You want to push a 66-kg box up a 30° ramp. The coefficient of kinetic friction between the ramp and the box is 0.35. With what magnitude force parallel to the ramp should you push on the box so that it moves up the ramp at a constant speed?

Question

You want to push a 66-kg box up a 30° ramp. The coefficient of kinetic friction between the ramp and the box is 0.35. With what magnitude force parallel to the ramp should you push on the box so that it moves up the ramp at a constant speed?
N

Henry · Answer

Wb = mg = 66kg * 9.8N/kg = 647 N. =
Wt. of box.

Fb = 647 N. @ 30 Deg. = Force of box.
Fp = 647*sin30 = 323.5 N. = Force parallel to ramp.
Fv = 647*cos30 = 560.3 N. = Force perpendicular to ramp.

Fk = u * Fv = 0.35 * 560.3 = 196.1 N. =
Force of kinetic friction.

Fn = Fap - Fp - Fk = 0, a = 0.
Fap - 323.5 - 196.1 = 0,
Fap - 519.6 = 0,
Fap = 519.6 N. = Force applied.