Physics Help Forum Algebra Dilemma

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Oct 4th 2009, 10:13 AM   #1
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Join Date: Sep 2009
Posts: 19
Algebra Dilemma

 In the figure a fastidious worker pushes directly along the handle of a mop with a force F. 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 mass m = 0.50 kg is in its head. If the mop head moves along the floor with a constant velocity, then what is F?
I found the force to be 6.36N. I found it using $\displaystyle \mu_k*(mg+Fcos(\theta))=Fsin(\theta)$.

 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.

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

Now I can't find a way to solve for $\displaystyle \theta$.
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Last edited by WhoCares357; Oct 4th 2009 at 10:21 AM.

 Oct 4th 2009, 10:28 PM #2 Physics Team   Join Date: Feb 2009 Posts: 1,425 Try using the trignometric identity $\displaystyle sin^2\ \theta\ +\ cos^2\ \theta\ =\ 1$
 Oct 5th 2009, 10:00 AM #3 Senior Member   Join Date: Jul 2009 Location: Kathu Posts: 123 Express your equation as mu_s*(cos(\alpha))-sin(\alpha)=-mg/F Remembering that mu_s is (Tan(\theta)) This is then a double angle formula in Cosine Now to get back to my game of space quest, where the mop has a negative angle of friction!! Last edited by YellowPeril; Oct 5th 2009 at 10:03 AM.

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