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Person pulling a block physics

  • Thread starter atarr3
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  • #1
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Homework Statement


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.


Homework Equations



Net force equations for static objects

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.
 
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Answers and Replies

  • #2
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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).
 
  • #3
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But I'm not trying to find the minimum F, I'm trying to find the minimum theta.
 
  • #4
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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]
 
  • #5
430
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As an afterthought, don't you think the minimum theta is zero?
 

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