# A 200 gram ball gets dropped from a roof at 15 meters high. A boy on the ground catches it. If 10...

## Question:

A 200-gram ball gets dropped from a roof at 15 meters high. A boy on the ground catches it. If 10 percent is translated to internal energy, then what was the increase of internal energy?

## Motion in a Gravitational Field:

When an object moves freely under gravity it possesses two types of energy, kinetic and potential. The gravitational field is a conservative field. Hence the sum total of the kinetic and potential energies will be conserved. When an object is released from a height its gravitational potential energy decreases while the kinetic energy increases. Thus during the motion energy gets transformed from one form to another.

A ball of mass {eq}\displaystyle { m=200 \ g = 0.2 \ kg } {/eq} is dropped from a roof at a height {eq}\displaystyle {h=15 \ m } {/eq} from the ground.

Initially, the ball possesses gravitational potential energy: {eq}\displaystyle {PE=mgh} {/eq}, where {eq}\displaystyle {g=9.8 \ m/s^2} {/eq} is the acceleration due to gravity.

That is {eq}\displaystyle {PE= 0.2 \times 9.8 \times 15 =29.4 \ J } {/eq}

As the ball falls from the given height, it loses potential energy. The energy now reappears as its kinetic energy.

Just as the ball reaches the boy's hands standing on the ground its energy is entirely kinetic and equals its initial potential energy, 29.4 J.

Given that 10% of this energy is translated to the internal energy of the ball possibly as heat.

Then the increase in its internal energy is: {eq}\displaystyle {0.1 \times 29.4 =2.94 \ J } {/eq}