Velocity when two object collide in an elastic collision

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Discussion Overview

The discussion centers around the velocities of two objects during an elastic collision, specifically exploring the implications of conservation laws on the outcomes of such collisions. Participants examine the conditions under which different velocity combinations can occur and the uniqueness of solutions in elastic collisions.

Discussion Character

  • Exploratory
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant suggests that there are infinite possible velocities for two colliding objects in an elastic collision, proposing scenarios where one object transfers all its kinetic energy to the other or retains some energy.
  • Another participant argues that conservation of both energy and momentum leads to a unique solution in elastic collisions, implying that multiple outcomes are not possible under these constraints.
  • A third participant notes that while conservation of momentum alone allows for multiple final velocities, the stipulation of a perfectly elastic collision restricts the outcomes to a single solution based on the relative velocities before and after the collision.

Areas of Agreement / Disagreement

Participants express disagreement regarding the number of possible outcomes in elastic collisions, with some asserting that multiple velocity combinations can exist while others maintain that a unique solution is determined by conservation laws.

Contextual Notes

The discussion highlights the dependence on the definitions of elastic collisions and the assumptions regarding energy conservation, as well as the mathematical relationships governing momentum and kinetic energy.

Who May Find This Useful

This discussion may be of interest to those studying mechanics, particularly in the context of collisions, as well as individuals exploring the implications of conservation laws in physics.

mahela007
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When two objects collide in an elastic collision, aren't there an infinite number of possible velocities that the objects can gain? Let's consider two objects each of mass 1kg. One of them is moving at 1 ms-1 and the other is stationary.
After the collision, the first object (the one which was moving) could come to rest and the other object could start moving at 1 ms-1.
That's one scenario in which the 1st object transfers all it's kinetic energy to the other object.

Couldn't the first object keep some of it's energy and only transfer a fraction of it's total KE to the other object? (In which case both objects would be moving after the collision). If that happens, then couldn't there be a several pairs of values for the velocity of Object 1 and object 2 which would comply with the conservation of momentum and the conservation of kinetic energy? How can we determine which one of these combinations of velocities will occur ?
 
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Hi mahela007! :smile:
mahela007 said:
… If that happens, then couldn't there be a several pairs of values for the velocity of Object 1 and object 2 which would comply with the conservation of momentum and the conservation of kinetic energy? How can we determine which one of these combinations of velocities will occur ?

No, conservation of both energy and momentum always gives a unique answer.

Try it and see. :wink:
 
We have been discussing more or less about this in the thread "Acceleration in an elastic collision", which you may want to look at for more detail. Conservation of momentum alone does allow for many final velocities. But, as tiny-tim implied, if you stipulate that the collision is perfectly elastic, that is to say, if all kinetic energy is conserved in the system, then there is only one possible solution. In particular, it's one complying with the requirement that the relative velocity of approach (before collision) = the relative velocity of separation (after collision).
 
Hm... Ok.. I'll check that and post back.
 

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