A dog of mass 10 kg sits on a skateboard of mass 2 kg that is initially traveling south at 2 m/s. The dog jumps off with a velocity of 1 m/s north relative to the ground. Which of the following is the best estimate of the velocity of the skateboard immediately after the dog has jumped?

If the translational velocity of an carousel horse is 3 m/s, and is located a distance of 2 m from the axis of rotation, what is the horse's angular velocity?

A student conducts an experiment to verify that a collision is elastic. The two identical cubes involved, object X and object Y, travel toward each other at the same initial speed. Which of the following equations should the student consider using to verify that the collision is elastic, and why?

A student must conduct an experiment to verify the conservation of momentum for a closed two-cart system. Cart X and cart Y travel toward each other and eventually collide. The student has determined the following procedure.
Step 1: Measure the mass of cart X and cart Y with a balance.
Step 2: Use a motion sensor to record data of the velocity of each cart before, during, and after the collision.
Step 3: Use the data and  $\sum_{\ }^{\ }p_f=\sum_{\ }^{\ }p_0$  to determine if the right-hand side of the equation is equal to the left-hand side of the equation.
Which of the following steps should the student add to the procedure so that the conservation of momentum can be experimentally verified?

An object of mass m attached to a spring with constant k oscillates with amplitude A. Assuming air resistance and the mass of the spring to be negligible, which of the following changes alone would cause the period of this oscillation to increase?

I. Increasing m

II. Increasing A

III. Using a spring with greater k

Two people of unequal mass are initially standing still on ice with negligible friction. They then simultaneously push each other horizontally. Afterward, which of the following is true?

A student is observing an object of unknown mass that is oscillating horizontally at the end of an ideal spring. The student measures the object’s period of oscillation with a stopwatch.

While the object is continuously oscillating, the student determines the maximum speed of the object during two oscillations. The first speed is 3.5 m / s and the second speed is 2.7 m / s. Which of the following could account for the decrease in the object’s maximum kinetic energy?

Object X of mass 4 kg travels with a speed of 3 m/s toward object Y of mass 2 kg that is initially at rest. Object X then collides with and sticks to object Y. After the collision, object X and object Y remain stuck together as they move. By how much does the kinetic energy of this system change, if at all?

A sphere of mass m1, which is attached to a spring, is displaced downward from its equilibrium position as shown above left and released from rest. A sphere of mass m2, which is suspended from a string of length l is displaced to the right as shown above right and released from rest so that it swings as a simple pendulum with small amplitude. Assume that both spheres undergo simple harmonic motion.

Which of the following is true for both spheres?

A block of mass 2.0kg on a horizontal surface is attached to a horizontal spring of negligible mass and spring constant 100N/m. The other end of the spring is attached to a wall, and there is negligible friction between the block and the horizontal surface. When the spring is unstretched, the block is located at x=0 m. The block is then pulled to x=0.5 m and released from rest so that the block-spring system oscillates between x=−0.5 m and x=0.5 m, as shown in the figure. Which of the following predictions is correct regarding the energy of the system?

A group of students must study the oscillatory motion of a pendulum. One end of a light string is attached to the ceiling, and the other end of the string is attached to a mass hanger so that small disks of various masses may be stacked on the hanger, as shown in the figure.

Students are provided with data in which an experiment was conducted to determine the relationship between the length of the pendulum and the period of oscillation. The data include a pendulum of length 0.5m, for which it took 81 s for the pendulum bob to oscillate 10 times. However, the experiment was conducted at a location that is not near Earth’s surface. The gravitational field strength where the experiment was conducted is most nearly...?

Three different experiments are conducted that pertain to the oscillatory motion of a pendulum. For each experiment, the length of the pendulum and the mass of the pendulum are indicated. In all experiments, the pendulum is released from the same angle with respect to the vertical.

If the students collect data about the kinetic energy of the pendulum as a function of time for each experiment, which of the following claims is true?

A pendulum has a length l and a bob of mass m. Which of the following is true of the linear momentum of the bob as it swings from its highest to lowest point?

A student must determine how the mass of a block affects the period of oscillation when the block is attached to a vertical spring. The value of the spring constant is known. The student writes the following experimental procedure.

1) Use an electronic balance to measure the mass of the block.

2) Attach the block to the vertical spring.

3) Displace the block from the system’s equilibrium position to a new vertical position.

4) Release the block from rest.

5) Use a meterstick to measure the vertical displacement of the center of mass of the block from the system’s equilibrium position to its maximum vertical position above the equilibrium position.

6) Use a stopwatch to measure the time it takes for the system to make ten complete oscillations.

7) Repeat the experiment for different vertical displacements and block masses.

Which of the steps of the procedure should the student revise to determine the effect of mass on oscillation period? Justify your selection.