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Static friction on inclined surface

  1. Oct 20, 2009 #1
    Hello all.

    I'm having issues trying to figure out the following problem.

    A boy with a mass of 52 kg and on a 56-degree slope is hanging on to a cord with a breaking strength of 152 newtons. What must be the coefficient of static friction between the boy and the surface?
     
  2. jcsd
  3. Oct 21, 2009 #2
    force down the slope:
    Fd = mg sin 560

    normal force:
    N = mg cos 560

    Friction holding the boy
    Fr = [tex]\mu[/tex]N

    maximum force provided by string
    Fs = 152

    Equating forces:
    the string must not break so the boy doesn't fall, so
    Fd [tex]\leq[/tex] [tex]\mu[/tex]N + Fs

    you can the solve for [tex]\mu[/tex], the coefficient of friction

    Hope this is correct and helps
     
  4. Oct 21, 2009 #3
    This works well. I had gotten almost everything together. The only thing I couldn't figure out was the equation of the forces.

    Thanks for your help.
     
  5. Oct 22, 2009 #4
    well, i was just being a little bit fancy

    if you want, i think you can use

    Fd = [tex]\mu[/tex]N + Fs

    the previous equation:
    Fd [tex]\leq[/tex] [tex]\mu[/tex]N + Fs
    just means that the force pulling the boy down must be less than or equal to the force holding the boy up (Fr and Fs)
    The only unknown variable is [tex]\mu[/tex], so as long as [tex]\mu[/tex] is big enough so that friction force is big, the boy would not fall.
     
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