physics answers

Question

Consider a rubber ball whose bounce has an efficiency of 80%. That means 80% of the kinetic energy before the bounce remains kinetic energy after the bounce. (The rest of the energy is converted to thermal energy.)

How high does the ball bounce on the fourth bounce?

Answer 1

Let H = original height

Energy is GPE = MgH

On first bounce energy is 80% = 0.8( Mgh ) lost energy in the form of heat = 0.2Mgh

2nd bounce = 0.8² Mgh

3rd bounce = 0.8³ Mgh

4th bounce = 0.8 ⁴ Mgh = 0.4096 Mgh

let h = final height after 4th bounce

h = 0.4096 H = 0.4096 times original height from where it was dropped

rounding off h = 0.41 times original height

If original height was 1 m , it will go up to 41 cm after 4th bounce

Height after nth bounce = 0.8ⁿ times H