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

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effect of the external forces is to dictate the motion of the body by making it lose mass, then Newton's second law is no longer applicable.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.
  • #36
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?

[Btw, I symphathize with your frustration about how your thread keeps being subtly hijacked.]
 
<h2> What are Newton's laws of motion?</h2><p>Newton's laws of motion are three fundamental principles that describe the behavior of objects in motion. The first law states that an object at rest will remain at rest, and an object in motion will continue in a straight line at a constant speed unless acted upon by an external force. The second law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. The third law states that for every action, there is an equal and opposite reaction.</p><h2> How are Newton's laws extended?</h2><p>Newton's laws have been extended through the concept of force. While Newton's laws describe the motion of objects in the absence of external forces, the concept of force allows for the consideration of forces acting on an object and how they affect its motion. This extension allows for a more comprehensive understanding of the behavior of objects in motion.</p><h2> Is the concept of force still defined?</h2><p>Yes, the concept of force is still defined and is a fundamental concept in physics. Force is defined as any influence that causes an object to undergo a change in motion. It is measured in units of Newtons (N) and can be represented by vectors, taking into account the direction and magnitude of the force.</p><h2> How does the concept of force relate to Newton's laws?</h2><p>The concept of force is essential in understanding and applying Newton's laws. The second law, which relates force, mass, and acceleration, is a direct result of the concept of force. Additionally, the third law, which states that forces always occur in pairs, is another example of how the concept of force is integral to Newton's laws.</p><h2> Can the concept of force be applied to all situations?</h2><p>Yes, the concept of force can be applied to all situations involving the motion of objects. Whether it is a simple case of an object being pushed or pulled, or a more complex scenario involving multiple forces, the concept of force allows for a comprehensive analysis of the motion of objects in all situations.</p>

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

What are Newton's laws of motion?

Newton's laws of motion are three fundamental principles that describe the behavior of objects in motion. The first law states that an object at rest will remain at rest, and an object in motion will continue in a straight line at a constant speed unless acted upon by an external force. The second law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. The third law states that for every action, there is an equal and opposite reaction.

How are Newton's laws extended?

Newton's laws have been extended through the concept of force. While Newton's laws describe the motion of objects in the absence of external forces, the concept of force allows for the consideration of forces acting on an object and how they affect its motion. This extension allows for a more comprehensive understanding of the behavior of objects in motion.

Is the concept of force still defined?

Yes, the concept of force is still defined and is a fundamental concept in physics. Force is defined as any influence that causes an object to undergo a change in motion. It is measured in units of Newtons (N) and can be represented by vectors, taking into account the direction and magnitude of the force.

How does the concept of force relate to Newton's laws?

The concept of force is essential in understanding and applying Newton's laws. The second law, which relates force, mass, and acceleration, is a direct result of the concept of force. Additionally, the third law, which states that forces always occur in pairs, is another example of how the concept of force is integral to Newton's laws.

Can the concept of force be applied to all situations?

Yes, the concept of force can be applied to all situations involving the motion of objects. Whether it is a simple case of an object being pushed or pulled, or a more complex scenario involving multiple forces, the concept of force allows for a comprehensive analysis of the motion of objects in all situations.

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