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Minimal coefficient of friction

  1. Feb 2, 2015 #1
    1. The problem statement, all variables and given/known data
    The rectangle in the drawing is held by the horizontal rope and the friction on the wall.
    What's the minimal coefficient of friction

    2. Relevant equations
    Friction force: f=μN

    3. The attempt at a solution
    Moments round the point of contact with the wall. the side of the rectangle is a, half the diagonal to the center is ##\sqrt {a}##. the distance of the CoM to the wall: ##\sqrt {a}\cdot\sin 55^0=1.16a##
    $$1.16a\cdot mg=T\cdot \sin 10^0\rightarrow T=6.68mg$$
    $$6.68mg\cdot\mu=mg\rightarrow\mu=0.15$$
    It should be 0.3
     

    Attached Files:

  2. jcsd
  3. Feb 2, 2015 #2

    BvU

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    So from the wall to the center of mass is 1.16 times the length of a side ? That's in mid-air ! ;)
     
  4. Feb 2, 2015 #3

    CWatters

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    Is it a square or rectangle? If it's a square check your calculation for "half the diagonal".
     
  5. Feb 2, 2015 #4
    I thank you very much BvU for i didn't laugh so much for some time
     
  6. Feb 2, 2015 #5
    I believe what you used for the normal force is incorrect.
     
  7. Feb 2, 2015 #6

    BvU

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  8. Feb 2, 2015 #7
    The distance of CoM from the wall: ##\frac{a}{\sqrt{2}}\cdot\sin 55^0=0.58a##
    $$0.58a\cdot mg=T\cdot \sin 10^0\rightarrow T=3.41mg$$
    $$3.41mg\cdot\mu=mg\rightarrow\mu=0.3$$
     
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