Question

A mass $M$ is held in place by an applied force $F$ and a pulley system as shown in figure. The pulleys are massless and frictionless.
(a) Draw a free body diagram for each pulley
(b) Find tension in each section of rope $T_1,T_2,T_3,T_4$
(c) Find the magnitude of $T_1$

Answer 1

$\left(a\right)$ The tension is the same along the full rope as pulleys are mass-less and friction less and the downward force will be equal to the three tensions that pull on it.

thus, $F-T_1=0$

$\left(b\right)$ Let, even the rope goes through pulley and net downward force will be-

$T_4=T_1+T_2+T_3$

and, $T_1=T_2=T_3=\frac{Mg}{2}$

Therefore, $T_4=\frac{3Mg}{2}$

$\left(C\right)$ Magnitude of $F=T_1=\frac{Mg}{2}$

And,

$T_4=T_1+T_2+T_3=\frac{3Mg}{2}$