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DarPodo

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## Homework Statement

In the figure a fastidious worker pushes directly along the handle of a mop with a force F. (Note: For picture, imagine a worker standing in the second quadrant pushing the mop head into the origin) The handle is at an angle θ = 23.58° with the vertical, and 0.30 and 0.22 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 = 0.40 kg is in its head. If the mop head moves along the floor with a constant velocity, then what is F?

Given:

θ = 23.58°

u(static) = 0.30

u(kinetic) = 0.22

m = .4kgI have solved for the first part of the question. My answer (which is verified correct) is 4.35 N.

I have having trouble solving part 2:

Show that if θ is less than a certain value θ0, then F (still directed along the handle) is unable to move the mop head. Find θ0.

## Homework Equations

Finding the angle for the second part I used:

u

_{s}*(Fcosθ+(m*g)) - Fsinθ = 0

## The Attempt at a Solution

After using the above equation with my TI-83 solver function my answer was 31.7 deg. My homework answer program (CAPA) said that it was wrong. I then used the quadratic formula and ended up with the same answer. FINALLY, I consulted with my brother, a Physics Professor, and he agreed that all of my work was correct and my answer was good.

So... Can someone spot an error? I used two different methods, received the same answer, and even consulted a Professor (my own Professor does not offer much help).

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