Is there any way that Newton's second law can be derived from the

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Discussion Overview

The discussion centers around the possibility of deriving Newton's second law from his first law of motion. Participants explore the relationships between these laws and their implications in classical mechanics.

Discussion Character

  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • Some participants argue that Newton's second law cannot be derived from the first law, as the first law merely states that a body will continue in uniform motion unless acted upon by a force.
  • Others suggest that while the second law quantitatively describes how velocity changes under force, the converse is possible: the first law can be derived from the second law.
  • One participant emphasizes that the first law qualitatively indicates that a resultant force causes acceleration, which is a key distinction from the second law.

Areas of Agreement / Disagreement

Participants generally agree that Newton's second law cannot be derived from the first law, but there is contention regarding the derivation of the first law from the second law, with differing views on the implications of these relationships.

Contextual Notes

Some limitations include the qualitative versus quantitative nature of the laws and the dependence on definitions of force and motion. The discussion does not resolve the mathematical or conceptual steps involved in these derivations.

Nstraw
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Is there any way that Newton's second law can be derived from the first
 
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Note that I'm asking for 2nd law from first law not first from 2nd
 


Nstraw said:
Is there any way that Newton's second law can be derived from the first

I don't think so. The first Newtons Law just states that body will continue to move in a streight line unifiormly unless force acts on it.
Second Law quantitatively describes how exactly the velocity changes under the influence of force.
 


Thanks. Well what do you think is the second law really the real law
 


Nstraw said:
Thanks. Well what do you think is the second law really the real law

Yup , we say that Newton's second law is real law of motion because Newton's first law and third law may be derived using his second law. However doing converse isn't possible.

So you cannot derive Newton's second law from the first. However doing converse is possible , i.e. first law can be derived from second law.
 


Newton's first law states that an object will be either at rest or moving with constant velocity ( constant speed in a straight line) if there is no resultant ( unbalanced) force acting on it.
If there is a resultant force acting then the object cannot be at rest or moving with constant velocity which means that it must be accelerating.
So the first law tells you, qualitatively , that a resultant force causes acceleration.
 


I understand now. Thank you all
 

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