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

Question

a fastidious worker pushes directly along the handle of : a mop with a force F . The handle is at an angle u with the vertical, and ms and mk are the coefficients of sta- tic 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 is in its head. (a) If the mop head moves along the floor with a constant velocity, then what is F? (b) Show that if u is less than a certain value u0, then F (still directed along the handle) is unable to move the mop head. Find u0.

Explanation / Answer

As the mop is moving at constant velocity , there is no accelration . Hence Kinetic friction is balance by the applie horizontal force

mk (mg + F cos (u) ) = F sin (u)

Hence, F = mk (mg)/(sin (u) - mk cos (u))

Here if , sin (u) - ms cos (u) = 0

then mop wont move

hence

uo = tan-1 ( ms)

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