Irving, a cat, has a favorite toy that is made up of a squeaky ball at the end of a string. The toy makes up a closed system. Irving’s owner dangles the toy so that the ball swings down and then swings back up again.

Question

Ignoring any friction, how are kinetic and potential energy related to each other as the ball swings back and forth?

As the ball moves upward, both kinetic and potential energy decrease.
As the ball moves downward, both kinetic and potential energy increase.
As the ball moves upward, kinetic energy decreases and potential energy increases.
As the ball moves downward, kinetic energy decreases and potential energy increases.

Answer 1

In the scenario described, as the ball swings back and forth in a closed system, the relationship between kinetic energy and potential energy can be understood in terms of their conversion from one form to the other.

When the ball is at its highest point (the top of its swing), it has maximum potential energy and minimum kinetic energy. As the ball swings downward, it loses potential energy and converts that energy into kinetic energy, increasing its speed.

Conversely, as the ball moves upward again, it gains potential energy (height) but loses kinetic energy (speed).

Based on this understanding, the correct relationships between kinetic and potential energy as the ball swings are:

• As the ball moves upward, kinetic energy decreases and potential energy increases.
• As the ball moves downward, kinetic energy increases and potential energy decreases.

Thus, the correct answer from the choices given is:

As the ball moves upward, kinetic energy decreases and potential energy increases.