Rita throws a ball straight up into the air and catches it at the same position from which she threw it. The ball has 18 J of mechanical energy when it leaves her hand.

Question

If no energy is lost due to friction, which statements about the energy of the ball are true? Check all that apply.

The potential energy at the top of the ball’s motion is 18 J.
The kinetic energy is less when the ball is thrown than when it is caught.
The kinetic energy increases as the potential energy decreases.
The kinetic energy decreases as the potential energy increases.
The total mechanical energy of the ball stays constant.
The mechanical energy decreases as the ball moves up and increases as the ball comes down.

Answer 1

Based on the situation described, where Rita throws a ball straight up and catches it back at the starting position with no energy loss due to friction, we can analyze the statements regarding the energy of the ball. Here are the statements evaluated for truth:

1. The potential energy at the top of the ball’s motion is 18 J.
   True. At the top of the motion, all the mechanical energy is converted into potential energy (since the kinetic energy is zero at that point). Therefore, the potential energy at the top is 18 J.

2. The kinetic energy is less when the ball is thrown than when it is caught.
   False. When the ball is thrown, it has maximum kinetic energy and zero potential energy. When it's caught, it again has maximum kinetic energy and zero potential energy (because it returns to the original position). The kinetic energy when thrown equals the kinetic energy when caught, which is 18 J in total mechanical energy.

3. The kinetic energy increases as the potential energy decreases.
   True. As the ball rises, potential energy increases and kinetic energy decreases. Conversely, as it falls, kinetic energy increases and potential energy decreases.

4. The kinetic energy decreases as the potential energy increases.
   True. This statement describes the behavior of the ball while it is going up. As it rises, potential energy increases while kinetic energy decreases.

5. The total mechanical energy of the ball stays constant.
   True. Since no energy is lost to friction or other non-conservative forces, the total mechanical energy remains constant at 18 J throughout the motion.

6. The mechanical energy decreases as the ball moves up and increases as the ball comes down.
   False. The mechanical energy remains constant throughout the motion; it does not decrease or increase.

Summary of True Statements:

• The potential energy at the top of the ball’s motion is 18 J.
• The kinetic energy increases as the potential energy decreases.
• The kinetic energy decreases as the potential energy increases.
• The total mechanical energy of the ball stays constant.