# A pendulum bob of mass 0.5kg hanging from a vertical string of length 20m attached to a fixed point is pulled to one side with the string taut until it makes an angle 30° to the vertical. Calculate the work done on the bob?

Mar 16, 2018

Using Law of conservation of energy and assuming that pendulum is ideal and no energy is lost in friction,

Work done on the bob$=$ Increase in potential Energy of bob

Increase in potential Energy of bob$= m g \Delta h$
where $m$ is mass of bob, $g = 9.81 \setminus m {s}^{-} 2$ is acceleration due to gravity and $\Delta h$ is change in height of bob.

As shown in the figure, $\Delta h = L - L \cos \theta$. Inserting given values we get

Work done on the bob$= 0.5 \times 9.81 \left(20 - 20 \setminus \cos {30}^{\circ}\right)$
$\implies$Work done on the bob$= 0.5 \times 9.81 \times 20 \left(1 - \frac{\sqrt{3}}{2}\right) = 13.1 \setminus J$