the tension $T_{fric}$ when friction was present?

(A)$T < T_{fric}$(B)$T = T_{fric}$(C)$T > T_{fric}$(D)The relationship cannot be determined without knowing the value of the acceleration.

3. A system is composed of three particles. Particle 1 has mass $2m$ and is located at $(0, d)$. Particle 2 has mass $m$ and is located at $(0, 0)$. Particle 3 has mass $3m$ and is located at $(2d, 0)$. What are the coordinates of the center of mass of the system?

(A)$(d, d/3)$(B)$(d, d/2)$(C)$(d/2, d/3)$(D)$(d, 2d/3)$

4. A planet has mass $M$ and radius $R$. A satellite of mass $m$ is in a circular orbit of radius $2R$ around the planet. Which of the following represents the magnitude of the net force on the satellite?

(A)$G\frac{Mm}{(2R)^2}$(B)$G\frac{Mm}{R^2}$(C)$\frac{mv^2}{R}$(D)$0$

5. An object is moving at a constant velocity of $5 \text{ m/s}$ in the positive x-direction. Which of the following statements about the object is necessarily true?

(A)There are no forces acting on the object.(B)The net force acting on the object is zero.(C)The object is in a vacuum.(D)A constant force is being applied to the object in the direction of motion.

Questions 7-9 refer to the following information.

6. Which of the following differential equations correctly describes the speed $v$ of the sphere as a function of time $t$? (Assume the downward direction is positive).

(A)$m\frac{dv}{dt} = Fg - FB - bv$(B)$m\frac{dv}{dt} = Fg + FB - bv$(C)$m\frac{dv}{dt} = bv - Fg + FB$(D)$m\frac{dv}{dt} = Fg - FB$

7. The sphere reaches a terminal velocity $vT$. Which of the following is the correct expression for $vT$?

(A)$\frac{m}{b}$(B)$\frac{F_g}{b}$(C)$\frac{Fg - FB}{b}$(D)$\frac{Fg + FB}{b}$

8. A person is standing on a scale in an elevator. The scale reads a value greater than the person's actual weight. Which of the following could describe the motion of the elevator?

(A)It is moving downward and slowing down.(B)It is moving upward at a constant speed.(C)It is moving downward at a constant speed.(D)It is moving upward and slowing down.

9. A block of mass $m$ is attached to an ideal spring of spring constant $k$ and hangs vertically in equilibrium. The spring is stretched by a distance $x0$ from its natural length. What is the value of $x0$?

(A)$k/mg$(B)$mg/k$(C)$g/k$(D)$mk/g$

10. A car of mass $m$ travels at a constant speed $v$ around a flat, unbanked circular track of radius $R$. The force providing the centripetal acceleration is the force of static friction, $f_s$. Which of the following expressions must be true?

(A)$f_s = mg$(B)$f_s = \frac{mv^2}{R}$(C)$f_s > \frac{mv^2}{R}$(D)$f_s < \frac{mv^2}{R}$

11. A thin rod of length $L$ lies along the x-axis from $x=0$ to $x=L$. The rod has a non-uniform linear mass density given by $\lambda(x) = cx^2$, where $c$ is a constant. Which of the following integrals correctly gives the position of the center of mass, $x_{cm}$?

(A)$\frac{\int{0}^{L} cx^2 dx}{\int{0}^{L} cL^2 dx}$(B)$\frac{\int{0}^{L} cx^3 dx}{\int{0}^{L} cx^2 dx}$(C)$\frac{\int{0}^{L} x dx}{\int{0}^{L} cx^2 dx}$(D)$\int_{0}^{L} cx^3 dx$

12. A book is at rest on a table. The force of gravity pulls down on the book. According to Newton's Third Law, what is the reaction force?

(A)The force of the table on the book.(B)The force of the book on the table.(C)The force of the book on the Earth.(D)The normal force of the table on the book.

13. According to Newton's Shell Theorem, the gravitational force exerted by a uniform spherical shell of mass $M$ on a particle of mass $m$ located inside the shell is zero. If a particle is placed at a distance $r/2$ from the center of a solid sphere of uniform density with mass $M$ and radius $R$, what is the magnitude of the gravitational force on the particle?

(A)$G\frac{Mm}{(R/2)^2}$(B)$G\frac{M/2}{(R/2)^2}m$(C)$G\frac{M/8}{R^2}m$(D)$G\frac{M/8}{(R/2)^2}m$

Questions 16-18 refer to the following information.

14. The block begins to slide when the angle reaches a critical value $\theta_c$. Which of the following is true at this angle?

