Question

An object slides down an inclined plane from an initial height of 30 meters.Its velocity at the foot of the plane is 20m/s.
The percentage of its initial potential energy which is deposited as heat is?

Answer 1

The initial potential energy

$$PE_i=mgh$$

The final kinetic energy

$$KE_f =\frac{mv^2}{2}$$

The heat losses

$$Q=PE_i-KE_f=mgh\left(1-\frac{v^2}{2gh}\right)$$

Hence, the percentage of its initial potential energy which is deposited as heat

$$\frac{Q}{PE_i}=1-\frac{v^2}{2gh}=1-\frac{20^2}{2\times 9.8\times 30}=0.32=32\%$$