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Homework Help: Conservation of Momentum question

  1. Nov 3, 2015 #1
    1. The problem statement, all variables and given/known data

    Two carts sit on a horizontal, frictionless track; the spring between them is compressed. The small cart has mass m, and the mass of the larger cart is M = 4.65m.
    NOTE: Every velocity needs magnitude and direction (given by the sign).

    a) Suppose the carts are initially at rest, and after the "explosion" the smaller cart is moving at velocity v = +8.71 m/s.
    - Find the velocity of the larger cart. V = (answer) m/s
    - Assume now that the mass of the smaller cart is m = 6.36 kg. Assuming there is no loss of energy: find the energy stored in the spring before the explosion. Wk = (answer)J
    - If the spring has spring constant k = 276 N/m: find x, the distance the spring was compressed before the "explosion".

    2. Relevant equations
    PE(spring) = 1/2 kx^2

    3. The attempt at a solution

    part a) I know that if both carts have the same mass then both will be moving away from each other at the same speed after the spring explodes, so it would be -8.71 . But one cart has higher mass, so one cart will move faster away. So I use the conservation of momentum formula
    MV+4.65M*O = M8.71+4.65M*V
    what do I do, solve for V? I cant, the algebra does not work out, am I missing a formula?
  2. jcsd
  3. Nov 3, 2015 #2


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    Science Advisor
    Homework Helper
    Gold Member

    Why do you have a V on the left?
    Note that every term has a factor m. What does that allow you to do?
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