Question

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.

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

True:
- The potential energy at the top of the ball’s motion is 18 J.
(At the top the speed is zero, so all the mechanical energy is potential: Utop = Etotal = 18 J.)
- The kinetic energy increases as the potential energy decreases.
(As the ball falls, gravitational potential energy is converted into kinetic energy.)
- The kinetic energy decreases as the potential energy increases.
(As the ball rises, kinetic energy is converted into gravitational potential energy.)
- The total mechanical energy of the ball stays constant.
(No nonconservative forces act, so mechanical energy is conserved at 18 J.)

False:
- The kinetic energy is less when the ball is thrown than when it is caught.
(Thrown and caught at the same height with no losses → speeds and kinetic energies are the same.)
- The mechanical energy decreases as the ball moves up and increases as the ball comes down.
(Mechanical energy remains constant; it merely shifts between K and U.)