Question

A man of mass 50 kg climbs up a ladder of height 10m. calculate the increase in his potential energy. ($g=9.8m{{s}^{-2}}$ )
a) 490J
b) 2450J
c) 4900J
d) 0J

Answer 1

The increase in the potential energy of the man is basically the work done by him to overcome the Earth’s gravitational force. The work done on a body is mathematically defined as, $W=F.d$ where F is the force on the body and d is the displacement of the body along the action of force. Hence from the above equation we can calculate the increase in the potential energy i.e. work done in moving up to a height of 10m against the gravitational force on the man.

Complete step by step answer:

The force of gravity is equal to the, ${{F}_{g}}=mg$ where m is the mass of the object and g is the acceleration due to gravity. In the above question a man climbs a ladder and goes up to a height of H as shown in the diagram. Hence work done by him is equals to,
$\begin{aligned} & W=F.d \\\ & W=mgH \\\ \end{aligned}$
Let us say the man goes from height h to a height H on the ladder. Hence its increase in potential energy (E)from the above equation we get,
$E=mgH-mgh$ Let us say the man started climbing from the ground i.e. h=0. Hence we get the increase in potential energy as,
$E=mgH$. The mass of the man is 50kg and climbs up to a height of 10m from the ground. Therefore the potential energy of the man is numerically equal to,
$\begin{aligned} & E=mgH \\\ & E=50\times 9.8\times 10 \\\ & E=4900J \\\ \end{aligned}$
Hence the correct answer to the above question is option C.

Note:
The expression we obtained for the increase in potential energy is valid up to a particular height. This is because the value of acceleration due to gravity changes with the altitude. It is also to be noted that the mass of the body has to be always expressed in terms of kg as it is the SI unit for mass.