Question

A block is pressed against a vertical wall by a force F, as the drawing shows. This force can either push the block upward at a constant velocity or allow it to slide downward at a constant velocity. The magnitude of the force is different in the two cases, while the directional angle G is the same. Kinetic friction exists between the block and the wall, and the coefficient of kinetic friction is 0.330. The weight of the block is 55.0 N, and the directional angle for the force F is theta = 46.0 degree. Determine the magnitude of F when the block slides (a) up the wall and (b) down the wall.

Answer 1

a) When it slides up, the sum of forces in vertical direction would be:

F cos$\theta$ - $\mu$k F sin$\theta$ - W = 0

F = W/ (cos $\theta$- $\mu$k sin$\theta$ )

F = 55/( cos46 - 0.33 x sin46) = 120.35 N

Hence, F = 120.35 N

b) in this case,

W - F cos$\theta$ - $\mu$k F sin$\theta$ = 0

F = W/ (cos$\theta$ + $\mu$k sin$\theta$)

F = 55/ (cos46 + 0.33 x sin46) = 59.01 N

Hence, F = 59.01 N