AP Physics C: Mechanics Unit 6 Practice Test & Exam | 18 Questions

Questions 1-3 refer to the following scenario.

1. Which of the following expressions best describes the block's acceleration $a(t)$ as a function of time?

(A)$a(t) = -20 \cos(10t)$(B)$a(t) = -10 \cos(10t)$(C)$a(t) = -20 \sin(10t)$(D)$a(t) = 10 \sin(10t)$

2. What is the kinetic energy of the block when it is at position $x = 0.1$ m?

(A)0.25 J(B)0.50 J(C)0.75 J(D)1.0 J

3. At which position $x$ is the block's speed equal to half of its maximum speed?

(A)$x = A/2$(B)$x = A/\sqrt{2}$(C)$x = A\sqrt{3}/2$(D)$x = A/4$

4. The motion of an object is described as simple harmonic. Which of the following statements must be true?

(A)The object's velocity is constant.(B)The object's acceleration is directly proportional to its displacement from equilibrium and in the opposite direction.(C)The period of oscillation depends on the amplitude of the motion.(D)The net force on the object is constant.

5. A 4.0 kg object is attached to an ideal spring and undergoes simple harmonic motion with a period of $\pi$ seconds. What is the spring constant of the spring?

(A)4.0 N/m(B)8.0 N/m(C)16 N/m(D)32 N/m

6. The position of a particle in simple harmonic motion is given by $x(t) = (0.25 \text{ m}) \cos(5\pi t + \pi)$. What is the first time after $t=0$ that the particle is at its equilibrium position, $x=0$?

(A)$t = 0.05$ s(B)$t = 0.10$ s(C)$t = 0.20$ s(D)$t = 0.50$ s

Questions 7-8 refer to the following graph.

7. The graph shows the potential energy $U$ of a particle as a function of its position $x$. The particle has total mechanical energy $E_{total}$, as indicated by the dashed line. At which of the following positions is the particle's kinetic energy at its maximum?

(A)$x = -A$(B)$x = 0$(C)$x = +A$(D)$x = A/\sqrt{2}$

8. Based on the potential energy graph, which of the following best describes the net force $F$ acting on the particle as a function of position $x$?

(A)$F$ is constant and positive.(B)$F$ is proportional to $x^2$.(C)$F$ is proportional to $-x$.(D)$F$ is proportional to $1/x$.

9. A uniform rod of length $L$ and mass $M$ is pivoted at one end and allowed to oscillate as a physical pendulum. Its moment of inertia about the pivot is $I = \frac{1}{3}ML^2$. A simple pendulum has a bob of mass $m$ and a string of length $L$. Both are released from a small angle. What is the ratio of the period of the physical pendulum, $T{phys}$, to the period of the simple pendulum, $T{simple}$?

(A)$1$(B)$\sqrt{2/3}$(C)$\sqrt{3/2}$(D)$2/3$

10. A simple pendulum of length $L$ has a period $T$ on Earth. If the pendulum is taken to a planet where the acceleration due to gravity is $4g$, what is its new period?

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

11. The motion of an object is described by the differential equation $\frac{d^2x}{dt^2} = -36x$, where $x$ is in meters and $t$ is in seconds. What is the period of the object's motion?

(A)$\pi/6$ s(B)$\pi/3$ s(C)$3\pi$ s(D)$6\pi$ s

12. A mass-spring system oscillates with amplitude $A$. The total mechanical energy of the system is $E_0$. If the amplitude of oscillation is tripled to $3A$, what is the new total mechanical energy of the system?

(A)$E_0 / 3$(B)$E_0$(C)$3E_0$(D)$9E_0$

13. A student wants to build a simple pendulum that has a period of 2.0 seconds (a "seconds pendulum"). Assuming $g \approx 9.8$ m/s², what length should the pendulum have?

(A)Approximately 0.25 m(B)Approximately 0.50 m(C)Approximately 1.0 m(D)Approximately 4.0 m

14. An object undergoing simple harmonic motion has its maximum speed when it is at the equilibrium position and zero speed at the endpoints of its motion. Where is the magnitude of its acceleration the greatest?

