Question

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

• A. $\frac{4 F+(2 M+m) g}{M+2 m}$
• B. $\frac{4 F+(M+m) g}{M+2 m}$
• C. $\frac{4 F-(M+m) g}{M+m}$
• D. $\frac{4 F-(M+m) g}{2 M+m}$

Answer 1

Answer: (C)

From the figure
$2 F+N-M g=M a$
$2 F-m g-N=m a$
$4 F-(M+ m) g=(M +m) a$
$a=\frac{4 F-(M+ m) g}{M+ m}$