Chapter 6, Problem 21Q

To determine

Describe the energy transformations when a child hops around on a pogo stick.

Answer to Problem 21Q

Solution:

The initial elastic potential energy that has been acquired by the work done by the child with his body on the pogo stick is gradually transformed into kinetic energy and gravitational potential energy when it rises. At the highest point of its elevation, its elastic potential energy and its kinetic energy are zero while its gravitational potential energy is maximum. Then in the descent that gravitational potential energy is gradually transformed into kinetic energy and then into elastic potential energy until it becomes maximum, where the kinetic energy is zero as well as its gravitational potential energy.

Explanation of Solution

Given:

A child hops on a pogo stick (there is a spring inside)

Initially, the child mounted on the pogo stick jumps exercising a bodywork on the toy. This work is transformed into an increase in the elastic potential energy of the pogo stick spring, this energy is gradually transformed into an increase in kinetic energy and gravitational potential energy, therefore, the child rises to a certain height. Once the child reaches his highest point he has maximum gravitational potential energy, zero kinetic energy and zero elastic potential energy. Then when it falls its gravitational potential energy is gradually transformed into kinetic energy until, when it reaches the point at which the spring begins to compress, it increases its elastic potential energy until it reaches a maximum compression (maximum elastic potential energy)with zero gravitational potential energy and zero kinetic energy. Then the child begins to rise again, repeating the cycle again.