(A)$Mg \sin \thetac = \muk Mg \cos \theta_c$(B)$Mg \sin \thetac = \mus Mg \cos \theta_c$(C)$Mg \cos \thetac = \mus Mg \sin \theta_c$(D)$Mg = \mu_s N$

15. Once the block begins to slide, what is its acceleration $a$ down the incline?

(A)$a = 0$(B)$a = g(\sin\thetac - \muk \cos\theta_c)$(C)$a = g(\sin\thetac - \mus \cos\theta_c)$(D)$a = g\sin\theta_c$

16. Suppose the block is sliding down the incline at angle $\thetac$. A student wants to apply an external force $F{app}$ to the block such that it moves up the incline at a constant velocity. What is the magnitude of the required force $F_{app}$ directed parallel to the incline?

(A)$Mg(\sin\thetac + \muk \cos\theta_c)$(B)$Mg(\sin\thetac - \muk \cos\theta_c)$(C)$Mg(\muk \cos\thetac - \sin\theta_c)$(D)$Mg \sin\theta_c$

17. Two ideal springs, with spring constants $k1$ and $k2$, are connected in series to a block of mass $m$. What is the equivalent spring constant $k_{eq}$ of the combination?

(A)$k1 + k2$(B)$\frac{k1 + k2}{2}$(C)$\frac{k1 k2}{k1 + k2}$(D)$\sqrt{k1^2 + k2^2}$

18. A satellite is in a circular orbit of radius $R$ around a planet of mass $M$. Its orbital period is $T$. If the satellite were moved to a new circular orbit of radius $4R$, what would be its new period?

(A)$2T$(B)$4T$(C)$8T$(D)$16T$

19. An inertial reference frame is a frame in which...

(A)all objects are at rest.(B)an object with zero net force acting on it moves with constant velocity.(C)the laws of physics are different from those in other frames.(D)the frame itself is accelerating.

20. A net force given by the vector $\vec{F} = (6t) \hat{i} - (12) \hat{j}$ N acts on a 3 kg object. What is the acceleration of the object at $t = 2$ s?

(A)$(2\hat{i} - 4\hat{j}) \text{ m/s}^2$(B)$(4\hat{i} - 4\hat{j}) \text{ m/s}^2$(C)$(12\hat{i} - 12\hat{j}) \text{ m/s}^2$(D)$(6\hat{i} - 12\hat{j}) \text{ m/s}^2$

21. A student is pushing a heavy crate across a rough floor at a constant velocity. The student is pushing with a force directed downwards at an angle $\theta$ below the horizontal. How does the magnitude of the normal force $N$ exerted by the floor on the crate compare to the magnitude of the crate's weight $mg$?

(A)$N = mg$(B)$N > mg$(C)$N < mg$(D)The relationship depends on the coefficient of friction.

22. An ideal spring with spring constant $k = 200$ N/m is compressed by 0.1 m. What is the magnitude of the force exerted by the spring?

(A)1 N(B)2 N(C)10 N(D)20 N

23. The gravitational field strength at the surface of Planet X is $g_X$. Planet Y has twice the mass and twice the radius of Planet X. What is the gravitational field strength at the surface of Planet Y?

(A)$g_X/4$(B)$g_X/2$(C)$g_X$(D)$2g_X$

24. An object is undergoing uniform circular motion. Which of the following statements is true?

(A)Its velocity is constant.(B)Its acceleration is constant.(C)Its speed is constant.(D)The net force on it is zero.

25. A system consists of a 1 kg mass at $x = -2$ m and a 3 kg mass at $x = +2$ m. Where is the center of mass of this system located?

(A)$x = 0$ m(B)$x = +0.5$ m(C)$x = +1$ m(D)$x = +1.5$ m

26. The force of static friction is a variable force. Which of the following best explains this?

(A)The coefficient of static friction changes depending on the applied force.(B)The normal force changes depending on the applied force.(C)The force of static friction adjusts its magnitude to be equal and opposite to the component of the applied force parallel to the surface, up to a maximum value.(D)The force of static friction is always equal to its maximum possible value, $\mu_s N$.

27. Two ideal springs with spring constants $k1$ and $k2$ are attached to a block of mass $m$ on a frictionless horizontal surface, one on the left and one on the right. This is a parallel arrangement. What is the effective spring constant of this system for horizontal oscillations?

(A)$k1 + k2$(B)$(1/k1 + 1/k2)^{-1}$(C)$(k1 k2)^{1/2}$(D)$|k1 - k2|$

28. A small object of mass $m$ is attached to a string of length $L$ and moves in a horizontal circle of radius $r$, forming a conical pendulum. The string makes an angle $\theta$ with the vertical. What is the speed $v$ of the object?

(A)$\sqrt{gL \sin\theta}$(B)$\sqrt{gL \cos\theta}$(C)$\sqrt{gr \tan\theta}$(D)$\sqrt{\frac{gr}{\sin\theta}}$

AP Physics C: Mechanics Unit 2: Force and Translational Dynamics Practice Exam

Exam Details

A. Multiple-Choice Questions (28 Questions)

AP Physics C: Mechanics Unit 2: Force and Translational Dynamics Practice Exam

Exam Details

A. Multiple-Choice Questions (28 Questions)