Question

A block of mass $200kg$ 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 $500N$ . 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

$F=mgsin\theta +f$
$=mgsin\theta +{\mu }_{s}R$
$=mgsin\theta +{\mu }_{s}mgcos\theta$
$=mg[sin\theta +{\mu }_{s}cos\theta ]$
$=200\times 10[sin45^{\circ }+0.5cos45^{\circ }]$
$F=\frac{200\times 10\times 3}{2\sqrt{2}}$
The number of men required will be
$\frac{200\times 10\times 3}{500\times \sqrt{2}2}\approx 5$