First slide

Work

Question

Two blocks of mass 3kg and 2kg are connected by a string passing over a light, friction less pulley. If the system is released from rest, net work done by gravity in 2s is ______ ${(g=10ms}^{- 2})$

Difficult

Solution

$\begin{array}{l} a = \frac{(m_{1} - m_{2}) g}{m_{1} + m_{2}} = \frac{1 \times 10}{5} = 2 {ms}^{- 2} \\ S_{1} = S_{2} = u t + \frac{1}{2} a t^{2} \\ = 0 + \frac{1}{2} \times 2 \times 4 = 4 m \\ W = W_{1} + W_{2} = m_{1} {gS}_{1} \cos 0^{\circ} - m_{2} g S_{2} \cos 180^{\circ} \\ W = [3 \times 10 \times 4] - [2 \times 10 \times 4] \\ W = 40 J \end{array}$

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