# Action/reaction pair, 3rd law

Pasted below is a screenshot from this super interesting website: https://ciechanow.ski/bicycle/

Are the blue and green forces in the diagram below an action/reaction pair? If so, how does the process of equilibration described in the text make sense? If not, how would the drawing be changed to show the relevant reaction forces?

• I'm not 100% sure what is your difficulty, but I have a half educated guess that maybe this post can be of help!
– Amit
Jun 5, 2023 at 23:29
• I think my difficulty lies in the idea that the red force would ever NOT be in balance with the green force given blue = green (by N3L) and red = blue. One thought is that maybe the imbalance gets created by the elasticity of the wall; part of the green force is getting temporarily "absorbed" until it reaches a certain threshold of compression, at which point the stored up force is released. Jun 5, 2023 at 23:56
• I think I see the difficulty then: N3L applies to the blue and green forces because the wall applies an equal and opposite force to the box, as the box applies to it. Note, both forces are acting on different objects. Now, the red force is postulated to appear "magically" out of nowhere, just as a proxy in place of some agency that's pushing on the box! You can imagine, that it is in fact a person doing this pushing. Then, there will also be an action reaction pair in accordance with N3L! The box will push back on the person with an equal and opposite force.
– Amit
Jun 6, 2023 at 0:00
• I understand all of that. my confusion stems from the chain of reasoning I laid out. specifically: blue = green (by N3L) and red = blue. Given those two relations, how can red ever NOT equal green (at least in magnitude)? Jun 6, 2023 at 0:16
• Now the next thing to realize, N3L always applies, even if the wall had a finite mass and not an infinite one as is idealized here. The compression of the wall is simply a slight relaxation of that, in admitting that at least the surface of the wall can be imagined as being made of many little molecules each with very small mass, and they will be accelerated due to the box's force and hence the wall's surface compressed. If the analysis was more complete, it would also show a diagram of a few molecules near the surface of the wall and force vector from the box's surface being applied to them
– Amit
Jun 6, 2023 at 0:17

The blue and green forces are an action-reaction pair: the force that the box exerts on the wall is equal and opposite to the force that the wall exerts on the box.

At equilibrium, the force balance on the box is $$F_{red}=F_{green}$$ The blue force does not figure in the force balance on the box because, when we do a force balance on an object, we include only the forces exerted on that object by other bodies, not the force that the object exerts on them.

• Ok, so given blue and green are an action/reaction pair, and given red equals blue, how can red and green ever be out of balance? that's what I meant when I asked about the equilibration process. Jun 5, 2023 at 22:17
• If the box is not touching the wall or if the box or wall can deform elastically, then $$F_{green}-F_{red}=ma_{box}$$ Jun 6, 2023 at 1:07

Are the blue and green forces in the diagram below an action/reaction pair?

Yes, the box pushes the wall and the wall pushes back the box.

If so, how does the process of equilibration described in the text make sense?

It considers a constant force and the elastic behaviour of the wall. I would say that the elastic behaviour of the box is more relevant, because by the picture it is a wooden box, more deformable than a concrete wall.

Are the blue and green forces in the diagram below an action/reaction pair?

Yes. The Blue and Green forces depict the pair described by Newton's Third law.

If so, how does the process of equilibration described in the text make sense?

Keep in mind that the process described in the text is occurring at the molecular level. Specifically, the website states that "the entire system very quickly finds its balance, and since the wall and box are very stiff, the final displacement isn’t perceptible."

The back and forth (equilibriation) motion that is being described is not actually perceptible. While this is not incorrect, it is also not incredibly useful to understand third law pairs in this way which seems to be the reason for your question in the first place.

For the sake of completeness, let's look at the other pairs as well:

The Red and Green forces are both acting on the same object. These cannot form a Newton's Third Law pair because the Third Law requires the forces to be acting on two different objects.

The Red and Blue forces do happen to be acting on different objects but are not acting in opposite directions (the other requirement of Newton's Third Law).

There is quite a lot of detail in the text that is wrong - but the art of physics is about ignoring irrelevant details. ;-)

You ask Are the blue and green forces in the diagram below an action/reaction pair? - the answer is yes. Every action has an equal and opposite reaction said Newton.

The next question is Are the red and green forces an action/reaction pair? - also yes if the box is stationary and stiff.

So your question boils down to Where does the red force originate?

• maybe the box was hit behind by a meteorite?
• someone with their feet on the ground is pushing the box?