5.3 and 5.4 Check

Cart X travels in the positive direction along a horizontal surface, and cart Y travels in the positive direction. The carts collide, and a student collects data about the carts’ velocities as a function of time before, during, and after a collision, as shown. The masses of both objects are known. Which of the following best indicates how the student should use the graph to determine whether the collision is elastic or inelastic and provides a correct justification?

• Using the known mass and known velocity for each cart to determine the kinetic energy of the system before and after the collision, because the kinetic energy changes in an inelastic collision

• Using the known mass and known velocity for each cart to determine the momentum before and after the collision, because the momentum changes in an inelastic collision

• Using the known mass and known velocity for each cart to determine the change in momentum for each object before and after the collision, because the momentum changes in an elastic collision

• Using the known mass and known velocity for each cart to determine the average force exerted on each object before and after the collision, because the forces exerted on the objects have different magnitudes in an inelastic collision

Answer explanation

A collision is classified as elastic or inelastic because of the change in kinetic energy of the system before and after the collision. If the collision is elastic, the kinetic energy of the system should not change from before the collision to after the collision. If the collision is inelastic, there should be a change in the kinetic energy of the system from before the collision to after the collision.

A student must conduct an experiment to verify the conservation of momentum. Cart X and Cart Y travel toward each other and eventually collide, as shown in the figure. The student has access to the two carts, one mass balance, and two motion detectors. If the mass of each cart is known, how should the student arrange one or both motion detectors so that the student can collect enough information about the motion of the carts, in order to verify the conservation of momentum of the system?

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Answer explanation

To verify the conservation of momentum, the momentum of the system before the collision should be the same as the momentum of the system after the collision. Therefore, a student must measure the initial velocities of Cart X and Cart Y and the final velocities of Cart X and Cart Y. This combination of motion detectors and their positions will allow for the velocities of each object to be measured before, during, and after the collision.

Block X of mass 2kg travels across a horizontal surface toward block Y of unknown mass that is initially at rest. Block X then collides elastically with block Y. A graph of the position as a function of time for block X is shown. Block X and block Y are made of the same material. Which of the following predictions is correct about the motion of block Y immediately after the collision?

• The acceleration of block Y immediately after the collision is greater than the acceleration of block Y immediately before the collision.

• The kinetic energy of block Y immediately after the collision is greater than the kinetic energy of block X immediately after the collision.

• The magnitude of the change in momentum of block Y from immediately before the collision to immediately after the collision is more than the magnitude of the change in momentum of block X .

• The momentum of the system consisting of block X and block Y immediately after the collision is less than the momentum of the system immediately before the collision.

Answer explanation

The slope of the position versus time graph for block X can be used to determine the speed of block X immediately before the collision and immediately after the collision. The kinetic energy of block X immediately before the collision can be determined by the following calculations.

K0=1/2mv0^2

K0=1/2(2kg)(3m/s)^2

K0=9J

The kinetic energy of block X immediately after the collision can be determined by the following calculations.

Kf=1/2mv0^2

Kf=1/2(2kg)(1m/s)^2

Kf=1J

Since the collision is considered to be elastic, the kinetic energy of block Y must be 8J, because the mechanical energy of the block X-block Y system is conserved.

Answer explanation

The impulse FΔt equals the change in momentum Δp.

A student must perform an experiment in which two objects travel toward each other and collide so that the data collected can be used to show that the collision is elastic within the acceptable range of experimental uncertainty. Which of the following measuring tools, when used together, can the student use to verify that the collision is elastic? Select two answers.

• A motion detector

• A meterstick

• A balance

• A stopwatch

Answer explanation

For an elastic collision of two objects, Σp0=Σpf, where p =mv for each object. Motion detectors can be used to determine the speed of each before and after the collision.

A balance can be used to determine the mass of each object.

• Linear momentum of the clay-block system

• Angular momentum of the clay-block system about the top of the string

• Total mechanical energy of the clay-block system

• Total mechanical energy of the clay-block-Earth system

Answer explanation

After the collision, the block-clay object moves as a pendulum. There is no external force acting on the system, so the total mechanical energy stays the same.

Block X slides along a horizontal surface with a speed vX toward block Y that is initially at rest, as shown in Figure 1. After block X collides with block Y, the two blocks remain stuck together and travel at a velocity of vXY, as shown in Figure 2. Frictional forces are considered to be negligible. Which of the following claims is correct regarding the momentum of the system containing only block X and the system that contains block X and block Y?

• The system containing block X is an open system, and the system of both blocks is an open system.

• The system containing block X is an open system, and the system of both blocks is a closed system.

• The system containing block X is a closed system, and the system of both blocks is an open system.

• The system containing block XX is a closed system, and the system of both blocks is a closed system.

Answer explanation

The momentum of block X changes in the collision as some of its momentum is transferred to block Y . Therefore, the system of block X is open in terms of momentum. However, because no external forces are exerted on the system of block X and block Y, the system is considered to be closed because its momentum is conserved.

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?

• The kinetic energies of the two people are equal.

• The speeds of the two people are equal.

• The momenta of the two people are of equal magnitude.

• The center of mass of the two-person system moves in the direction of the less massive person.

• The less massive person has a smaller initial acceleration than the more massive person.

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?

• 1 m/s north

• 1 m/s south

• 3 m/s south

• 7 m/s south

• 17 m/s south

An experiment is performed in which a collision occurs between cart X and cart Y. Data are collected about each cart before and after a collision takes place. Which data from the table should the student use to verify the conservation of momentum for each trial, and what is a justification for using those data?

• The initial and final velocity of cart X and the initial and final velocity of cart Y, because the speeds should be compared before and after the collision.

• The mass of cart X, the initial velocity of cart X, and the final velocity of cart X, because the momentum of cart X should be determined before and after the collision.

• The mass of cart Y, the initial velocity of cart Y, and the final velocity of cart Y, because the momentum of cart Y should be determined before and after the collision.

• All data are necessary to verify the conservation of momentum, because all information for each cart should be known.

Answer explanation

All columns of data are necessary to verify the conservation of momentum. To verify the conservation of momentum for each trial, multiply the mass of each cart by the respective cart’s initial velocity and final velocity. Compare the total momentum of the two-cart system before the collision to the total momentum of the system after the collision.