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Homework Help: Newton, freefall acceleration problem

  1. Feb 12, 2008 #1
    The weight of the cart is 4 N. The weight of the hanging mass is 4 N.
    Friction of the cart on the track is a constant force of 2 N magnitude.
    The mass of the string, the mass of the pulley, and the friction of the pulley can be neglected.
    What is the magnitude of the acceleration of the cart if g is the free-fall acceleration?
    Picture attached.

    The answer is to be given in terms of g.

    Okay, here's what I have so far:

    By drawing a free body diagram I manage to get these two equations for the forces acting on both the cart and the hanging mass:

    I'm assuming positive acceleration to the right of the cart and down for the mass.

    For the cart: T - Ff = ma
    For the mass: T - mg = ma
    (since they have the same weight, there is only one m)
    We know that the weight of these two is 4N each so for both, 4 = ma (i'm predicting this might not be right...)

    I'm having trouble applying their given information (4N weight for both masses) with the equations I'm coming up with, for example I don't know what this 4N corresponds to...
    Is it 4N = m.a for the cart and 4N = mg for the hanging mass?

    How do I apply the information they are giving me?


    Attached Files:

  2. jcsd
  3. Feb 12, 2008 #2


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    Homework Helper

    For mass ma = mg - T.
    For cart 4N is the normal reaction. In this problem it is not needed.
    For the cart: T - Ff = ma
    For the mass: mg- T = ma .Solve for T.
    Hence find a by substituting m = 4/g
  4. Feb 12, 2008 #3
    This doesn't really help me understand...
    I end up having 2 equations:
    1) T - Ff = ma
    2) -T + mg = ma

    Then I end up with

    mg - Ff = 2ma (by combining 1 and 2)

    and I'm stuck there.
  5. Feb 12, 2008 #4
    Just figured it out...

    we know that m1g=4 and m2g=4 => m1 = 4/g, m2 = 4/g

    So in the end, after substituting in 1 and 2 we get

    1) T1 - 2 = (4/g)a
    2) -T1 + 4 = (4/g)a

    By adding these 2 equations (to get rid of the T) we end up with
    2 = 8a/g
    which gives a = g/4.
  6. Feb 12, 2008 #5


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    Homework Helper

    That is the answer.
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