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Compressed Spring Between Two Boxes

  1. May 5, 2015 #1
    1. The problem statement, all variables and given/known data
    Two blocks of masses M and 2M are on a frictionless horizontal surface and are held in place with a compressed spring of negligible mass between them. If the blocks are then released and the block of mass 2M leaves the spring with a velocity v, the velocity of the center of mass of the blocks is

    A zero
    B -(v/2)
    C -(2v/3)
    D -(3v/2)
    E -2v

    2. Relevant equations
    n/a ?

    3. The attempt at a solution
    I do not understand how the center of mass relates to the movement of the blocks. I remember from class that if an object exploded into thousands of pieces the center of mass would still be at the original position.
    So I assume it is A. Zero.
     
  2. jcsd
  3. May 5, 2015 #2
    Can you explain why it would be zero? I mean, you are right. But it might be beneficial to examine the problem a little more deeply.
     
  4. May 5, 2015 #3
    I am not quite sure but I thought it is similar or identical sort of to an explosion.
     
  5. May 5, 2015 #4
    It is very similar to an explosion. Try using conservation of linear momentum and the equation for the velocity of the center of mass of a system of particles (or blocks, in this case) to show why your answer is correct.
     
  6. May 5, 2015 #5
    For linear momentum :
    Pi=Pf
    0 = m(-2v) + (2mv)
    0 = -2mv + 2mv
    0 = 0
    Linear momentum is conserved.

    Hmm, I don't really know an equation for the velocity of the center of mass of a system of particles. I know that the velocities of the boxes are both in opposite directions.
     
  7. May 6, 2015 #6
    It isn't too difficult to prove.

    Start with the equation for the center of mass of a system of particles. If you don't know that either, you can find it here http://hyperphysics.phy-astr.gsu.edu/hbase/cm.html.

    Any ideas on what you can do to this equation to create an equation for the velocity of the center of mass?
    It involves calculus.
     
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