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 theta = 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 theta is less than a certain value theta0, then F (still directed along the handle) is unable to move the mop head. Find theta0.

Explanation / Answer

Answer Details
= 24.83, s = 0.32 and k = 0.21, m = 0.60 kg

a) component forces:

Fcos +mg= N
Fsin - k*N = 0
Fsin - 0.21*(Fcos +mg) = 0
0.2293F =1.2348
F = 5.385 N

b) component forces again:

Fcos +mg= N
Fsin - s*N = 0
Fsin - s*(Fcos +mg) = 0
5.385 sin - 1.7232 cos = 1.8816

Divide both sides of eqaution by (5.3852+1.7322)0.5 ,we get

0.952 sin - 0.306 cos = 0.3328

sin(-17.818) = 0.3328

- 17.818 = 19.4388

= 37.2568

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