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Collar and Box

  1. Feb 22, 2010 #1
    1. The problem statement, all variables and given/known data
    Collar A starts from rest at t=0 and moves upward with a constant accleration of 9cms^-2. Knowing that collar B moves downward with a constant velocity of 45.7cms^-1, determine the time at which the velocity of block c is zero and the corresponding position of block c

    2. Relevant equations

    Xa + Xb + Xc = constant

    dXa/dt + dXb/dt + dXc/dt = 0

    Va + Vb + Vc = 0

    dVa/dt + dVb/dt + dVc/dt = 0

    Aa + Ab + Ac = 0

    Aa = 9cms^-2 constant
    Va = 9t cms^-1
    Xa = 4.5t^2 + Xao cm

    Ab = 0
    Vb = -45.7cms^-1
    Xb = -45.7t + Xbo cm

    3. The attempt at a solution

    At first I thought that 9t - 45.7 = 0 is the equation to find the time t when the velocity of block C is 0, but the picture confused me as it shows like when B goes down , block C will go up and when A goes up block C will go up as well, so the block will keep going up, won't it be like that? and even if i found out the time t, the position of block C can not be found as the initial positions of A, B, and C are unclear.
    Help me please TT

    Attached Files:

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  2. jcsd
  3. Feb 22, 2010 #2
    my 5 cents advice: look at the diagram in terms of rope distance.

    the travelling path of C will be something like:
    the ropes on the right side will lossen at the rate of twice of the velocity of collar B.

    This makes C falls.

    the rope on the left connecting C to A will pull up C at a rate of 1/2 of wadever distance gained since A only pulls on one side of the rope.

    This makes C raise.

    Hope it helps
  4. Feb 24, 2010 #3
    Thanks a lot!
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