Question

A body of mass $m=10kg$ is sliding on a surface inclined at an angle $\theta ={30}^o$ with the horizontal. Calculate the acceleration of the body. The coefficient of kinetic friction between the body and the surface is ${\mu }_k=0.4$.

Answer 1

$N=mg\cos 30=mg\frac{\sqrt{3}}{2}$

$fs=\mu N=\mu mg\frac{\sqrt{3}}{2}$

$mg\sin \theta -fs=ma$

$mg\sin {30}^o-\mu mg\frac{\sqrt{3}}{2}=ma$

$\frac{g}{2}-\mu g\frac{\sqrt{3}}{2}=a$

$5-\left(5\sqrt{3}\right)\left(0.4\right)=a$

$\Rightarrow a=1.5m/s^2$ down the indine