# An object of mass 40 kg is raised to a height of 5 m above the ground.

Question.
An object of mass 40 kg is raised to a height of 5 m above the ground. What is its potential energy ? If the object is allowed to fall, find its kinetic energy when it is half-way down.

Solution:

Given, mass of object, m = 40 kg ;

height, h = 5 m ;

Acc. due to gravity, $g=10 \mathrm{~ms}^{-2}$

Initial potential energy at a height of 5 m,

$E_{p 1}=m g h=40 \times 10 \times 5=2000 \mathrm{~J}$

Initial kinetic energy, $\mathrm{E}_{\mathrm{K} 1}=0$

Final potential energy at a height of $2.5 \mathrm{~m}$

$\mathrm{E}_{\mathrm{p} 2}=\mathrm{mgh}^{\prime}=40 \times 10 \times 2.5=1000 \mathrm{~J}$

Final kinetic energy, $\mathrm{E}_{\mathrm{K} 2}=?$

By conservation of energy,

Initial mech. energy = Final mech. energy

or $E_{P 1}+E_{K 1}=E_{P 2}+E_{K 2}$

or $2000+0=1000+\mathrm{E}_{\mathrm{K} 2}$

or $E_{K 2}=2000-1000 J=1000 J$