in Newtons 3rd law, where does the second body get its energy to react?

Question

A very basic question, and apologies if I have overlooked something obvious. In newtons 3rd law, presumably energy is transfered to the second body from the first body (which itself was subject to an external force), and this is how the second body 'produces' the equal but opposite force.

If this is right, I then get confused/bothered by the implicit assumption of back and forth energy transferance, all happening instantaneously. Is it really an instantaneous process, or does this back and forth slow the system?

Answer 1

Newton's third law states that if body 1 exerts a force on body 2 ($\vec{F}_{1,2}$), body 2 necessarily exerts a force $\vec{F}_{2,1}$ on body 1 that is opposite to $\vec{F}_{1,2}$.

If body 1 doesn't move (or only in a direction perpendicular to $\vec{F}_{1,2}$), no work is done and no energy is transferred.

Now, let's say body one does move in the same direction as the force it exerts on body 2. Then the work it does on body 2 is: $$W_{1,2}=\vec{F}_{1,2}.\Delta \vec{x} > 0 $$ so energy is transferred from body 1 to body 2. Now $$W_{2,1}=\vec{F}_{2,1}.\Delta \vec{x} = -\vec{F}_{1,2}.\Delta \vec{x} = -W_{1,2} $$ so body 2 doesn't transfer energy to body 1, but absorbs it (as is already stated with $W_{1,2}>0$). So body 2 doesn't need energy to exert the reaction-force, even when there is movement.

Answer 2

f=m*a force is mass times acceleration

If one body is still (relative to the other body) then the force it enacts on the body that hits it is dependent on it's own mass.

Meaning it is braking the body that hit's it or slowing it down. Or one body is speeding the other up thereby transferring it's acelleration.

So the force opposite to the acting force is more like the resting mass of the wall you hit into.

I hope that's clear enough.

Wikipedia has also an explanation for this. Essentially F1 = -F2

Answer 3

There is actually not an energy exchange happening at all, but energy transformation. A common example may be 2 gravitationally massive bodies attracting. What you see is both of the bodies accelerating toward one another, or the transformation of gravitational potential energy into kinetic energy. The gravitational potential energy is a characteristic of both objects (i.e., both objects must be in the system to include the energy), so the energy actually comes from both objects.

I hope that answers your question. If not, feel free to comment with further inquiries!

Answer 4

Good question.

It is very didactic to think that atomic bonds behave like springs.

see for details

When you push something, you are actually unbalancing the equilibrium position of the atoms in that solid because you are compressing them. Then, they exert a force to go back to their normal position, in which the potential energy is minimum.

The same reasoning applies when you pull something, e.g, a string. This time you are "elongating" the atomic bonds, so they exert an opposite force to go back to their equilibrium position

Then, the energy of the reaction force comes from the potential energy of the atomic bonds that you have unbalaced.

Answer 5

This text is excerpted from Richard Fitzpatrick's Newtonian Motion:

"It should be noted that Newton's third law implies action at a distance. In other words, if the force that object $i$ exerts on object $j$ suddenly changes then Newton's third law demands that there must be an immediate change in the force that object $j$ exerts on object $i$. Moreover, this must be true irrespective of the distance between the two objects. However, we now know that Einstein's theory of relativity forbids information from traveling through the Universe faster than the velocity of light in vacuum. Hence, action at a distance is also forbidden. In other words, if the force that object $i$ exerts on object $j$ suddenly changes then there must be a time delay, which is at least as long as it takes a light ray to propagate between the two objects, before the force that object $j$ exerts on object $i$ can respond."

I could have responded it myself, but I came across this today and thought it would be more didactical.