Question

A block of mass 200kg is being pulled up by men on an inclined plane at angle of ${45}^{\circ }$ as shown. The coefficient of static friction is 0.5. Each man can only apply a maximum force of 500 N. Calculate the number of men required for the block to just start moving up the plane:

• A. 10
• B. 15
• C. 5
• D. 3

Answer 1

The correct option is C 5


Let ‘x’ be the number of men required for the block to just start moving up the plane then,

$xF=mgsin{45}^{\circ }+f_r$

$f_r={\mu }_{s}R=\mu mgcos{45}^{\circ }$
$\Rightarrow x\times 500=mg[\frac{1}{\sqrt{2}}+\frac{1}{2}\times \frac{1}{\sqrt{2}}]$
$500x=\frac{200\times 10}{\sqrt{2}}\times \frac{3}{2}$
$x=5$.

Thus the number of men required for the block to just start moving up the plane is 5.