Question

A minimum force $F$ is applied to a block of mass $102kg$ to prevent it from sliding on a plane with an inclination angle ${30}^o$ with the horizontal. If the coefficient of static and kinetic friction between the bock and the plane are $0.4$ and $0.3$ respectively, then the force $F$ is:

• A. $307N$
• B. $224N$
• C. $157N$
• D. $zero$

Answer 1

The correct option is C $157N$

Given that,

Mass $m=102kg$

Angle $\theta ={30}^0$

Friction coefficient ${\mu }_s=0.4$

We know that,

$F=mg\sin \theta -{\mu }_{s}mg\cos \theta$

$F=102\times 10\times \frac{1}{2}-0.4\times 102\times 10\times \frac{\sqrt{3}}{2}$

$F=510-353.3$

$F=156.7$

$F=157N$

Hence, the force is $157N$