Using Special Case of Elastic Collisions in one dimension

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Discussion Overview

The discussion revolves around the application of the special case of elastic collisions in one dimension, particularly focusing on scenarios involving bodies of different masses. Participants explore the implications of the relative velocity equation in elastic collisions and its applicability beyond equal mass scenarios.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • Some participants inquire whether the principle of velocity exchange in elastic collisions applies when the colliding bodies have different masses.
  • It is noted that the equation stating the reversal of relative velocity in elastic collisions holds true regardless of the masses involved.
  • One participant clarifies that while the relative velocity reverses, this does not imply that the velocities are simply exchanged, which is a more specific case.
  • An example is provided to illustrate the concept of relative velocity before and after the collision, emphasizing that the final speeds cannot be determined solely from the reversal of relative velocity and must also consider conservation of momentum.

Areas of Agreement / Disagreement

Participants generally agree on the validity of the relative velocity equation in elastic collisions, but there remains some uncertainty regarding the implications of this equation when applied to bodies of different masses. The discussion does not reach a consensus on the broader implications of these principles.

Contextual Notes

Participants express confusion regarding the interpretation of the reversal of relative velocity and its relationship to determining final speeds, indicating a need for further clarification on the interplay between different principles in elastic collisions.

Seydlitz
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Is it to possible to use the special case of elastic collisions in one dimension with bodies that posses different mass. Ordinarily I know that if the body has same mass the velocity of the bodies will simply be exchanged but is the fact also hold for body with different masses?

[tex]v_1 - v_2 = v_2' - v_1'[/tex]
 
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Seydlitz said:
Is it to possible to use the special case of elastic collisions in one dimension with bodies that posses different mass. Ordinarily I know that if the body has same mass the velocity of the bodies will simply be exchanged but is the fact also hold for body with different masses?
The equation you posted--which states that the relative velocity reverses in an elastic collision--applies regardless of the masses. But it does not allow you to conclude that velocities are simply exchanged. (That's even more of a special case.)
 
Doc Al said:
The equation you posted--which states that the relative velocity reverses in an elastic collision--applies regardless of the masses. But it does not allow you to conclude that velocities are simply exchanged. (That's even more of a special case.)

Ah okay, so what the above equation actually state? I'm confused with the meaning that the relative velocity is simply reversed.
 
Seydlitz said:
Ah okay, so what the above equation actually state? I'm confused with the meaning that the relative velocity is simply reversed.
I'll give an example. Before they collide, say m1 is moving with speed 3 m/s to the east and m2 is moving with speed 4 m/s to the west. Taking east as positive, the relative velocity of m2 with respect to m1 before the collision is: V2 - V1 = -4 - 3 = -7 m/s.

So the relationship expressed in the equation above states that whatever happens during the elastic collision, they must end up such that the relative speed of m2 with respect to m1 after the collision is: V'2 - V'1 = +7 m/s. That's what reversed means. Of course this fact alone is not enough to determine those final speeds. You'll have to combine it with another relationship, such as conservation of momentum.
 
Ah now I get it, thank you for the help Doc. :D

This problem does not actually appear in my test today but it is really helpful to gain new insight from this.
 

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