Answer to Question #112424 in Field Theory for Ayuba haruna

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

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