SOLUTION: A student uses a force of magnitude 85 N to push a 4.6 kg block across the ceiling of his room. If the coefficient of kinetic friction between the block and the ceiling is 0.46, wh

As I understand the problem (without the given picture), the force F is the slant vector F = (H,V) with 
the vertical component V and horizontal component H.


For vertical component you have this equation

V = 4.6*9.81 + N               (1)

where N is the normal force to the ceiling.  //This equation expresses the force balance in vertical direction.


For horizontal component you have this equation

H = k*N = 0.46*N               (2)

where k = 0.46 is the kinematic friction coefficient.


You are also given that

 = 85,    (3)

which expresses the given magnitude of the force F.


By substituting (1) and (2) into (3), you get your governing equation

 = 85.   (4)

It serves to determine the unknown value of N.


The first step to solve equation (4) is to square both sides:

 +  = .


The rest is routine arithmetic. I leave it to you.