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Finding the friction before slipping

  1. Nov 11, 2015 #1
    1. The problem statement, all variables and given/known data
    There is a string that is attached to a bar as shown below in the picture. What is the coefficient friction between the bar and floor before bar starts slipping.
    Reference https://www.physicsforums.com/threa...t-of-friction-using-torque-and-forces.723351/

    3ebcd17e8b532329dde12bc2534a4a32.png

    2. Relevant equations
    Moment which is
    moment (torque) = F r (position)

    3. The attempt at a solution

    I have chosen a pivot point about the point where the bar contacts with the ground.


    The equation for the torque about the point where bar contacts with the ground ->
    - mg *1.4863 - T*1.814989 = 0
    I found 1.814989 by using the cross product.

    Then
    Fx = 0
    -Tsin21 - f(friction) = 0
    -Tsin21 - u(coefficient of friction) *N = 0

    Fy = 0
    -mg + N + T*cos21 = 0

    Now, i'm stuck and i don't how to proceed further. Also, i'm confused about this part ->
    So the formula for friction is f = u*N, is N equals to mg ?
     
  2. jcsd
  3. Nov 11, 2015 #2

    haruspex

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    Not always, and not in this instance.
    The normal force from a solid surface is the minimum magnitude force necessary to prevent the object penetrating the surface.

    The signs look a bit odd in your equations, but I'm not sure what conventions you've adopted. It might all come out ok.
     
  4. Nov 11, 2015 #3
    So if normal force in this case is not equal to m*g, can i solve this problem with 5 unknowns?
     
  5. Nov 11, 2015 #4

    haruspex

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    I assume you mean T, n, u, m and f (friction).
    You have four equations.
    It can happen that you have enough information to determine some unknowns but not all.
    In the present case, T and m are the only unknowns which involve a mass dimension, so you can find the ratio of those but not their individual values. This leaves you with only four unknowns, effectively.
     
  6. Nov 11, 2015 #5

    ehild

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    You will find that m cancels.
     
  7. Nov 11, 2015 #6

    haruspex

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    Well, not exactly. See my post #4.
     
  8. Nov 11, 2015 #7

    ehild

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    When the bar just starts to slip the friction is μN. The task is to find μ. It is not needed to know T or m. It is a homogeneous system of equations, the determinant should be zero, you get μ from this condition.
     
  9. Nov 11, 2015 #8

    haruspex

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    Sure, but Jack lists T and m as unknowns. So what will actually happen is that these will reduce to a single unknown T/m. That is not quite the same as saying m will cancel out.
     
  10. Nov 12, 2015 #9

    ehild

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    It is also needed to use N/m an unknown instead of N. That is, we can choose m arbitrary,
    If you choose to solve the system of equation by eliminating N first then T you are left with an equation of form m f(μ) = 0, wich can be divided by m.
     
  11. Nov 12, 2015 #10

    haruspex

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    Yes, I missed that one.
     
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