Box 1 is in contact with the ground and Box 2 on top of Box 1. Boxes 1 and 2 are initially at rest, as shown in Figure 1. An external force is then exerted on Box 1. Figure 2 shows the free-body diagram for Box 2 while the external force is exerted on Box 1. The forces exerted on Box 1 are not shown. Which of the following could describe the motion of the boxes?

Three forces are exerted on an object in equilibrium, as shown. The magnitudes of $$F_1$$ and $$F_2$$ and the angle $$\theta$$ can be changed. The magnitude of $$F_3$$ remains constant. Which of the following changes, if any, to $$F_1$$ and $$F_2$$ would keep the object in equilibrium as $$\theta$$ increases to $$90^\circ$$?

The graph shows the velocity as a function of time for an object moving along the x-axis. Which of the following equations could correctly represent the motion of the object?

A block is pushed from rest by a force of magnitude $$F$$ a distance $$L$$ along an inclined ramp, as shown in Figure 1. The block leaves the end of the ramp and reaches the ground to the right of the ramp with speed $$v_1$$.

The ramp is now raised to a greater angle with the horizontal, and the block is again pushed from rest by a force of magnitude $$F$$ a distance $$L$$, as shown in Figure 2. The block leaves the end of the ramp and reaches the ground to the right of the ramp with speed $$v_2$$. Frictional forces are negligible. Which of the following correctly compares $$v_1$$ and $$v_2$$?

A disk of mass $$M$$ and radius $$R$$ is rotating clockwise about its center. At time $$t = t_0$$, the disk has angular momentum $$L_0$$ and a force is applied tangent to the edge of the disk, as shown in the top view. The magnitude of the force is modeled by $$F(t) = At^2$$, where $$A$$ is a positive constant with appropriate units. What is the magnitude of the angular momentum of the disk at a later time $$t = t_1$$?

A block of mass $$m_0$$ is in contact with the inner wall of a hollow cylinder and does not slip as the cylinder rotates with angular speed $$\omega_0$$, as shown. The minimum coefficient of static friction necessary to prevent the block from slipping is $$\mu_0$$. What minimum coefficient of static friction $$\mu$$ is necessary to prevent a block of mass $$2m_0$$ from slipping when the cylinder rotates with angular speed $$2\omega_0$$?

Three blocks of masses $$M$$, $$2M$$, and $$3M$$ are connected by strings across two pulleys, as shown. The strings and pulleys have negligible mass. The $$2M$$ block is at rest on a rough horizontal surface. The coefficient of kinetic friction between the $$2M$$ block and the surface is $$\mu$$. The blocks are released from rest and then accelerate. Which of the following equations represents the acceleration $$a$$ of the blocks?

Uniform bars Q, R, and S, each of mass $$M$$ and length $$L$$, can rotate with negligible friction about the fixed pivot points shown in the figure. At time $$t = t_0$$, a force of magnitude $$F$$ is exerted on each bar at the angle and point of contact shown. The torques exerted on the bars Q, R, and S are $$\tau_Q$$, $$\tau_R$$, and $$\tau_S$$, respectively. The angular accelerations of bars Q, R, and S are $$\alpha_Q$$, $$\alpha_R$$, and $$\alpha_S$$, respectively. Which of the following correctly ranks the magnitudes of these quantities at $$t = t_0$$?

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Satellite 1 is at the position shown in Figure 1 while traveling in a circular orbit of radius $$r$$ around a planet. The velocity and acceleration of Satellite 1 are represented by the vectors $$\boldsymbol{v}_1$$ and $$\boldsymbol{a}_1$$, respectively, shown in Figure 2. Satellite 2 is in a circular orbit around the same planet with velocity and acceleration vectors $$\boldsymbol{v}_2$$ and $$\boldsymbol{a}_2$$, respectively. Which of the following shows a correct pair of orbital and vector diagrams for Satellite 2?

The table shows the position of an object on an xy-coordinate plane at each second during the time interval $$0 \leq t \leq 4$$ s. Which of the following is a correct claim about the x- or y-component of the object's acceleration, $$a_x$$ or $$a_y$$, respectively, and provides correct justification using the object's position?

Blocks A, B, and C with masses 1.0 kg, 3.0 kg, and 2.0 kg, respectively, are on a level floor. There is negligible friction between the blocks and the floor. Block A moves at +8.0 m/s, while blocks B and C are at rest, as shown in Figure 1. Block A collides with and sticks to Block B. Blocks A and B then collide with but do not stick to Block C. After the collision, Block C moves at +2.0 m/s, as shown in Figure 2. What is the velocity of blocks A and B after they collide with Block C?

An ideal spring-block system oscillates in one-dimensional motion. A motion sensor records the velocity $$v$$ of the block as a function of time $$t$$, as shown. Which of the following graphs best illustrates how the velocity $$v$$ of the block varies as a function of position $$x$$?

Cart A of mass $$m_A$$ moves with an initial velocity $$v_A$$ and then collides elastically with Cart B. The velocity of Cart A as a function of time is shown in the graph. Which of the following correctly describes the mass and initial velocity of Cart B, $$m_B$$ and $$v_B$$, respectively?

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