The handle of a floor mop makes an angle θ = 28.6o with the horizontal. Assume the handle is massless, and the mop has mass M = 1.4 kg. The coefficient of kinetic friction between the mop and the floor is μk = 0.386. Find F, the magnitude of the force, exerted downward along the handle, that will cause the mop to slide across the floor without acceleration.
→ Σ F_up = Σ F_down and Σ F_left = Σ F_right
→ Some trig. functions like the one with cosine and sine.
→ F_r = µF_N
The Attempt at a Solution
I drew the free body diagram, and I have mgsin(θ) in the "down" direction. Also, since you are exerting the force downward, F must be also in "down" direction. I believe that the normal force is F_N "up". Then, the friction force goes "left" direction, and the mgcos(θ) goes "right direction". I also drew the mop forming 28.6° with the horizontal.
I am thinking of forming these equations...
F_N = F + mgsin(θ) [up = down]
F_r = mgcos(θ) [left = right]
..Then, I solve for F and got 24.7 N, which is the wrong answer.