Question

Define potential energy. Derive an expression for it. On what factors does gravitational potential energy depends.

Answer 1

Potential energy - Definition

1. Potential energy is defined as the energy possessed by a body due to its position or change in shape.

Deriving an expression for potential energy

1. Consider a body of mass $m$ present at a height $h$.
2. Force $F$ lifts the body to the height $h$.
3. The work done is given by $force\left(F\right)\times displacement\left(h\right)$
4. [Note: Here displacement (s) = height (h)]
5. As force $\left(F\right)$ = mass $\left(m\right)\times$acceleration due to gravity $\left(g\right)$,
6. Work done = $m\times g\times h$
7. The work done is converted to potential energy and is equal to $mgh.$
8. Hence, $P.E.=mgh$

Factors on which the gravitational potential energy depends

1. Mass of the body $\left(m\right)$
2. Height at which the body is present from the ground $\left(h\right)$
3. Acceleration due to gravity $\left(g\right)$