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.
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