physics question

Question

A 2.5 kg rubber ball is dropped from rest 5.0 m above ground. Upon its rebound, the ball only reaches a height of 4.0 m. How much energy was dissipated during the bounce? Please ignore losses due to air resistance.

a) 25 J

b) 5.0 J

c) 50 J

Answer 1

Hi Ana,

To solve this question, we will rely on the following equation for potential energy:

Ep=m*g*h

where m is the mass, g is gravity (I'll assume gravity as 9.81 m/s^2) and h is height

when we start, the ball is not moving, so its total energy can be found from the equation provided above.

Ep1=2.5*9.81*5

Then, the ball bounces off the floor, and transfers some of its energy into the ground. The energy it has left only allows it to reach a height of 4 meters. using the same equation with the new height:

Ep2=2.5*9.81*4

we will get a new potential. The difference between the two is the energy lost to the ground (Ep1-Ep2)

Answer 2

The energy lost would be the difference when the balls are at rest at the highest point (potential energy)

So, that would be

mg(h₂-h₁) = (2.5 kg)(9.8 m/s²)(5-4 m) = 24.5 Kg-m²/s² = 24.5 J