Doubt in Law of mutual interaction

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Discussion Overview

The discussion revolves around the Law of Mutual Interaction as described in classical mechanics, specifically focusing on the implications of Newton's third law regarding the relationship between the accelerations of two interacting particles with different inertial masses. Participants explore the concept of consistency relations in classical mechanics and whether these relations hold when the masses are unequal.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions whether the consistency relation holds when two particles with different inertial masses interact, suggesting that the ratio of accelerations would be constant but not equal to one.
  • Another participant asserts that Newton's third law implies an equal and opposite force, leading to a relationship between the masses and accelerations that does not present a concern regarding consistency.
  • A third participant emphasizes that the topic is fundamental to classical mechanics.
  • Some participants express confusion about the original question, indicating that the algebra involved appears clear and self-consistent in classical mechanics.
  • It is noted that while the ratio of accelerations is constant for different masses, it aligns with the ratio of the masses, suggesting no violation of consistency conditions.

Areas of Agreement / Disagreement

Participants express differing views on the implications of the consistency relation when dealing with different inertial masses. Some assert that the situation is self-consistent, while others question the clarity of the original inquiry and its implications.

Contextual Notes

The discussion highlights potential ambiguities in the interpretation of the consistency relation and its application to systems with unequal masses, but does not resolve these ambiguities.

manimaran1605
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Book: Classical mechanics (textbook) by Douglas Gregory (cambridge publications)
Law of mutual interaction states that when two particle (let it be P1 and P2) interacts, the particle (P1) induces an instantaneous acceleration (a21) on particle P2 and the particle P2 induces an instantaneous acceleration (a12) on particle (P1). If the (inertial)masses of the particles are same, then the magnitude of acceleration be the same, and the ratios of acceleration will be constant ( for this case it is 1)(consistency relation)
That is what Newton's third law says
My question is for different (inertial)masses the ratio will be constant ( but not unity) ( it does not satisfy consistency relation) Am i right? If yes
My question is consistency relation is important in classical mechanics?
 
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If P1 interacts with P2 then Newton's 3rd law of motion implies that P2 interacts with P1 with an "equal but opposite " force. Then if the masses are M1 and M2 we will have M1*a1 = - M2*a2, and the ratio of the accelerations can be seen to depend upon the masses.

I don't see what your concern is.
 
It is a core topic in classical mechanics sir.
 
Let me restate: I don't understand what the question is - the algebra seems clear.

I don't see any problems with "consistency" - classical mechanics is self-consistent.
 
manimaran1605 said:
My question is for different (inertial)masses the ratio will be constant ( but not unity) ( it does not satisfy consistency relation) Am i right? If yes
The ratio of the accelerations will be constant but not unity for different masses (and it will be the ratio of the masses, themselves constant so it's not surprising that the ratio of the accelerations is constant). This does not violate any consistency condition.
 
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