Question

A plank with a box on it at one end is gradually raised about the other end. As the angle of inclination with the horizontal reaches ${30}^0$ the box starts to slip and slides 4.0 m down the plank in 4.0s. The coefficients of static and kinetic friction between the box and the plank will be, respectively:

Answer 1

Refer image,

$\theta$ = Angle of friction

$\tan \theta =\frac{F}{R}$

$\tan \theta =us$...........(1)

$\Rightarrow \frac{F}{R}=us$

$\Rightarrow \theta ={\tan }^{-1}\left(us\right)$ (From (1))

$us=\tan 30=\frac{1}{\sqrt{3}}=0.6$

$s=ut+\frac{1}{2}a{t}^2$

$a=g(\sin \theta -u_k\cos \theta )$

$\Rightarrow u=\frac{1}{2}g(\sin 30-u_k\cos 30)u^2$

$\Rightarrow 5\sqrt{3}{u}_k=4.5\Rightarrow u_k=0.51$

$u_s=0.6$ and $u_k=0.51$