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Find the largest mass that can sit on an incline without accelerating

  1. Sep 26, 2010 #1
    1. The problem statement, all variables and given/known data
    A mass M1 = 10 kg rests on an incline of
    angle θ = 60deg. Find the largest M2 such that no
    accelerations occur.

    a picture of the problem: http://s861.photobucket.com/albums/ab174/alkaline262/?action=view&current=prob14.jpg

    2. Relevant equations


    3. The attempt at a solution

    here are the forces for m1(i think)

    note: N is normal force T is string tension

    (-a1,0) (0,N) (-m1gsin(60), -mg1cos(60)) (T1,0)
    equations here for m1:

    -m1a1 = T1 -m1gsin(60)
    0 = N- m1gcos(60)
    here are the forces for m2(i think)

    (0,-a2) (0,T2) (0,-m2g)

    equation for m2:

    -m2a = T2 -m2g

    all right now, i feel like i should be eliminating T, because it will be equal between the two equations:

    T1 = -m1a + sin(60)m1g
    - T2 = -m2a + m2g
    0 = -m1a + m2a +sin(60)m1g - m2g

    okay i dont know what to do, or if what i have done is right, but i let a = 0 and solved for m2 here anyways :/

    m2 = sin(60)m1
    we know m1 = 10 so,

    max m2 = 8.7 kg

    any advice would be appreciated

  2. jcsd
  3. Sep 27, 2010 #2
    an easier way would be taking the g components for m1 and since the (perpendicular-to-the-plane component) is balanced by normal reaction you can neglect it. Then the {along-the-inlinedplane(say gx) * mass1} should be equated to (mass2 * g) . and then get the answer easily...
    m1 * gx = m2 * g

    And your answer seems to be right approximately.(i havent exactly calculated)
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