Question

What is the value of ${\mu }_s,$ the coefficient of static friction?

• A. $\frac{4}{3\sqrt{3}}$
• B. $\frac{2}{3\sqrt{3}}$
• C. $\frac{4}{2\sqrt{3}}$
• D. $\frac{1}{2\sqrt{3}}$

Answer 1

The correct option is A $\frac{4}{3\sqrt{3}}$

When the force tries to move the block, the friction acts upwards and is equal to ${\mu }_{s}mgcos\theta$.

$⟹F={\mu }_{s}mgcos\theta -mgsin\theta$

When the force pulls,

$F=mgsin\theta -{\mu }_{k}mgcos\theta$

Thus ${\mu }_{s}mgcos\theta -mgsin\theta =mgsin\theta -{\mu }_{k}mgcos\theta$

$\theta ={30}^{\circ },{\mu }_s=2{\mu }_k$

$⟹{\mu }_s=\frac{4}{3\sqrt{3}}$

$⟹F={\mu }_{s}mgcos\theta -mgsin\theta =\frac{mg}{6}$