2 part Physics question

Question

1. You have a box of books on the floor with a total mass of 100-kg. You attach a rope to the box at an angle of 30 degrees above the horizontal. If the coefficient of kinetic friction is .22 between the box and the floor, what force is needed to slide the box at a constant velocity?
2. In the previous problem, if you pushed the same box with a stick at a direction of 30 degrees below the horizon, what would be the pushing force required?

Answer 1

For Part (a): If the velocity is constant, then acceleration is zero. So horizontal component of F is equal to the friction force. The former is Fcosθ where θ is 30 degrees. The latter friction force is given by the formula f = üN, where ü is the coefficient of friction and N is the normal force. But N = mg - Fsin θ, because the sum of forces in the vertical direction must be zero. So, now all you have to do is substitute the right side in this last equation for N in the first equation which is F cosθ = üN and then solve for F. Tricky because you need three equations and two oft them are a consequence of the net force being zero in both the vertical and horizontal direction.

For (b) F would be the same as in (a) because the equations cited in a would not change. The vertical component would still be F sin 30 and the horizontal component would be F cos 30.