Question

A boy weighing $25kg$ climbs up from the first floor at a height of $3m$ above the ground to the third floor at a height of $9m$ above the ground. What will be the increase in his gravitational potential energy? (Take $g=10Nk{g}^{-1}$)

Answer 1

Step 1: Given data

1. Mass of the boy is $m=25kg.$
2. The boy climbs up from the 1st floor at a height of $3m$ to the third floor of height $9m$.
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. 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 increase of potential energy

The gravitational potential energy of the boy at a height of $3m$ (first floor) is,

$$\begin{gathered} U_3=mgh=25\times 10\times 3 \\ or{U}_3=750joule...............\left(1\right) \end{gathered}$$

Again, the gravitational potential energy of the boy at a height of $9m$ (third floor) is,

$$\begin{gathered} U_9=mgh=25\times 10\times 9 \\ or{U}_9=2250joule...............\left(2\right) \end{gathered}$$

So, the increase in gravitational potential energy is,

$$\begin{gathered} ∆U=U_9-U_3=2250-750 \\ or∆U=1500joule \end{gathered}$$

Therefore, the increase in his gravitational potential energy is $1500J$.