Question

A block of mass $ 200\, kg $ is being pulled up by men on an inclined plane at angle of $ 45^{\circ} $ as shown in the figure.

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

Answer: (C)

Total force required

$F=mg\, sin \,\theta +f$
$=mg\,sin\,\theta +\mu_{s}R$
$=mg\,sin\,\theta +\mu_{s}\,mg\,cos\,\theta$
$=mg[sin\, \theta+\mu_{s}\,cos\,\theta]$
$=200 \times 10[sin \,45^{\circ}+0.5\,cos\,45^{\circ}]$
$F=\frac{200\times 10\times 3}{2 \sqrt {2}}$
The number of men required will be
$\frac{200\times 10\times 3}{500\times \sqrt{2}{2}} \approx 5$