Question

You need to raise a heavy block by pulling it with a massless rope. You can either (a) pull the block straight up height h, or (b) pull it up a long, frictionless plane inclined at a 15^o angle until its height has increased by h. Assume you will move the block at constant speed either way. Will you do more work in case a or case b? Or is the work the same in both cases? Explain.

Short answer

Work done is equal in both cases.

Step-by-step solution

Given information

A heavy block by pulling it with massless rope when
a) Block is pulled up straight to height h
b) Block is pulled up in an inclined plane at 15^o

Compare the work done between (a) and (b)

Explanation

In the case (a) when it is directly pulled then work done is

W = F x h = mgh ................(a)

In the case when it is on inclined at 15^o

$$\begin{gathered} \sin A=\frac{h}{d} \\ d=\frac{h}{\sin A} \\ W=mg\sin A\frac{h}{\sin A} \\ W=mgh\dots ..................\left(b\right) \end{gathered}$$

From (a) and (b) we can say work done will be same.