Practice Test 7 - AP Physics C Mechanics

20 questions. Answer them in any order, then submit to see your score and every explanation.

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1. A 4.0 kg block sliding at 6.0 m/s on a frictionless surface collides elastically with a 2.0 kg block moving at 3.0 m/s in the opposite direction. After the collision, the 2.0 kg block moves at 7.0 m/s in its original direction. A student calculates that the 4.0 kg block's final velocity should be 1.0 m/s in its original direction. Which statement best describes this result?
2. Based on the scenario, how does the velocity vector change over time for a projectile under uniform gravity with no air resistance?
3. A disk of radius $2R$ rotates from rest about its center with a constant angular acceleration $\alpha$. Consider point A at radius $R$ and point B at radius $2R$. After a non-zero time $t$, what is the ratio of the magnitude of the total linear acceleration of point B to that of point A, $a_B / a_A$?
4. A simple pendulum consists of a bob of mass $m$ attached to a string of length $L$. The pendulum is pulled back to a maximum angle $\theta_{max}$ with the vertical and released from rest. What is the total mechanical energy of the pendulum-Earth system with respect to the lowest point of the swing?
5. Two cars, A and B, start at the same point. Car A travels north at a constant speed $v$. Car B starts from rest and accelerates east with a constant acceleration $a$. What is the velocity of car B relative to car A at time $t$?
6. Planet X has mass $M$ and radius $R$. Planet Y has mass $2M$ and radius $4R$. An object of mass $m$ is placed on the surface of each planet. What is the ratio of the gravitational force on the object on Planet Y to the force on the object on Planet X, $F_Y / F_X$?
7. The position of a particle moving in three-dimensional space is given by $\vec{r}(t) = (2t^2)\hat{i} + (\cos(\pi t))\hat{j} + (3t)\hat{k}$ in SI units. What is the speed of the particle at $t = 1$ s?
8. A skater of mass $60\,\text{kg}$ pushes on a rigid wall and accelerates away at $0.80\,\text{m/s}^2$ for $0.50\,\text{s}$. During the push, the wall exerts a horizontal force on the skater of $F_{\text{wall}\to \text{skater}}=4.8\times10^{1}\,\text{N}$ away from the wall. The skater's hands remain in contact with the wall only during this interval. What is the relationship between $\vec F_{\text{skater}\to \text{wall}}$ and $\vec F_{\text{wall}\to \text{skater}}$?
9. A particle starts from rest at the origin and moves along the x-axis with an acceleration $a_x(t) = C t^{1/2}$, where $C$ is a positive constant. Which of the following represents the particle's position $x(t)$ as a function of time?
10. The graph of angular velocity $\omega$ versus time $t$ for a rotating rigid body is a straight line with a positive slope, passing through the origin. What does this indicate about the body's motion?
11. An object starts from rest and experiences an acceleration given by $a(t) = A\cos(\frac{\pi}{2}t)$, where $A$ is a constant. What is the object's change in velocity during the time interval from $t=0$ to $t=1$ s?
12. A wheel starts from rest and rotates with constant angular acceleration $\alpha$. After rotating through an angle $\theta_1$, its angular velocity is $\omega_1$. After rotating through an additional angle $\theta_2$, its angular velocity becomes $\omega_2$. Which expression correctly relates these quantities?
13. A uniform solid sphere of mass $M$ and radius $R$ rolls without slipping down an inclined plane of angle $\theta$. At the bottom of the incline, it encounters a horizontal surface with coefficient of kinetic friction $\mu_k$. If the sphere was released from rest at height $h$ above the horizontal surface, what is the distance it travels on the horizontal surface before coming to rest?
14. An object is dropped from rest from a height $H$ and simultaneously another object is launched horizontally with an initial speed $v_0$ from the same height $H$. Which object reaches the horizontal ground first, assuming negligible air resistance?
15. Based on the scenario, how does the velocity vector change over time for uniform circular motion?
16. A yo-yo of mass $m$ is modeled as a solid cylinder of radius $R$ with a string wrapped around an inner axle of radius $r$. It is released from rest and falls as the string unwinds. The rotational inertia of the yo-yo is $I$. The tension in the string is $T$. Which pair of equations correctly describes its translational and rotational motion?
17. A hollow cylinder and a solid cylinder, both with the same mass $M$ and radius $R$, are released simultaneously from rest at the top of an inclined plane. Both roll without slipping. When the solid cylinder has traveled a distance $d$ down the incline, what distance has the hollow cylinder traveled?
18. A block of mass $m$ is dropped from a height $h$ above the top of a vertical spring with spring constant $k$. The block sticks to the spring and compresses it. Which equation must be solved to find the maximum compression $x$ of the spring?
19. A hockey puck slides on a sheet of frictionless ice at a constant speed of $10 \text{ m/s}$. What is the net force acting on the puck?
20. A heavy crate rests motionless on a horizontal floor. According to Newton's First Law, what can be concluded about the forces acting on the crate?

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