Is energy conserved???

Question

A 0.10-kg ball is dropped from a height of 10 m and rebounds to a height of 8.0 m.

 

a.) Is energy conserved in the ball?

 

b.) If not, how much energy was lost, and what happened to it?

Answer 1

When energy is conserved, the sum of all of the energies is zero.

 

KE + PE = 0

 

KE = -PE

 

The negative sign initiates loss of energy.

 

KE = (1/2)mv²        and      PE = mgh

 

where:

m = mass

v = velocity

g = acceleration due to gravity = 9.81 m/s²

h = height

 

We will only need to find PE. We will calculate this twice since there is a rebound.

 

PE = (0.10 kg)(9.81 m/s²)(10 m)

     = 9.81 joules

 

PE = (0.10 kg)(9.81 m/s²)(8 m)

     = 7.85 joules

 

The two values of PE are not the same.  Therefore, energy is not conserved.  To find how much energy was lost, subtract the two values of PE.

 

9.81 joules - 7.85 joules = 1.8 joules

 

 1.96 joules was lost.  Since this is potential energy, 1.96 joules was transferred to kinetic energy.