Question

practice it!
the diagram shown shows a ball as it continually swings back and forth on a string.
select the statement(s) that are true about the diagram.

• point c has both potential and kinetic energy.
• point d has a large amount of potential energy and has a small amount of kinetic energy.
• point b has the most amount of kinetic energy and the least amount of potential energy.
• point b has the largest amount of potential energy and the least amount of kinetic energy.
• point a has no kinetic energy and the most amount of potential energy.

Explanation:

To determine the true statements, we analyze the energy (potential and kinetic) of the swinging ball:

1. Analyze Point C

• At Point C, the ball is moving (so has kinetic energy) and is above the lowest point (so has potential energy). Thus, “Point C has both potential and kinetic energy” is true.

2. Analyze Point D

• Point D is at a relatively high height (so large potential energy) but is moving slowly (since it is near the peak of its swing), so it has a small amount of kinetic energy. Thus, “Point D has a large amount of potential energy and has a small amount of kinetic energy” is true.

3. Analyze Point B

• Point B is the lowest point of the swing. At the lowest point, the ball’s height is minimum (so least potential energy) and its speed is maximum (so most kinetic energy). Thus:
• “Point B has the most amount of kinetic energy and the least amount of potential energy” is true.
• “Point B has the largest amount of potential energy and the least amount of kinetic energy” is false (contradicts the above).

4. Analyze Point A

• Point A is at a high height (so most potential energy) and is momentarily at rest (at the peak of its swing), so it has no kinetic energy. Thus, “Point A has no kinetic energy and the most amount of potential energy” is true.

True Statements:

• Point C has both potential and kinetic energy.
• Point D has a large amount of potential energy and has a small amount of kinetic energy.
• Point B has the most amount of kinetic energy and the least amount of potential energy.
• Point A has no kinetic energy and the most amount of potential energy.

(Note: The statement “Point B has the largest amount of potential energy and the least amount of kinetic energy” is false, as explained.)

Answer:

To determine the true statements, we analyze the energy (potential and kinetic) of the swinging ball:

1. Analyze Point C

• At Point C, the ball is moving (so has kinetic energy) and is above the lowest point (so has potential energy). Thus, “Point C has both potential and kinetic energy” is true.

2. Analyze Point D

• Point D is at a relatively high height (so large potential energy) but is moving slowly (since it is near the peak of its swing), so it has a small amount of kinetic energy. Thus, “Point D has a large amount of potential energy and has a small amount of kinetic energy” is true.

3. Analyze Point B

• Point B is the lowest point of the swing. At the lowest point, the ball’s height is minimum (so least potential energy) and its speed is maximum (so most kinetic energy). Thus:
• “Point B has the most amount of kinetic energy and the least amount of potential energy” is true.
• “Point B has the largest amount of potential energy and the least amount of kinetic energy” is false (contradicts the above).

4. Analyze Point A

• Point A is at a high height (so most potential energy) and is momentarily at rest (at the peak of its swing), so it has no kinetic energy. Thus, “Point A has no kinetic energy and the most amount of potential energy” is true.

True Statements:

• Point C has both potential and kinetic energy.
• Point D has a large amount of potential energy and has a small amount of kinetic energy.
• Point B has the most amount of kinetic energy and the least amount of potential energy.
• Point A has no kinetic energy and the most amount of potential energy.

(Note: The statement “Point B has the largest amount of potential energy and the least amount of kinetic energy” is false, as explained.)