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Collision with 3 particles and inelastic string

  1. Oct 14, 2012 #1
    The problem :

    3 identical balls lie on a smooth horizontal surface, the 3rd ball moving with a velocity v while the other 2 are stationary and inter-connected via a taut inelastic string. Ball 3 strikes ball 2 normally making angle = 30 degrees with the string. Energy is conserved. We need to find post-impact velocities and impulsive tension.

    My attempt :

    By the usual principle that elastic collisions between identical bodies exchange velocities, ball 3 should become stationary while ball 2 acquires V and a part of it gets canceled by tension which then acts on ball 1 and the final result is such that both balls 1 and 2 move with equal final velocities.

    However this doesn't match the options given. What exactly am I doing wrong ?
     
  2. jcsd
  3. Oct 14, 2012 #2

    mfb

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    2016 Award

    Staff: Mentor

    Do you have a sketch of the setup? Where is ball 1, relative to the collision of ball3/ball2?

    Ball 1 and 2 could rotate around their common center of mass afterwards (together with a common movement), depending on the setup. In addition, ball 1 could be involved in the first collision, as the string is inelastic.
     
  4. Oct 14, 2012 #3
    Crude ASCII art :

    B1
    ....-
    .....-
    ......-
    .......-
    ........-
    ..........-
    B3->.....B2

    The angle B3B2B1 is 30 degrees, obviously. The string is represented by the "-"s.
     
  5. Oct 15, 2012 #4

    mfb

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    Well in that case, B2 cannot move with the original velocity of B3 - it has to transmit a force to B1, therefore B2 will be slower.
    You can set up an equation system with all conserved quantities as equations and solve that.
     
  6. Oct 15, 2012 #5
    So conserving angular momentum, linear momentum, and energy should be enough, yeah ?
     
  7. Oct 15, 2012 #6

    mfb

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    2016 Award

    Staff: Mentor

    You need an additional equation to express that force in the string can act in the direction of the string only.
    1 equation for angular momentum
    2 equations for linear momentum
    1 equation for energy
    1 equation for the string
    This leaves one degree of freedom, which corresponds to the impact point of B3. If they collide head-on, you can an additional equation for the direction of momentum transfer (here, it is identical with zero vertical velocity of B3 after the collision).
     
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