Question

A mass of $4kg$ rests on a horizontal plane. The plane is gradually inclined until at an angle $\varphi =15^{\circ }$ with the horizontal, the mass just begins to slide. What is the coefficient of static friction between the block and the surface?

• A. $0.27$
• B. $0.58$
• C. 1
• D. $1.73$

Answer 1

Answer: (A)

$mg\sin \theta =f_s$
$mg\cos \theta =N;\tan \theta =\frac{f_s}{N}$
But ${\left(f_s\right)}_{\max }={\mu }_s\cdot N$
or ${\mu }_s=\frac{{\left(f_s\right)}_{\max }}{N}=\tan {\theta }_{\max }=\tan 15^{\circ }=0.27$