Question

A 149-kg crate is being pushed across a horizontal floor by a force P that makes an angle of 30.7 ° below the horizontal. The coefficient of kinetic friction is 0.264. What should be the magnitude of P, so that the net work done by it and the kinetic frictional force is zero?

Answer 1

The work done by P is zero if the object is at rest.
The object remains at rest if F(friction) = P(horizontal component)

Ff = (mu)(N), N = mg + P(sin30.7) =1461.7 + 0.511P =====>
Ff = (0.264)(1461.7 + 0.511P) = 385.88 + 0.135P

Px = P(cos30.7) = 0.86P

Ff = Px ====> 385.88+ 0.135P = 0.86P ===>
Answer: P = 532.356 N

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