Question

A non-ideal 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

a) The initial energy of the ball is (potential energy):

$$E_1 = mgh_1$$

where $m = 1kg$ is the mass of the ball, $g = 9.8N/kg$ is the gravitational acceleration, and $h_1 = 10m$ is the initial height.

The energy of the ball after it bounces to a height of $h_2 = 7m$ is:

$$E_2 = mgh_2$$

The amount of energy loss is:

$$Q = E_1 - E_2 = mg(h_1 - h_2)\\ Q = 1\cdot 9.8\cdot (10-7) = 29.4J$$

b) According to the energy conservation law, the ball can not gain extra energy from nothing to bounce to a height of 12-m. It can only bounce not higher then initial 10 m.

c) We can give extra energy to the ball. For example, not releasing it at the beginning, but throwing it downward.