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Person pulling a block physics

  1. Jan 21, 2010 #1
    1. The problem statement, all variables and given/known data
    A person pulls on a block with a force F, at an angle theta with respect to the horizontal. The coefficient of friction between the block and the ground is mu. For what theta is the F required to make the block slip a minimum.

    2. Relevant equations

    Net force equations for static objects

    3. The attempt at a solution

    So I'm pretty sure I've got all of my equations right, but I'm having trouble simplifying my results further.
    [tex]Ff=\mu N[/tex] when the box slips and [tex]N=Mg-Fsin\theta[/tex] Substitution gives [tex]\mu\left(Mg-Fsin\theta\right)=Fcos\theta[/tex] I don't know how to solve for theta.
    Last edited: Jan 21, 2010
  2. jcsd
  3. Jan 21, 2010 #2
    For theta for minimum F, write F as an explicit function of theta and differentiate w.r.t theta. Put it equal to zero(the calculus concept of maxima and minima).
  4. Jan 21, 2010 #3
    But I'm not trying to find the minimum F, I'm trying to find the minimum theta.
  5. Jan 21, 2010 #4
    Ok I think I have it now. I maximize the denominator in [tex]F=\frac{\mu Mg}{cos\theta+\mu sin\theta}[/tex] so the derivative is [tex]\mu cos\theta-sin\theta=0[/tex] So [tex]tan\theta=\mu[/tex]
  6. Jan 22, 2010 #5
    As an afterthought, don't you think the minimum theta is zero?
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