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A block of mass 200 \mathrm{~kg}  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 \mathrm{~N}. The Number of men required for the block to just start moving up the plane.

Option: 1

1


Option: 2

15


Option: 3

5


Option: 4

3


Answers (1)

best_answer

Here, mass of the block, m=200 \mathrm{~kg}.
coefficient of static friction,  \mu_S=0.5=\frac{1}{2}
angle of incline plane,  \theta=45^{\circ}
Maximum force that each man can apply.  F=500 \mathrm{~N}

Let N  number of men are required for the block to just start moving up the plane-
N F =m g \sin \theta+f \\
=m g \sin \theta+\mu_s R=m g \sin \theta+\mu_s m g \cos \theta \\
=m g\left[\sin \theta+\mu_s \cos \theta\right]

N F =200 \times 100\left[\sin 45^{\circ}+\frac{1}{2} \cos 45^{\circ}\right] \\
NF=200 \times 10\left[\frac{1}{\sqrt{2}}+\frac{1}{2 \sqrt{2}}\right]=\frac{200 \times 10 \times 3}{2 \sqrt{2}} \\
N =\frac{200 \times 10 \times 3}{2 \sqrt{2} \times 500}=5

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SANGALDEEP SINGH

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