A woman attempts to push a box of books that has mass 36.5 kg up a ramp inclined at an angle 27.5 degrees above the horizontal. The coefficients of friction between the ramp and the box are mu_s and mu_k. The force F applied by the woman is horizontal.
Assume that mu_s is 0.860 and that mu_k is 0.320. What magnitude of force must the woman apply to keep the box moving up the ramp at constant speed?
acceleration = 0
w = 36.5(9.8) = 357.7
μs = fs/n
μk = fk/n
n - 357.7cos(27.5) - Fsin(27.5) = 0
Fcos(27.5) - 357.7sin(27.5) - fs = 0
(fs = μs*n)
The Attempt at a Solution
I know μs= [Fcos(27.5) - 357.7sin(27.5)] / [357.7cos(27.5) + Fsin(27.5)]
I tried solving for F and i got 219.8 but that is wrong and i think it may have to do with something about not factoring in the μk.