First slide

Connected bodies

Question

In order to raise a mass m a man ties it to a rope and passes the rope over a frictionless pulley. He climbs the rope with an acceleration 3g/2 relative to the rope. If the mass of the man is m/2 and the mass of the rope is negligible, the tension in the rope is

Difficult

A

$\frac{3 m g}{2}$
B

$\frac{5 m g}{3}$
C

$\frac{7 m g}{6}$
D

$\frac{9 m g}{7}$

Solution

$g i v e n a_{m R} = a_{m} - a_{R} = \frac{3 g}{2}; a_{m} = (\frac{3 g}{2} - a_{R}) (a s m a n a n d r o p e m o v i n g i n o p p s o t e d i r e c t i o n) e q u a t i o n f o r t h e m a n T - \frac{m g}{2} = \frac{m}{2} a_{m} = \frac{m}{2} (\frac{3 g}{2} - a_{R}); T = \frac{5 m g}{4} - \frac{1}{2} m a_{R} - - - - (1) e q u a t i o n f o r t h e m a s s T - m g = m a_{R} - - - - (2) s o l v i n g f o r T w e g e t T = \frac{7 m g}{6}$

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