Question

In order to raise a block of mass $100$ kg a man of mass $60$ kg fastens a rope to it and passes the rope over a smooth pulley. He climbs the rope with an acceleration $\frac{5g}{4}$ relative to rope. The tension in the rope is $(g=10m{s}^{-2})$.

Answer 1

$T-100g=100a$

$T-60g=60(\frac{5}{4}g-a)$

$-40g=160a-75g$

$160a=35g$

$a=\frac{35}{160}\times 10=\frac{35}{16}m/s^2$

$T=100g+100a$

$1000+100\times \frac{35}{16}$

$\frac{4000+875}{4}=\frac{4875}{4}=1218.75N$