The handle of a floor mop of mass m makes an angle θ with the vertical direction; see Fig. Let be the coefficient of kinetic friction between mop and floor and the coefficient of static friction between mop and floor. Neglect the mass of the handle. (a) Find the magnitude of the force F directed along the handle required to slide the mop with uniform velocity across the floor. (b) Show that if θ is smaller than a certain angle θ 0 the mop cannot be made to slide across the floor no matter how great a force is directed along the handle. What is the angle θ 0 ?

The handle of a floor mop of mass m makes an angle θ with the vertical direction; see Fig. Let  be the coefficient of kinetic friction between mop and floor and  the coefficient of static friction between mop and floor. Neglect the mass of the handle. (a) Find the magnitude of the force F directed along the handle required to slide the mop with uniform velocity across the floor. (b) Show that if θ is smaller than a certain angle θ₀ the mop cannot be made to slide across the floor no matter how great a force is directed along the handle. What is the angle θ₀?