Question

What is the power done by gravity to make a ball of mass 0.25 kg roll from 5.5 m above the ground to the bottom along a curved path if it takes 4.34 s to do so?

Answer 1

Given,

The mass of the ball, m=0.25 kg

The height at which the ball was situated, h=5.5 m

The time it takes for the ball to reach the bottom of its path, t=4.34 s

The gravitational force is a conservative force and thus the work done by gravity does not depend on the path of the ball.

The work done by the gravity to bring the ball to the bottom is given by,

`W=\text{mgh}`

Where g is the acceleration due to gravity.

On substituting the known values,

`\begin{gathered} W=0.25*9.8*5.5 \\ =13.48\text{ J} \end{gathered}`

The power dissipated in bringing the ball to the bottom is given by,

`P=(W)/(t)`

On substituting the known values,

`\begin{gathered} P=(13.48)/(4.34) \\ =3.11\text{ W} \end{gathered}`

Therefore the power dissipated by gravity to bring the ball to the bottom of its path is 3.11 W.