Ql: A block is pressed against a vertical wall by a force P, as the drawing show

Question

Ql: A block is pressed against a vertical wall by a force P, 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 is the same. Kinetic friction exists between the block and the wall, and the coefficient of kinetic friction is 0.250. The weight of the block is 39.0 N, and the directional angle for the force P is 30.0 Detemine the magnitude of P when the block slides (a) up the wall and (b) down the wall. P

Explanation / Answer

Q1. given force = P

angle = theta

coefficeint of kinetic friciton, k = 0.25

W = 39 N

theta = 30 deg

a. when block slides up the wall

friciotn ats downwards

hence

from force balnce

Pcos(theta) = mg+ Psin(theta)*k

hence

P = mg/(cos(theta) - ksin(theta)) = 52.62977463 N

b. when the block slides down the wall, frcition acts upwards

Pcos(theta) + k*Psin(theta) = mg

P = mg/(cos(theta) + k*sin(theta)) = 39.35317889 N

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