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 ${30}^o$, the box starts to slip and slides $4.0m$ down the plank in $4.0s$. The coefficients of static and kinetic friction between the box and the plank will be, respectively

• A. $0.4$ and $0.3$
• B. $0.6$ and $0.6$
• C. $0.6$ and $0.5$
• D. $0.5$ and $0.6$

Answer 1

Answer: (C)

$0.6$ and $0.5$

Static coefficient of friction is ${\mu }_s=\tan {30}^o=0.577\approx 0.6$

For kinetic friction, $ma=mg\sin 30-f=mg\sin 30-{\mu }_{k}mg\cos 30$

$a=g\sin 30-{\mu }_{k}g\cos 30....\left(1\right)$

and also using $S=ut+1/2a{t}^2,$

$\Rightarrow 4=0+\left(1/2\right)a(4{)}^2$

or $a=0.5m/s^2$

Now from (1) we get, $0.5=10\left(1/2\right)-{\mu }_k\left(10\right)\left(\frac{\sqrt{3}}{2}\right)$

or ${\mu }_k=\frac{4.5}{5\sqrt{3}}=0.5$