Question

A boy weighing $50kg$ climbs up a vertical height of $100m$. Calculate the amount of work done by him. How much potential energy does he gain$(g=9.8m/s^2)$?

Answer 1

Step 1: Given data

1. Mass of the boy is $m=50kg.$
2. The boy climbs up at a height $h=100m$.
3. acceleration due to gravity is $g=9.8m/s^2$.

Step 2: Gravitational potential energy

1. The gravitational potential energy at any point in a gravitational field of a system of masses is the amount of work done in bringing a unit mass from infinity to that point.
2. So, gain in potential energy = work done by the boy.
3. Gravitational potential energy due to a point mass m at a height h is,$U=mgh$, where g is the acceleration due to gravity, m is the mass of the body and h is the height of the body.

Step 3: Finding the work done (gain in potential energy)

The gravitational potential energy of the boy at a height of $100$ meters is,

$$\begin{gathered} U=mgh \\ orU=50\times 9.8\times 100 \\ orU=49000J \\ orU=49000J \\ orU=49kJ \end{gathered}$$

Therefore, the gain in potential (work done) energy is $49KJ$ joule.