I got a) and b) here. I can't find the mathematical expression of c). THE SETUP: A floor mop of mass m is pushed with a force F directed along the handle, which makes an angle THETA with the vertical. The coefficient of friciton with the floor is MU. a) (i got this) draw the diagram b) (i got this) for given THETA, MU, find the force F required to slide the mop with uniform velocity across the floor. MY ANSWER: in the x direction, F = MUmg/sin(THETA) (all of which are constants, so the velocity will be constant, i assume) c) show that if THETA is less than the angle of repose, the mop cannot be started across the floor by pushign along the handle. My issue is that I can't find a way to mathematically express an angle more than the angle of repose without using numbers. (This is a theoretical problem, no numbers given). I tried it with THETA equaling the angle of repose, which resulted in F = mg/cosTHETA which seems to imply that the force has changed it's direction to down/up, but that's a loose association.