Chapter 6, Problem 95P

In Fig. 6-61 a fastidious worker pushes directly along the handle of a mop with a force $\stackrel{\to }{F}$. The handle is at an angle θ with the vertical, and µ_s and µ_k 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 is in its head. (a) If the mop head moves along the floor with a con stant velocity, then what is F? (b) Show that if θ is less than a certain value θ₀, then $\stackrel{\to }{F}$ (still directed along the handle) is unable to move the mop head. Find θ₀.

Figure 8-81 Problem 95.