In the figure a fastidious worker pushes directly along the handle of a mop with

Question

In the figure a fastidious worker pushes directly along the handle of a mop with a force &. The handle is at an angle 8 = 45degree with the vertical, and p_s = 0.65 and = 0.36 are the coefficients of static and kinetic friction between the head of the mop and the floor. Ignore the mass of the handle and assume that all the mop's mass m = 0.62 kg is in its head, (a) If the mop head moves along the floor with a constant velocity, then what is F> If 9 is less than a certain value theta_0, then F (still directed along the handle) is unable to move the mop head. Find theta_0.

Explanation / Answer

Constant velocity means accleration = 0

Force balance in y-direction

total Fy = 0 = N - mg - F*cos A

N = mg + F*cos A

in x-direction

total Fx = 0 = F*sin A - uk*N

F*sin A = uk*N

F*sin A = uk*(mg + F*cos A)

F = uk*m*g/(sin A - uk*cos A)

F = 0.36*0.62*9.81/(sin 45 deg - 0.36*cos 45 deg)

F = 4.84 N

B.

Critical theta will be when

sin theta - us*cos theta = 0

tan theta = us

theta = arctan (0.65) = 33.02 deg

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