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Friction and tension

  1. Oct 19, 2006 #1
    Two masses accelerate along a flat horizontal surface. They are connected by a rope. There is no friction between M_2 and the surface but friction between M1 is described by mu_k. the rope connecting M1 and M2 (M2 is right of M1) breats at a tension T_o. What is the maximum force F that can be applied to the system (pulling M2) that can be applied to the system without the rope breaking.

    This is what I did so far.

    I drew the free body diagrams for both. For M1, I have Normal force pointing up, graviyt down, friction to the left, and tension to the right.

    For M2, I have gravity down, normal force up, F to the right, and T to the left.

    For M1

    x) T-f_k = (m1)*a
    y) N - M1*g = 0

    For M2

    x) F-T = M2*a
    y) N2- M2*g = 0

    So I got T = m1a + f_k
    and F = T + M2 * a

    I plugged things in and got

    F = (M1 + M2)a + mu_k * N1

    However, I know this is the wrong answer. I am suppose to express F in terms of T_o somehow. What am I suppose to do from here?
  2. jcsd
  3. Oct 19, 2006 #2


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    Homework Helper

    You will have two expressions for the acceleration of each mass (F=ma).
    Divide one equation by other and eliminate the acceleration a. Solve for T_o.
  4. Oct 19, 2006 #3
    If I divide I get

    (T-f_k)/(F-T) = m1/m2

    What do I do now? I know that I cannot use a in the final answer but both of the relationships I got from the free body diagrams involves a.
  5. Oct 19, 2006 #4


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    Sorry, I should have said solve for F, in my last post.

    (T-f_k)/(F-T) = m1/m2
    (m2/m1)(T-f_k) = F-T
    F = T + (m2/m1)(T-mu_k.m1)
  6. Oct 19, 2006 #5
    Thanks very much.
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