Question

A plank of length 20 m and mass 1 kg is kept on a horizontal smooth surface. A cylinder of mass 1 kg is kept near one end of the plank. The coefficient of friction between the two surfaces is 0.5. Plank is suddenly given a velocity 20m/s towards left. Find the time which plank and cylinder separate.

Answer 1

$N_1=mg$

frictional force on Plank is;

$f={\mu }_1{N}_1=0.5mg$

Deacceleration of plank = $a=\frac{f}{m}=0.5g$

Time taken to cover $20m$ by plank is

$20=ut-\frac{1}{2}a{t}^2$

$20=20t-\frac{1}{2}\times 0.5g\times t^2$

$20=20t-2.5t^2$

$t^2-8t-8=0$

$t=\frac{8\pm \sqrt{64+32}}{2}$$=\frac{8\pm 9.8}{2}$$=\frac{17.8}{2}=8.8s$