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A packing crate of mass 40 kg is pulled by a rope as shown in above fig. the coefficient of static friction between the crate and the floor is 0.35. if the =30 determine the magnitude of the force P required for impending motion of the crate.

A packing crate of mass 40 kg is pulled by a rope as shown in above fig.
the coefficient of static friction between the crate and the floor is 0.35.
if the =30 determine the magnitude of the force P required for impending
motion of the crate.

Grade:12th Pass

1 Answers

Sumit Majumdar IIT Delhi
askIITians Faculty 137 Points
9 years ago
Dear student,
There is no figure attached with the question. But assuming that there is a force which pulls the mass and the force makes an angle of 30 degree with the horizontal, we would get:
Fcos\theta-f=ma\Rightarrow Fcos\theta-\mu N=ma
Fsin\theta+N=mg \Rightarrow N=mg-Fsin\theta
Hence, on solving, we get:
Fcos\theta-\mu \left ( mg-Fsin\theta \right )=ma\Rightarrow Fcos\theta-\mu mg +\mu Fsin\theta=ma\Rightarrow F\left ( cos\theta+\mu sin\theta \right )=ma+\mu mg\Rightarrow F=\frac{m\left ( a+\mu g \right )}{\left ( cos\theta+\mu sin\theta \right )}Substituting the values, would give the required answer.
Regards

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