E1.5 Work - Energy Theorem:

Net work on an object causes a change  in the kinetic energy. The work done in a body due to a force is equal to the change in its kinetic energy. 

i.e. Work done = Change in Kinetic Energy

Consider a body of mass $M$, moving with a initial velocity $u$  when a constant force $F$ is acts on it. Let final velocity of the body becomes $v$ after covering a distance $d$ in a direction of force. Then, work done by the force is given by

$W = F.d$ .......... (i)

From the Newton's law of Motion:

$F = ma$ .......... (ii)

From equation (i) and (ii)

$F = ma.d$ .......... (iii)

And from the Kinematics, we know the formula:

$v^2 = u^2 + 2ad$

$d = \frac{v^2 - u^2}{2a}$ .......... (iv)

From the equation (i), (iii) and (iv), we get

$W = ma\;(\frac{v^2 - u^2}{2a})$

      $= m\;(\frac{v^2}{2} - \frac{u^2}{2})$

     $= \frac{1}{2}\,mv^2 - \frac{1}{2}\,mu^2$

      = Final K.E - Initial K.E.

∴ Work done = Change in Kinetic Energy

So, the work done on moving the body by the force is equal to the increase in its kinetic energy.

Return to Main Menu