I found the force to be 6.36N. I found it using $\displaystyle \mu_k*(mg+Fcos(\theta))=Fsin(\theta)$.In the figure a fastidious worker pushes directly along the handle of a mop with a forceF. The handle is at an angle θ = 31.33° with the vertical, and 0.42 and 0.32 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 massm= 0.50kgis in its head. If the mop head moves along the floor with a constant velocity, then what isF?

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

I setup the equation $\displaystyle \mu_s*(mg+Fcos(\theta))-Fsin(\theta)=0$.

Now I can't find a way to solve for $\displaystyle \theta$.