A fastidious worker pushes directly along the handle of a mop with a force F. Th

Question

A fastidious worker pushes directly along the handle of a mop with a force F. The handle is at an angle ? = 24.83° with the vertical, and 0.32 and 0.21 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 = 0.60 kg is in its head. If the mop head moves along the floor with a constant velocity, then what is F?Show that 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

If mop is moving than kinetic friction will act and acceleration is 0 so Fnet = 0

friction = horizontal force

0.21*(m*g - F*cos24.83) = F*sin24.83

F = 2.06 N

here 2.06 N force is able to overcome the friction but if this mop would have been on rest than this force would not be able to move the mop because of static friction

0.32*(m*g - F*cos24.83) = F*sin24.83

F = 2.7 N

so a minimun of 2.7 N of force is required to move the mop if mop is on rest

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