Question

Work done by a force is given by W- F.S where F is force and S is the displacement. Show that
a) Work done is also equal to change in kinetic energy

b) Work done is also equal to change in potential energy using this expression​

Answer 1

a) By Work Energy Theorem, work done on an object is the change in kinetic energy of the body produced by the force acting on it in its direction.

Let a body moving with uniform velocity u be acted upon by a constant acceleration a such that its velocity changes to v,

We know,

$v^2= u^2- 2as$ [By third equation of motion]

$=> s= \frac{v^2-u^2}{2a}$

Work done = $F.s$

Force (F) = $ma$

Equating both sides we have,

$F.s = (ma) (\frac{v^2-u^2}{2a})\\F.s = \frac{1}{2}m(v^2-u^2)\\F.s = Kf- Ki$= change in kinetic energy (proved)

b) Let a body be transferred from a  height h to h1.

s= $h1- h$

F = $mg$ (Since work done is against gravity)

F.s = $mg(h1-h)$ = $Pf- Pi$ = change in potential energy (shown)