- #1

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- 93

- Homework Statement
- 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. 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.

- Relevant Equations
- #T_1 cos \theta = T_2##

##W## is the weight of the man.

##T_1 cos \theta = T_2## --> The horizontal component of ##T_1 = T_2## right ?

##T_1 cos \theta = T_1 \frac {d}{\sqrt {4h^2 + d^2}} = T_2##

##T_1 sin \theta = \frac {W}{2}##

##T_1 = \frac {W}{2 sin \theta}##

##T_2 = \frac {W}{2 sin \theta} \frac {d}{\sqrt {4h^2 + d^2}}##

By taking ##sin \theta## as ##\frac {2h}{\sqrt{4h^2 + d^2}}##

##T_2 = \frac{Wd}{4h}##

By taking ##T_1 = \frac {T_2}{cos \theta}##

We get ##T_1 = \frac {W \sqrt{4h^2 + d^2}}{4h}##

But ##T_1## and ##T_2## are supposed to be the same right ?