Newton's third law states that each force has an equal and opposite force. If I kicked a ball, it would apply the same force on me. Is this due to the ball's inertia? To clarify, is the ball exerting a force on me because it wants to stay in its original position?
$\begingroup$
$\endgroup$
1
-
2$\begingroup$ related: physics.stackexchange.com/q/66057 $\endgroup$– leongzCommented Apr 27, 2018 at 21:39
Add a comment
|
1 Answer
$\begingroup$
$\endgroup$
3
Newton's third law is a consequence of conservation of momentum, which we have never been able to falsify. Consider a system of two particles with total momentum $\vec P$ such that
$$ \vec P = \vec p_1 + \vec p_2. $$
Noting the relationship between force and impulse, $\vec F = \frac{d\vec p}{dt}$, we can take a time derivative to find
$$ \frac{d\vec P}{dt} = \frac{d\vec p_1}{dt} + \frac{d\vec p_2}{dt} = \vec F_{\rm 2\, on\, 1} + \vec F_{\rm 1\, on\, 2}. $$
If the total momentum is conserved, then $\frac{d \vec P}{dt} = 0$, and we have $$ \vec F_{\rm 2\, on\, 1} = - \vec F_{\rm 1\, on\, 2}.$$
The ball exerts a force back on you in order to conserve linear momentum.
-
-
$\begingroup$ V.F. The total momentum is still constant. $\endgroup$– Bill NCommented Apr 28, 2018 at 2:31
-
$\begingroup$ I don't disagree with that, but in your derivation, you rely on the relationship F=dp/dt for each particle, which does not seem to be valid in the static case. $\endgroup$– V.F.Commented Apr 28, 2018 at 14:41