Question

A painter of mass $M$ stand on a platform of mass $m$ and pulls himself up by two ropes which hang over pulley as shown. He pulls each rope with the force $F$ and moves upward with uniform acceleration $a$. Find $a$ neglecting the fact that no one could do this for long time.

Answer 1

figure shows $FBD$ of platform + man moving upward with constant acceleration "$a$"

Now using Newton's second law , i.e. $F=m\times a$

from the figure it is clear that

$4F-(M+m)\times g=(M+m)\times a$

solving we get ,$a=\frac{4F-(M+m)\times g}{M+m}$