The discussion centers on the interpretation of Newton's 2nd Law in the context of variable mass systems, specifically addressing the equation F→ext(t)=dm(t)/dt * v→(t) + m * dv→(t)/dt. Participants argue that this formulation raises questions about the definition of force and whether it can still be applied universally. The consensus is that while Newton's laws apply to momentum exchanges, the dimensional inconsistency of the equation suggests a need for a refined understanding of force, particularly when mass loss occurs. The conversation also touches on the implications of massless particles, such as photons, on classical mechanics.
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Andrew Mason said:I would propose to restrict the definition of "body" to baryonic matter (using it in the general sense to include electrons in atoms). After all, the concept of force originated with macroscopic objects containing baryonic matter. I realize that this may not work if you want to include as bodies such objects as dark matter, neutrinos, free electrons, black holes etc. However, the concept of force is not particularly useful, if it can apply at all, to such objects.
How about: "A body is an object comprised of baryonic matter, the quantity and identity of which does not change with time".
If we accept your definition of "body" as baryonic matter with fixed constituents, you are already out of the constant mass case - as required by relativistic quantum theory.Andrew Mason said:We could then define "force" as a physical interaction with the body that changes the motion of a body.
As a matter of personal preference I would define force as the rate of change of momentum with respect to time. That makes it easy to generalize to relativity where the rate of change of the four momentum with respect to proper time is a tensor.Orodruin said:If by ”force” you mean ”any momentum exchange” (including momentum lost or gained by mass entering or exiting your system) then Newton’s second law F = dp/dt holds as is.
It is certainly the case that force=dp/dt. But if one defines force as dp/dt then one has to define momentum. If momentum is defined as mass x velocity, one has to define mass in a quantifiable way. But the only way to define mass in a quantifiable way (without resorting to something based on the number of protons+electrons + neutrons) is by its inertia ie.: m=(dp/dt)/(dv/dt) and everything becomes circular. I think the OP was trying to avoid that.Dale said:As a matter of personal preference I would define force as the rate of change of momentum with respect to time. That makes it easy to generalize to relativity where the rate of change of the four momentum with respect to proper time is a tensor.
Then momentum can be defined through Noether’s theorem.Andrew Mason said:If momentum is defined as mass x velocity,
As others have said, this scenario is incompletely specified. Where does the lost mass go? Can you formulate a Lagrangian that covers all entities in the system?dextercioby said:Let me try to pose post 1 in another form then. Hypotheses once more: two bodies of masses ##m_1 (t)## variable which is acted on by a body of mass ##m_2## (constant) through a force we call it ##\vec{F}_{2,1} (t)##. The effect of the body ##m_2## is to make the other one both move and lose mass in time. Question: can we use the 3 known Newton's laws to calculate their motion (##\vec{x}_{1} (t), \vec{x}_{2} (t)##)? If yes, how? If not, why?