A student, crazed by final exams, uses a force of magnitude 86 N and angle θ = 61° to push a 5.2 kg block across the ceiling of his room, as in Figure 6-52. If the coefficient of kinetic friction between the block and the ceiling is 0.34, what is the magnitude of the block's acceleration?

Question

A student, crazed by final exams, uses a force   of magnitude 86 N and angle θ = 61° to push a 5.2 kg block across the ceiling of his room, as in Figure 6-52. If the coefficient of kinetic friction between the block and the ceiling is 0.34, what is the magnitude of the block's acceleration?

Henry · Answer

Wb = mg = 5.2kg * 9.8N/kg = 51N. =
Weight of block.

Fb = [51N,0deg).
Fp = 51sin(0) = 0 = Force parallel to
ceiling.
Fv=51cos(0) = 51N=Force perpendicular to ceiling.

Ff = u*Fv = 0.34 * 51 = 17.34N. = Force
of kinetic friction.

Fn = Fap*cosA - Fp - Ff,
Fn = 86cos61 - 0 - 17.34 = 24.4N. = Net force.

Fn = ma,
a = Fn / m = 24.4 / 5.2 = 4.68.