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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.
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Solution
\[\text{ Given }, \]
\[\text{ Mass of the block, m = 30 kg} \]
\[\text{ Speed acquired by the block,} \nu = 40 \text{ cm/s } \]
\[ = 0 . 4 \text{ m/s } \]
\[\text{ Distance covered by the block, s = 2 m } \]
Let a be the acceleration of the block in the downward direction.
From the diagram, the force applied by the chain on the block,
\[\text{ F } = \left( \text{ ma - mg }\right)\]
\[ = \text{ m } \left( \text{ a - g } \right)\]
\[\text{ a } = \frac{\nu^2 - \text{ u }^2}{2\text{s}}\]
\[ = \frac{16}{- 4} = 0 . 04 \text{ m/ s}^2 \]
\[\text{ Work done by the chain, } \]
\[\text{ W = Fs } \cos \theta\]
\[= \text{ m } \left(\text{ a - g} \right) \times \text{s} \cos 0^\circ\]
\[ = 30 \left( 0 . 04 - 9 . 8 \right) \times 2\]
\[ = - 30 \times \left( 9 . 76 \right) \times 2\]
\[ = - 585 . 6 = - 586 \text{ J }\]
\[\Rightarrow \text{ W = - 586 J }\]
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