A cord is used to lower vertically a block of mass $M$ by a distance $d$ with constant downward acceleration $

Question

A cord is used to lower vertically a block of mass $M$ by a distance $d$ with constant downward acceleration $\frac{g}{4}$. Work done by the cord on the block is:

Accepted Answer

Let the tension in the cord be $T$. The block is moving downwards with a constant acceleration $a = \frac{g}{4}$.
Applying Newton's second law of motion to the block in the downward direction:
$$Mg - T = Ma$$ 
$$T = M(g - a) = M\left(g - \frac{g}{4}ight) = \frac{3Mg}{4}$$

The force exerted by the cord (tension $T$) is directed vertically upwards, while the displacement $d$ is directed vertically downwards. The angle between the force and displacement vectors is $	heta = 180^\circ$.
The work done by the cord on the block is given by:
$$W = Td \cos 180^\circ = -Td$$ 
$$W = -\left(\frac{3Mg}{4}ight)d = -\frac{3Mgd}{4}$$

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