Question

A 1-kg ball is 10-m above a table when it is dropped. It bounces to a height of 7-m. a) How much energy is transferred to heat & sound during the bounce?b) Explain why this ball cannot bounce to a height of 12-m if it is dropped. c) What could you do to make the ball bounce to a height of 12-m?

Answer 1

Given,

The mass of the ball, m=1 kg

The initial height of the table, h₁=10 m

The height to which the ball bounces after being dropped, h₂=7 m

a)

From the law of conservation of energy total energy of a system should always remain the same. Thus the energy transferred to heat and sound during the bounce must be equal to the gravitational potential energy lost by the ball.

The gravitational potential energy lost by the ball is given by,

`\begin{gathered} E=mg\Delta h \\ =mg(h_2-h_1) \end{gathered}`

Where g is the acceleration due to gravity.

On substituting the known values,

`\begin{gathered} E=1*9.8*(7-10) \\ =-29.4\text{ J} \end{gathered}`

The negative sign indicates the energy was lost by the ball.

Thus the energy transferred to heat and sound during the bounce is 29.4 J

b)

The energy of the ball when it is at a heigh of 10 m is less than the energy when it is at the height of 12 m. And from the law of conservation of energy, energy can neither be created nor be destroyed. Thus the ball cannot possess higher energy than its initial energy unless some energy is supplied to it from an external source. Hence, the ball can not bounce to a height of 12 m.

c)

In order to make the ball bounce to a height of 12 m, we need to supply some energy to the ball. This can be done by placing a stretched spring under the ball so that the spring will transfer its potential energy to the ball. Or we can supply initial kinetic energy to the ball by throwing it instead of dropping it.