Question

A $40\text{kg}$ girl is swinging on a swing from rest. Then, the power delivered when moving with a velocity of $2\text{m/s}$ upwards in a direction making an angle ${60}^{\circ }$ with the vertical is

• A. $248\sqrt{3}\text{W}$
• B. $392\sqrt{3}\text{W}$
• C. $448\text{W}$
• D. $580\text{W}$

Answer 1

The correct option is B $392\sqrt{3}\text{W}$

Two force are acting on bob, tension and weight. Power of tension will be zero and that of weight is,

$\text{P = mgv cos}({90}^{\circ }+\theta )$
$\text{P = mgv cos}({90}^{\circ }+{60}^{\circ })$
$=-\text{mgv. sin}{60}^{\circ }$
$=-40\times 9.8\times 2\times \frac{\sqrt{3}}{2}=-392\sqrt{3}\text{W}$
$\therefore$ Power delivered is $392\sqrt{3}\text{W}$