Question

A block slides down an inclined surface of inclination ${30}^o$ with the horizontal. Starting from rest it covers $8m$ in the first two seconds. Find the coefficient of kinetic friction between the two.

Answer 1

frictional force,

$f=\mu mg\cos \theta$

Let the accerelation of block is a

$mg\sin \theta -f=ma$

$mg\sin \theta -\mu mg\cos \theta =ma$

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

Distance covered by the block is 8m in 2 seconds.

we have,

$8=\frac{1}{2}a{t}^2$

$\Rightarrow 8=\frac{1}{2}g(\sin \theta -\mu \cos \theta )t^2$

$\Rightarrow 8=10\times \frac{1}{2}(\frac{1}{2}-\mu \times \frac{\sqrt{3}}{2})(2{)}^2$ [$\theta ={30}^{\circ }$]

$\Rightarrow 4=5-\mu \left(5\sqrt{3}\right)$

$\Rightarrow \mu =\frac{1}{5\sqrt{3}}$