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Old Oct 4th 2009, 10:13 AM   #1
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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 $\displaystyle \mu_k*(mg+Fcos(\theta))=Fsin(\theta)$.

The next question asks
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.
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Old Oct 4th 2009, 10:28 PM   #2
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Try using the trignometric identity

$\displaystyle
sin^2\ \theta\ +\ cos^2\ \theta\ =\ 1
$
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Old Oct 5th 2009, 10:00 AM   #3
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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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