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 F. The handle is at an angle = 49° with the vertical, and s = 0.70 and k = 0.33 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 = 0.61 kg is in its head. (a) If the mop head moves along the floor with a constant velocity, then what is F? (b) If is less than a certain value 0, then F (still directed along the handle) is unable to move the mop head. Find 0.

Explanation / Answer

Here ,

theta = 49 degree

us = 0.70

uk = 0.33

m = 0.61 kg

a) let the force needed is F

normal force is N

N = m * g + F * cos(theta)

Now, for motion across the floor

uk * N = F * sin(theta)

0.33 * (0.61 * 9.8 + F * cos(49)) = F * sin(49)

solving for F

F = 3.66 N

the force F needed is 3.66 N

part b)

for the angle theta0

us * N > F * sin(theta0)

0.70 * (0.61 * 9.8 + F * cos(theta0)) > F * sin(theta0)

ignoring m*g term

tan(theta0) > 0.70

theta0 > 35 degree

hence , for angle less than 35 degree , mop will not move

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