Q.
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
Explanation
(c) Total force required
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$F = mg\sin{\theta + f}$
$= mg\sin{\theta + \mu_{s}R}$
$= mg\sin{\theta + \mu_{s}\ mg\cos\theta}$
$= mg(\sin{\theta + \mu_{s}\cos{\theta)}}$
$= 200 \times 10(\sin{45{^\circ} + 0.5\cos{45{^\circ})}}$
$F = \frac{200 \times 10 \times 3}{2\sqrt{2}} = 5$
The number of men required will be
$\frac{200 \times 10 \times 3}{500 \times 2\sqrt{2}} = 5$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.