A floor mop of mass m has a handle that makes an angle theta with the vertical d

Question

A floor mop of mass m has a handle that makes an angle theta with the vertical direction. Let mu k be the coefficient of kinetic friction between the mop and the floor, and mu, be the coefficient of static friction between the mop and the 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 constant velocity across the floor. (b) there is a certain angle theta 0 such that if theta is smaller than theta0, the map cannot be made to slide across the floor no matter how great a force is directed along the handle. What is the angle theta 0?

Explanation / Answer

If the force f is applied to the mob the x component of the applied force will act on it.

The x component of the applied force is Fsin?

The friction will be = ?kmg

The appled force force must be higher than friction hence Fsin? > ?kmg

In order to take a movement the angle must be ?0 = tan-1 (?s) otherwise the mob wont move

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