(A)At the equilibrium position ($x=0$)(B)At the points of maximum displacement ($x=\pm A$)(C)Halfway between equilibrium and maximum displacement ($x=\pm A/2$)(D)The acceleration is constant throughout the motion.

15. A physical pendulum consists of a uniform disk of mass $M$ and radius $R$ pivoted at its rim. The moment of inertia of a disk about its center of mass is $\frac{1}{2}MR^2$. What is the period of this pendulum for small oscillations?

(A)$2\pi\sqrt{\frac{R}{g}}$(B)$2\pi\sqrt{\frac{2R}{g}}$(C)$2\pi\sqrt{\frac{3R}{2g}}$(D)$2\pi\sqrt{\frac{R}{2g}}$

16. A block of mass $m1$ is attached to a spring of constant $k$ and oscillates with period $T1$. A second block of mass $m2 = 4m1$ is attached to an identical spring. What is the period of oscillation, $T_2$, for the second block?

(A)$T2 = T1/2$(B)$T2 = T1$(C)$T2 = 2T1$(D)$T2 = 4T1$

17. The position of an object is given by $x(t) = A\cos(\omega t + \phi)$. At time $t=0$, the object is at $x = A/2$ and is moving in the negative $x$-direction. Which of the following is a possible value for the phase constant $\phi$?

(A)$0$(B)$\pi/3$(C)$\pi/2$(D)$2\pi/3$

Refer to the figure below.

18. Which of the following force laws would lead to simple harmonic motion if it were the net force acting on a particle? Section II: Free-Response Directions:Show all your work. Your response will be graded on the correctness and completeness of your methods as well as your final answers. FRQ 1[Skills: 7.A, 2.C, 2.B | Topics: 7.1, 7.3, 7.4] A block of mass $M$ is attached to an ideal spring of spring constant $k$ and rests on a frictionless, horizontal surface. The block is displaced a distance $A$ from its equilibrium position ($x=0$) and released from rest. FRQ 2[Skills: 4.A, 5.B, 5.D | Topic: 7.2] You are given a set of five objects with known masses, a spring with an unknown spring constant $k$, a stand with a clamp, a meterstick, and a stopwatch. You are tasked with determining the spring constant $k$ experimentally. i. State the quantities you would measure. ii. Describe the equipment you would use for each measurement. iii. Describe the overall process. Using the best-fit line shown in the graph, calculate the value of the spring constant $k$. FRQ 3[Skills: 2.B, 7.A | Topic: 7.5] A physical pendulum consists of a thin, uniform rod of mass $M=1.2$ kg and length $L=1.0$ m. The rod is pivoted at a point a distance $d=0.25$ m from its center. The moment of inertia of the rod about its center of mass is $I_{CM} = \frac{1}{12}ML^2$. FRQ 4[Skills: 1.B, 6.A, 7.C | Topic: 7.4] An object of mass $m$ is in simple harmonic motion. The graph below shows the kinetic energy $K$ of the object as a function of its position $x$. The object's maximum kinetic energy is $K_{max}$ and its amplitude of oscillation is $A$.

(A)The potential energy of the system is defined to be zero at $x=0$. On the axes below, sketch a graph of the potential energy $U$ as a function of position $x$. Label the maximum potential energy on the vertical axis in terms of $K_{max}$.(B)Justify the shape of the graph you sketched in part (a).(C)Using the information from the graph, determine the spring constant $k$ in terms of $K_{max}$ and $A$.(D)Using the information from the graph, determine the maximum speed $v{max}$ of the object in terms of $K{max}$ and $m$.

AP Physics C: Mechanics Unit 6: Energy and Momentum of Rotating Systems Practice Exam

Exam Details

A. Multiple-Choice Questions (18 Questions)

AP Physics C: Mechanics Unit 6: Energy and Momentum of Rotating Systems Practice Exam

Exam Details

A. Multiple-Choice Questions (18 Questions)