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Kinetic energy problem during collision

  1. Oct 12, 2013 #1
    Hi friends,
    I have an issue in solving a Kinetic energy problem during collision.
    Please Help me in solving this.
    Thank you all in advance.

    The problem is as:

    https://fbcdn-sphotos-g-a.akamaihd.net/hphotos-ak-prn2/1375160_1432382953655477_313625437_n.jpg

    Attempt:

    https://fbcdn-sphotos-b-a.akamaihd.net/hphotos-ak-prn1/993716_1432381396988966_2038831136_n.jpg
    https://fbcdn-sphotos-f-a.akamaihd.net/hphotos-ak-ash4/q87/s720x720/1380153_1432381516988954_1217795620_n.jpg

    Friends according to question all the options, (A),(B),(C),(D) are correct. Please try to help me in this.
    I will appreciate the help.
     
  2. jcsd
  3. Oct 13, 2013 #2

    haruspex

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    As you know, the total energy should be the same at all times. If the KE is going to vary during the collision, where else is energy being stored?
     
  4. Oct 14, 2013 #3
    I think In the terms of heat or sound. But as the question perfectly states that the collision is elastic hence the total K.E. should remains same. And it is happening also before collision and after collision K.E. is 3 J. total.
     
  5. Oct 14, 2013 #4

    ehild

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    The problem is about the process of collision. The particles are like elastic balls. As the first one reaches the stationary particle, they start to interact and push each other. The balls deform and the deformation goes on till they move with respect to each other. At an instant, they move together with the same velocity, like in an inealastic collision, but the energy is not lost, it is stored as elastic energy, as in a compressed spring. During the second stage of the process, the elastic force between the compressed balls starts to accelerate them away from each other, till the balls completely separate. The PE is maximum when the balls move together with the same velocity.

    ehild
     

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    Last edited: Oct 14, 2013
  6. Oct 14, 2013 #5
    Well,l it is clear that, during collision some amount of K.E. will be stored as the elastic P.E. in both the balls.
    But still how the minimum K.E. can be calculated in this process. It is not clear.
     
  7. Oct 15, 2013 #6

    ehild

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    The KE is minimum when the PE is maximum, and it is maximum at maximum compression. At that instant, the balls move together, like in an inelastic collision. What is that common velocity?


    ehild
     
  8. Oct 15, 2013 #7
    for initial, K.E. = 1/2 mv2 = 3 J
    v = √(6/m)

    At the instant of collision,

    Common velocity will me v/3
    i.e. 1/3(√(6/m))
     
  9. Oct 15, 2013 #8

    ehild

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    And the kinetic energy of the system?

    ehild
     
  10. Oct 15, 2013 #9
    Yes it is fulfilling the requirement. Thanks for taking intrust in it. See you around.
     
  11. Oct 15, 2013 #10

    ehild

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    You are welcome.

    ehild
     
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