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Problem with kinetic energy

  1. Sep 25, 2007 #1
    Hello everyone

    There is this device called Newton's Cradle

    http://www.heurekashop.fi/files/magneetti/productpics/496picture2Upload.jpg [Broken]

    You lift one ball and let it impact with other balls, the impact is followed by other ball bouncing from the other side.

    However, when you lift 2 balls, the impact is followed by 2 other balls bouncing. Why is that? I would initially guess that only one ball bounces, the answer can not be very simple since I actually asked a professor of physics about this and he didn't really know the answer.
    Last edited by a moderator: May 3, 2017
  2. jcsd
  3. Sep 25, 2007 #2
    The simple answer is that this involves elastic collisions where no deformation occurs. Both kinetic energy and momentum are conserved. When you satisfy both conditions, you get 1 ball = 1 ball, 2 balls = 2 balls, etc as the only possible solution.
  4. Sep 25, 2007 #3
    But also 2 balls = 1 ball would satisfy the conditions if the ball would get twice the momentum and it also would make more sense.
  5. Sep 25, 2007 #4

    Doc Al

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    Staff: Mentor

    How would that conserve energy? And why would it make more sense?
  6. Sep 25, 2007 #5
    Both conditions have to be satisfied. If you have 2 balls, each of mass m, moving with velocity v before the collision, the combined momentum is 2mv and the combined kinetic energy is mv^2. After the collision, these must still be true.
    If you had only one ball leaving, its momentum would have to be 2 mv. Since its mass is m, its velocity must be 2v. However, that would make the kinetic energy 2mv^2. So, this cannot be a solution.
    This is a standard problem in Physics. The solution is well known and accepted. Thousands (millions?) of students have played with Newton's cradles and tried to get a different result. All have failed.
    If this solution were not true, it would be impossible to play the game of pool (billiards) as we know it.
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