Question

A light inextensible string that goes over a smooth fixed pulley as shown in the figure connects two blocks of masses $0.36kg$ and $0.72kg$. Taking $g=10m{s}^{-2}$, find the work done (in Joule) by string on the block of mass $0.36kg$ during the first second after the system is released from rest.

Answer 1

$a=\frac{\text{ Net pulling force }}{\text{ Total mass }}=\frac{0.72g-0.36g}{0.72+0.36}=\frac{g}{3}$
$s=\frac{1}{2}a{t}^2=\frac{1}{2}\left(\frac{g}{3}\right)(1{)}^2=\frac{g}{6}$

$T-0.36g=0.36a=0.36\frac{g}{3}$
$\therefore T=0.48g$
Now, $W_T=TS\cos 0^{\circ }$
(on $0.36kg$ mass)
$=(0.48g)\left(\frac{g}{6}\right)(1)$
$=0.08\left(g^2\right)=0.08(10{)}^2=8J$