# Extending Newton's laws -- Is the concept of force still defined?

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• dextercioby
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In summary, it is argued that the correct interpretation of Newton's 2nd Law for one body of mass reads "The dynamics (i.e. vector sum of all external forces acting on the body = "all its interactions") dictates the kinetics (i.e. time derivative of the momentum vector = "motion")", under the assumption that the body's mass will not change during the action of the external forces and after that. However, if the effect of the external forces is to dictate the motion of the body by making it lose mass, then Newton's second law is no longer applicable. Dimensionally inconsistent, this definition implies a new definition of force. Forces may be defined only in the presence of minimum two bodies.
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?
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?