Question

A tennis ball is released from a height of 4.0 m above the floor. After its third bounce off the floor, it reaches a height of 183 cm. What percentage of its mechanical energy does it lose with each bounce?
23%

27%

20%

15%

Answer 1

Answer:

The percentage of its mechanical energy does the ball lose with each bounce is 23 %

Explanation:

Given data,

The tennis ball is released from the height, h = 4 m

After the third bounce it reaches height, h' = 183 cm

                                                                       = 1.83 m

The total mechanical energy of the ball is equal to its maximum P.E

                                      E = mgh

                                          = 4 mg

At height h', the P.E becomes

                                      E' = mgh'

                                           = 1.83 mg

The percentage of change in energy the ball retains to its original energy,

                                 $\Delta E\%=\frac{1.83mg}{4mg}\times100\%$

                                  ΔE % = 45 %

The ball retains only the 45% of its original energy after 3 bounces.

Therefore, the energy retains in each bounce is

                                   ∛ (0.45) = 0.77

The ball retains only the 77% of its original energy.

The energy lost to the floor is,

                                E = 100 - 77

                                   = 23 %

Hence, the percentage of its mechanical energy does the ball lose with each bounce is 23 %