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Chapter 6: Problem 82

Which of the following is greatest at the peak of the curve? a. the ball's kinetic energy b. the ball's speed c. the rate at which the bat supplies energy to the ball d. the total work the bat has done on the ball

Short Answer

Expert verified
The correct answer is d. The total work the bat has done on the ball is greatest at the peak of the curve.

Step by step solution

01

Understand the Kinetic Energy

The kinetic energy of the ball is given by the formula \(KE = 1/2 mv^2\), where \(m\) is the mass and \(v\) is velocity. At the peak of the curve, the ball's velocity \(v\) is zero. Therefore, the ball's kinetic energy at the peak is also zero.
02

Understand the Speed

Speed is the magnitude of velocity. At the peak of the curve, the ball is momentarily stationary. Therefore, the ball's speed is also zero at the peak.
03

Understand the Rate of Energy Supply

The rate at which the bat supplies energy to the ball ceases as soon as the ball loses contact with the bat. This happens before the ball reaches the peak of its trajectory. Therefore, at the peak, the rate at which the bat supplies energy to the ball is zero.
04

Understand the Total Work Done

The bat does work to the ball while it is in contact. This work translates to the energy of the ball (both kinetic and potential). After the bat loses contact, no additional work is done on the ball. Therefore, the total work the bat has done on the ball is at its greatest at the peak, as no more work will be added afterwards.

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