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What happens when ball traveling at constant speed hit resting ball with

  1. same mass
  2. more mass
  3. less mass

(ie. how diagram of balls speeds looks like)

Balls are made of same material and they collide in vacuum, there are no external forces (gravity etc.), moving ball hits resting ball head on.

Case 1 collisions are elastic.

Case 2 collisions are inelastic.

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closed as off-topic by Bill N, Norbert Schuch, user36790, ACuriousMind, Kyle Kanos Feb 13 '16 at 14:52

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    $\begingroup$ Is this a homework question? $\endgroup$ – Farcher Feb 12 '16 at 14:31
  • $\begingroup$ There's not quite enough information to give a full answer. $\endgroup$ – garyp Feb 12 '16 at 14:34
  • $\begingroup$ @Farcher No. Just wondering. $\endgroup$ – not joe Feb 12 '16 at 14:39
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    $\begingroup$ Is the collision elastic (bounce without losing kinetic energy) or completely inelastic (stick together) or something in between? $\endgroup$ – garyp Feb 12 '16 at 14:46
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    $\begingroup$ Collision head on or at an angle? Are the collisions elastic (no loss of kinetic energy or inelastic (loss of kinetic energy after collision)? $\endgroup$ – Farcher Feb 12 '16 at 14:47
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In Elastic Collision Velocity of $Ball_1$ is Given by $v_1=u_1\frac{m_1-m_2}{m_1+m_2}+\frac{2u_2m_2}{(m_1+m_2)} $

$Ball_2$ $V_2=\frac{2m_1u_1}{(m_1+m_2)}+\frac{u_2(m_2-m_1)}{m_1+m_2}$ Where u is initial Velocity(Velocity before Collision)

In Inelastic Collision Kinetic Energy after Impact is Less than kinetic energy before impact. The Loss in Kinetic Energy converted into Heat Energy

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  • $\begingroup$ It looks like units don't add up in first equation. $\endgroup$ – not joe Feb 12 '16 at 15:06
  • $\begingroup$ This is Correct $v_1=u_1\frac{m_1-m_2}{m_1+m_2}+\frac{2u_2m_2}{(m_1+m_2)}$ $\endgroup$ – Ganesh Feb 12 '16 at 15:09
  • $\begingroup$ if $m_1=m_2$ then $v_1=u_2$ $\endgroup$ – Ganesh Feb 12 '16 at 15:11
  • $\begingroup$ if $m_1=m_2$ $v_2=u_1$ $\endgroup$ – Ganesh Feb 12 '16 at 15:14
  • $\begingroup$ This assumes a 1-dimensional collision. If you allow two dimensions, many more things can happen. The OP did not specify. $\endgroup$ – Bill N Feb 12 '16 at 15:25
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In the limiting case when there is no dissipation (loss of energy), this is called an elastic collision, and answers are well known (see other answers).

In the real world, this is never exactly the case, and depending on how much energy is dissipated (in the vacuum, by deformation of the bodies) you will have a result more or less close to this ideal limit. In the more complex cases, calculating the dynamics of deformation of each body (by numerical approximation in general) is necessary to have a definite answer.

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As per your question events 2 & 3 (i.e. more mass and less mass are relatively the same events). Here I am considering that the events occur in one dimension.

Event 1: When two bodies of equal mass collide elastically, their velocities get mutually interchanged.

Events 2 & 3 are same: When a very lighter mass collides with heavy mass elastically, the heavier body continues to move with almost the same speed.

The above conclusions should be intuitively clear although. See Wikipedia on elastic collisions.

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    $\begingroup$ It's interesting that energy is always transferred from the higer energy ball to the lower energy ball. If that were not the case, our world would be quite strange. $\endgroup$ – garyp Feb 12 '16 at 14:48

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