physics help w/ question...?

Question

a box of books weighing 325 N moves at a constant velocity across the floor when the box is pushed with a force of 425 N exerted downward at an angle of 35.2 degrees below the horizontal. Find ,uk between the box and the floor...?

Answer 1

pushed into ground
forward accelerating force = F cos 35.2
F sin 35.2 component adds to the weight>>>>
friction force fc = uk[mg + F sin 35.2]
Net force = ma = F cos 35.2 - uk[mg + F sin 35.2]

moves with constant speed v = const, a=dv/dt =0

F cos 35.2 - uk[mg + F sin 35.2] =0
uk = F cos 35.2 /[mg + F sin 35.2]
uk = 425 cos 35.2 /[325 + 425 sin 35.2]
uk = 0.61

Answer 2

Let W = mg = 325 kg-m/sec^2, a = 0, and P = 425 kg-m/sec^2 at theta = 35.2 degree wrt the horizontal.

Then f = ma = 0 = p - F; where F = kN = kmg = kW is the friction force in opposition to p = P cos(theta), the horizontal push. Thus p = F; so that P cos(theta) = kW and k = P cos(theta)/W where everything on the RHS is known so you can do the math.

The physics lesson here is that p < P because not all the push P is going into pusing the books along the floor. You would do better to lean down further and put all that P into the box with theta = 0.