Chapter 6, Problem 20Q

To determine

Why to avoid injury the instructor is supposed to release the ball without pushing it?

Answer to Problem 20Q

Solution:

If the ball is given an initial push, the work exerted by the instructor’s hands on the ball is transformed into initial kinetic energy, so when the ball returns to the instructor reaches a higher height, which causes the ball to impact in the instructor’s nose.

Explanation of Solution

Given:

A ball hanging from a steel wire is released at a height near the nose of the instructor.

When the ball is released by the instructor the total mechanical energy is conserved, that is; the ball is released from a certain height and when it returns, it is at the point where it was released it reaches the same initial height. What happens is that when the ball is released it does not have kinetic energy but if it has gravitational potential energy, as the ball descends the gravitational potential energy is gradually transformed into kinetic energy until it reaches the lowest point of the trajectory where the kinetic energy is maximum, and the gravitational potential energy is zero. Then the ball ascends, and the kinetic energy gradually transforms into gravitational potential energy until it reaches its maximum height, then the ball descends, and the energy is transformed in a similar way to its rise until it reaches the point from where it was released.