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$\left(g=9.8m/{s}^{2}\right)$?

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Solution

## Step 1: Given dataMass of the boy is $m=50kg.$The boy climbs up at a height $h=100m$.acceleration due to gravity is $g=9.8m/{s}^{2}$.Step 2: Gravitational potential energyThe 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.So, gain in potential energy = work done by the boy.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,$U=mgh\phantom{\rule{0ex}{0ex}}orU=50×9.8×100\phantom{\rule{0ex}{0ex}}orU=49000J\phantom{\rule{0ex}{0ex}}orU=49000J\phantom{\rule{0ex}{0ex}}orU=49kJ$Therefore, the gain in potential (work done) energy is $49KJ$ joule.

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