Question

A body of mass $10kg$ is placed on an inclined plane of angle ${30}^o$ . If the coefficient of limiting friction is $\frac{1}{\sqrt{3}}$ , find the force required to just push the body up.

Answer 1

Let the force required to push the body up is $F$.

Then $\mu mg+mg\sin 30=F$

$\frac{1}{\sqrt{3}}\times 10\times 9.8+10\times 9.8\times \frac{1}{2}=F$

$F=98\times \left(\frac{1}{2}+\frac{1}{\sqrt{3}}\right)$

$F=98\times \frac{\left(\sqrt{3}+2\right)}{2\sqrt{3}}$

$F=98\times 1.0774$

$F=105.58N$