Change in Momentum from mass contribution to the moving object

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Discussion Overview

The discussion revolves around the change in momentum when mass is added to a moving system, specifically a wheelbarrow containing water. Participants explore the implications of Newton's second law in scenarios where mass enters the system with different initial velocities, and the effects of external forces on momentum.

Discussion Character

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

Main Points Raised

  • Some participants question how to apply Newton's second law when mass enters a system, especially regarding the initial velocity of the mass.
  • There is a contention about the correctness of the expression $$F = \frac d {dt}(mv) = \frac{dm}{dt}v + m\frac {dv}{dt}$$, with some arguing it is incorrect due to the changing mass being a physical process.
  • One participant suggests that the concept of 'accretion' is related to inelastic collisions, while others clarify its technical usage.
  • Several participants express interest in understanding why the commonly presented version of Newton's second law may not be accurate in certain contexts.
  • There is a discussion about the implications of defining force in systems where mass changes without external forces, illustrated through a thought experiment involving colored balls.
  • Some participants discuss the relevance of relativistic mass and its implications in the context of Einstein's relativity, noting that the concept has fallen out of favor due to confusion it causes.
  • Others emphasize the importance of correctly defining system boundaries and how that affects the interpretation of mass and force.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the correctness of the expression for Newton's second law or the implications of changing mass in a system. Multiple competing views remain regarding the interpretation of mass and force in both classical and relativistic contexts.

Contextual Notes

Participants highlight limitations in the formalism of Newton's second law when applied to variable mass systems, noting that assumptions about mass entering or leaving a system can lead to confusion in defining force.

  • #61
A.T. said:
In this particular case, with no relative velocity, no force is needed to accelerate the added mass to the velocity of the cart on addition.
until the moment the element of mass enters the cart. After the addition this element of mass ##dm## will produce its effect on the way the whole system reponds to the constant force.
 
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  • #62
It seems that now is a good time to close this thread. The OPs question has been answered and not much else can be added.
 
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