Question

A superball has a coefficient of restitution of .90. The ball is dropped from an intitial height of 1.60m.

a) if the ball is allowed to bounce 3 times, how high will it rebound after the third bounce?
b) If the ball has a mass of 48g, calculate the amount of the ball's orignal energy that was lost in the three impacts with the floor.

Answer 1

a

`H_3 = 0.85 \ m`

b

`PE = 0.3528 \ J`

Step-by-step explanation:

From the question we are told that

The coefficient of resolution is
`C_r = 0.90`

The initial height is
`H_i = 1.60 \ m`

Considering question a

The number of times the ball bounced is
`k = 3`

Generally the height attained after the 3rd bounce is mathematically represented as

`H_3 = H_i * (C_r)^(2 * k )`

=>
`H_3 = 1.60 * 0.90^(2 * 3 )`

=>
`H_3 = 0.85 \ m`

Considering question b

The mass is m = 48 g = 0.048 kg

Generally the amount of potential energy that was lost is mathematically represented as

`PE = mg [ H_i - H_3 ]`

=>
`PE = 0.048 * 9.8 [1.60 - 0.85 ]`

=>
`PE = 0.3528 \ J`