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Speed of object after collision related to spring

  1. Oct 12, 2016 #1
    1. The problem statement, all variables and given/known data
    As shown in the figure below, object A (mass: m) is at rest on a smooth, horizontal surface, and a lightweight spring that compress / stretches in the horizontal direction is attached to it. Object B, which has the same mass m, approaches A from the left side with speed v and collides with the spring. The spring compresses and A begins to move. A, B, and the spring travel in a straight line. What is the speed of A when the spring is at maximum compression?
    qwe_zps299uruf2.png

    2. Relevant equations
    conservation of energy
    momentum?

    3. The attempt at a solution
    I tried using conservation of energy:

    Kinetic energy of B before hitting the spring = elastic potential energy of spring at maximum compression + kinetic energy of A

    But then I stuck because I don't know how to change the spring constant and maximum compression to other variables
     
  2. jcsd
  3. Oct 13, 2016 #2

    haruspex

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    so consider
    Do the conditions for momentum conservation exist here?
     
  4. Oct 17, 2016 #3
    Yes, taking both boxes and spring as a closed system.

    At maximum compression, object A and B will move with same speed?

    Using conservation of momentum:
    mAuA + mBuB = (mA+mB) V
    V = 1/2 v

    Is this correct?
     
  5. Oct 17, 2016 #4

    haruspex

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    That's it.
     
  6. Oct 17, 2016 #5
    Thanks a lot for the help
     
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