Is newton's second law a consequence of the principle of conservation of energy? How can we arrive at net force = rate of change of momentum using only the law of conservation of energy?

Fahdvfm

Fahdvfm

Answered question

2022-11-07

Is newton's second law a consequence of the principle of conservation of energy? How can we arrive at
net force = rate of change of momentum
using only the law of conservation of energy?

Answer & Explanation

lesinetzgl5

lesinetzgl5

Beginner2022-11-08Added 18 answers

Start with
1 2 m x ˙ 2 + V ( x ) = E
with V your potential and E a constant. Now take the time derivative:
m x ˙ x ¨ + d V d x x ˙ = 0 m x ¨ = d V d x
and there you have it, provided you identify the derivative of the potential with the force.
Do remember, though, that Newton's law is more general, because there exist nonconservative forces. This derivation only works for forces that come from a potential.

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