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Forces and friction

  1. Sep 20, 2010 #1
    1. The problem statement, all variables and given/known data
    A 6 kg object sits on a horizontal surface with coefficient of friction = .8. What is the minimum force (not necessarily horizontal) necessary to make the object slide?

    2. Relevant equations
    fr = u * N
    where fr = the friction force
    u = coefficient of friction
    N = the normal force

    3. The attempt at a solution
    I knew there was something more to this problem- In lecture, my prof talked about a "magic" angle theta in the positive x and positive y direction that would take the least amount of force to move an object is one was pulling on the object at said "magic" angle. Since no value was mentioned, I assume the angle varies with the mass and the force being applied to the object.

    As usual for me, I have an apparently sound free body diagram, apparently sound equations, and too many unknowns. I have normal force N, force of gravity mg, friction force fr, and the force on the object F.

    Fnet,x = F cos theta - fr = ma
    (my prof doesn't believe in the difference between Fk and Fs (static and kinetic friction) so when a = 0 is when the minimum force is being exerted to make the block move)
    Fnet,x = F cos theta = fr
    Fnet,y = N - mg + F sin theta = ma
    acceleration is zero in the y direction so:
    F sin theta = mg - N

    I can sub in u * N for fr and set tan theta equal to (mg - N) / (u * N), but I don't know N or theta and I'm trying to get to F.

    Am I approaching these problems wrong or do I just keep getting lost along the way? I feel like I keep getting stuck in the same places.
  2. jcsd
  3. Sep 20, 2010 #2

    Doc Al

    User Avatar

    Staff: Mentor

    Looks good to me, so far.


    Eliminate N. Solve for F in terms of theta.

    These are tricky. You're doing fine. Keep playing with it.
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