1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook