A window washer pushes a scrub brush up a vertical window at constant speed by a

Question

A window washer pushes a scrub brush up a vertical window at constant speed by applying a force F as shown in the figure (Figure 1). The brush weighs 13.1 N and the coefficient of kinetic friction is 0.170. The coefficient of static friction is exactly twice the coefficient of kinetic friction. Calculate the magnitude of the force F. Express your answer with the appropriate units. Calculate the magnitude of the normal force exerted by the window on the brush. (If this number came out too large, we might grow concerned about breaking the window!) Express your answer with the appropriate units.

Explanation / Answer

given
brush weight = W = 13.1 N

coeffeifficent kinetic friction = mu_k = 0.170

SFx = max

from the diagram

n-Fcos53.1 = 0

n = F cos53.1

fk = mu_k n = mu_k F cos53.1

SFy = may

F sin53.1 - w - fk = 0

F sin53.1 - w – mu_k F cos53.1 = o

F = w/sin53.1 –mu_k cos53.1

F = 13.1N/sin53.1 -(0.17) cos53.1 = 18.80 N

n = F cos53.1 = 18.80 N cos53.1 = 11.3N

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