Understanding the Relationship Between Force and Momentum: F=dp/dt Explained

  • Context: Undergrad 
  • Thread starter Thread starter John_Doe
  • Start date Start date
Click For Summary

Discussion Overview

The discussion centers around the relationship between force and momentum, specifically the equation F=dp/dt. Participants explore the theoretical foundations, historical context, and implications of this relationship in both classical and modern physics. The conversation includes mathematical derivations, conceptual clarifications, and differing interpretations of the equation's significance.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants explain the derivation of F=dp/dt using the chain rule and the relationship between momentum and mass-velocity.
  • Others argue that F=dp/dt is a definitional equation in modern physics, contrasting it with the historical formulation of F=ma.
  • A participant emphasizes that Newton originally expressed force as F=d(p)/dt, suggesting this formulation is more fundamental than F=ma.
  • Concerns are raised about the Galilean invariance of the equations, with some arguing that F=ma is simpler and more universally applicable than F=dp/dt.
  • Some participants highlight the importance of considering mass variation in certain systems, such as rockets, where F=dp/dt is necessary for accurate modeling.
  • A later reply questions the need for a solid proof of F=dp/dt, suggesting that its validity as a scientific statement should be logically consistent.

Areas of Agreement / Disagreement

Participants express differing views on the foundational nature of F=dp/dt versus F=ma, with no consensus reached on which formulation is more fundamental or universally applicable. The discussion remains unresolved regarding the implications of mass variation and the necessity of each equation in different contexts.

Contextual Notes

Participants note that the discussion involves assumptions about mass conservation and the applicability of classical mechanics versus modern physics frameworks. The implications of relativistic effects on the equations are also mentioned, indicating a complexity that is not fully resolved within the discussion.

  • #61
What's the lagrangian you're using?
 
Physics news on Phys.org
  • #62
Physics Monkey said:
This factor is important because it allows you to set the rest of the integrand to zero (in general, just because the integral of a function is zero doesn't mean the function is zero). Hope this helps.
By the way, you wouldn't happen to go to Georgia Tech would you?
Thanks for the part in bold, I was actually looking at what I'd written after wondering why it wasn't \delta{S} = constant.
As for your question, I go to NUI Maynooth in Ireland.
What's the lagrangian you're using?
A general one for a conservative force.
 

Similar threads

Graduate Conflicting results about Stress tensor symmetry on EM field
  • · Replies 18 ·
Replies
18
Views
1K
Graduate Is there some geometrical interpretation of force from Newton's Laws?
  • · Replies 4 ·
Replies
4
Views
2K
High School Question in the momemtum-impulse theorem derivation
  • · Replies 9 ·
Replies
9
Views
2K
High School Understanding Momentum: The Relationship Between Mass, Velocity, and Force
  • · Replies 29 ·
Replies
29
Views
3K
High School Calculating Force of Ball-Spring Collision
  • · Replies 1 ·
Replies
1
Views
1K
Graduate The definition of generalised momentum
  • · Replies 43 ·
2
Replies
43
Views
5K
Undergrad What is the Exact Meaning of F=dp/dt?
  • · Replies 5 ·
Replies
5
Views
6K
Undergrad Definite and indefinite integration in the definition of work
  • · Replies 4 ·
Replies
4
Views
8K
Graduate A question about the relationship between momentum and force
  • · Replies 9 ·
Replies
9
Views
2K
Graduate Question for anyone with Morin's "Introduction to Classical Mechanics"
  • · Replies 7 ·
Replies
7
Views
2K