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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/s2)?


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Solution

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/s2.

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,

U=mghorU=50×9.8×100orU=49000JorU=49000JorU=49kJ

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


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