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Collision [of Ideas!]

  1. Oct 17, 2004 #1
    A 2.0 kg block slides along a frictionless tabletop at 6.0 m/s toward a second block (at rest) of mass 4.5 kg. A coil spring, which obeys Hooke's law and has spring constant k = 850 N/m, is attached to the second block in such a way that it will be compressed when struck by the moving block.

    (a) What will be the maximum compression of the spring?

    (b) What will be the final velocities of the blocks after the collision?
    (Assume the initial direction of the 2.7 kg block is positive.)

    (c) Is the collision elastic? (Compare energy values to the nearest joule.)

    I don't know how I should treat the spring attached to the mass...and does the 4.5kg move when the first block hits it?
  2. jcsd
  3. Oct 17, 2004 #2


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    You can use energy and momentum conservation to solve this problem.

    Initially, the kinetic energy and momentum are all carried by the first block. When contact is made via the spring, both blocks will have momentum and kinetic energy PLUS they will have potential energy due to the spring. In the energy conservation equation you can eliminate one of the speeds by using the momentum conservation relation.

    This gives a relation between the amount of compression and the speed of one of the blocks (it's quadratic!) and you can determine the maximum compression either with calculus (if you've had that) or by using the properties of quadratic equations (parabolas).

    Actually, you use the energy conservation equation to find the speed that gives the minimum compression and use that result to find the maximum compression.

    If you are familiar with the "center of mass frame" I think it would be a lot easier to do the problem in that frame - if not then nevermind! :-)
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