Oblique Collisions and Momentum Conservation in Identical Mass Objects

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Discussion Overview

The discussion revolves around the principles of momentum conservation in oblique collisions involving two identical mass objects. Participants explore the mathematical relationships and vector properties associated with these collisions, particularly focusing on the conditions under which momentum conservation equations hold true.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant states that in an oblique collision between identical mass objects, the two objects move at right angles to each other, referencing a specific equation related to momentum conservation.
  • Another participant confirms that the equations discussed are vector equations and provides a mathematical expansion of the momentum terms, leading to the conclusion that the dot product of the momenta must equal zero.
  • A different participant questions the omission of a term in the mathematical derivation, suggesting that the final expression should include additional components of the momentum vectors.
  • One participant proposes using a substitution to clarify the relationship between the momentum terms in the equations presented.

Areas of Agreement / Disagreement

Participants express differing views on the mathematical derivation related to the momentum equations, indicating that there is no consensus on the correct interpretation or completion of the equations involved.

Contextual Notes

The discussion highlights potential limitations in the mathematical steps presented, particularly regarding the treatment of vector components and the assumptions underlying the momentum conservation equations in oblique collisions.

jsmith613
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In an oblique collision (when one object hits another object of IDENTICAL mass at a slight angle the two objects move at right angles to each other.

my book says

p2 = p12 + p22

For momenum conservtation:

p= p1+ p2

apparently these equations can only be consistent of the collision occurs at right angles. why?
 
Last edited:
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These are vectors, right?
p.p = (p1+p2).(p1+p2) [2nd equn]
= p1.p1 + 2.p1.p2 + p2.p2
= p.p + 2.p1.p2 [1st equn]
Hence p1.p2 = 0
 
haruspex said:
These are vectors, right?
p.p = (p1+p2).(p1+p2) [2nd equn]
= p1.p1 + 2.p1.p2 + p2.p2
= p.p + 2.p1.p2 [1st equn]
Hence p1.p2 = 0

where has p2.p2 gone in the final line
surely the final line should be
= p1.p2 + p2.p2, no?
 
Last edited:
1st equn says p.p = p1.p1 + p2.p2
To get from my second line to my third line, use this to substitute p.p for p1.p1 + p2.p2.
 

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