Your task is to determine the value of the friction force F and the smallest non

Question

Your task is to determine the value of the friction force F and the smallest non-negative P necessary to prevent the crate from sliding down the incline and the smallest value of P necessary to push the crate up the incline.

If crate is about to slide downwards :

Friction force F [N] : 2539.0148
Smallest non-negative force P necessary to prevent sliding downwards [N] :

For impending upward motion :

Friction force F [N] : 
Smallest value of force P necessary to push the crate up the incline [N] :

Your task is to determine the value of the friction force F and the smallest non-negative P necessary to prevent the crate from sliding down the incline and the smallest value of P necessary to push the crate up the incline.

Explanation / Answer

All right so what forces do we have acting in the plane of the incline: Friction, P, and some of mg. The amount of mg will be mg sin . So we want friction and P to cancel that, we want the minimum P so we want friction to be maximum, or N. So we have the equation P+N=mg sin . we now need to know what N is so we look perpendicular to the plane and set the sum of forces to zero. that direction we have N-mg cos =0. So we solve for N and then put it into the other equation to get P.

for part 2, our push P is now going to oppose the friction and mg sin . (since friction always opposes motion), so we will have P=N+mg sin . Friction will be maximum at N since we want it to start moving.

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