Question

A block of mass 30 kg is being brought down by a chain. If the block acquires a speed of 40 cm/s in dropping down 2 m, find the work done by the chain during the process.

Answer 1

$$\begin{gathered} \mathrm{Given}, \\ \mathrm{Mass}\mathrm{of}\mathrm{the}\mathrm{block},m=30\mathrm{kg} \\ \mathrm{Speed}\mathrm{acquire}\text{d}\mathrm{by}\mathrm{the}\mathrm{block},\nu =40\mathrm{cm}/s \\ =0.4\mathrm{m}/s \\ \mathrm{Distance}\mathrm{covered}\mathrm{by}\mathrm{the}\mathrm{block},s=2\mathrm{m} \end{gathered}$$
Let a be the acceleration of the block in the downward direction.

From the diagram, the force applied by the chain on the block,

$$\begin{gathered} \mathrm{F}=\left(ma-mg\right) \\ =m\left(a-g\right) \end{gathered}$$

$$\begin{gathered} a=\frac{{\nu }^2-u^2}{2\mathrm{s}} \\ =\frac{16}{-4}=0.04\mathrm{m}/s^2 \\ \mathrm{Work}\mathrm{done}\mathrm{by}\mathrm{the}\mathrm{chain}, \\ \mathrm{W}=Fs\cos \mathrm{\theta } \end{gathered}$$
$$\begin{gathered} =m\left(a-g\right)\times \mathrm{s}\cos 0° \\ =30\left(0.04-9.8\right)\times 2 \\ =-30\times \left(9.76\right)\times 2 \\ =-585.6=-586\mathrm{J} \\ \Rightarrow W=-586\mathrm{J} \end{gathered}$$