A 1.23E+2-kg crate is being pushed across a horizontal floor by a force P that makes an angle of 27.5° below the horizontal. The coefficient of kinetic friction is 0.210. What should be the magnitude of P, so that the net work done by it and the kinetic frictional force is zero?

Question

A 1.23E+2-kg crate is being pushed across a horizontal floor by a force P  that makes an angle of 27.5° below the horizontal. The coefficient of kinetic friction is 0.210. What should be the magnitude of P, so that the net work done by it and the kinetic frictional force is zero?

anonymous · Answer

i'll just give you the equation 
$$\sum Fx = F \cos \theta - f  $$
$$f = N \mu k$$
$$\sum Fy = F \sin \theta + N - mg$$
$$\sum Fy = 0$$
$$N = mg - F \sin \theta $$
$$f =  mg - F \sin \theta  \mu k$$
then you say that the net force is zero
$$\sum Fx = 0$$
$$\ F \cos \theta = f  $$
$$\ F \cos \theta = mg - F \sin \theta  \mu k $$
you got the mass, the sin and cos and the coefficient, plug it into the equation and for the F, divide the result by cos