Q. 124.3( 14 Votes )

A man has fallen into a ditch of width d and two of his friends are slowly pulling him out using a light rope and two fixed pulleys as shown in figure (5-E4). Show that the force (assumed equal for both the friends) exerted by each friend on the road increases as the man moves up. Find the force when the man is at a depth h.



Answer :


Let be the force applied by the two friends. The tension in both the side of the rope is equal to the force applied by the friends.


Let be the angle rope makes with the person horizontally.


Vertical equilibrium, ------(1)


Now consider the triangle with the slant rope inside the well.



Thus,


Theta decreases as man moves up, and as theta decreases . thus for equation (1), tension must increase so that it is equal to R.H.S.


Putting the above in equation (1), we get,




Thus, the force exerted by the friends


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