# Is my understanding of Newton's third law correct. And why is this law taught the way it usually is? [closed]

For years, Newton's third law has always bugged me. Sure, on some level I could believe it. After all, it must be true else I wouldn't be able to jump off the ground. But it always seemed extremely counterintuitive that an inanimate object with no muscles or battery or other power source could produce a very real force.

Recently, I've been revisiting the issue, and had a major revelation when reading this brilliant answer by @Rocketmagnet, which essentially describes Newton's third law as it applies to fundamental forces.

Once you accept that, for example, the repulsive forces associated with electromagnetism always come in force pairs, and that the force is inversely proportional to the (square of the) distance between two "objects", then the reactive forces we experience in our everyday lives make complete sense. Sure, my muscles may be providing the energy to drive the contact point, between my foot and the ground, closer and closer together, but that is completley incidental. What matters here is that, as a result of the decreased distance between my foot and the ground, the electromagnetic repulsive force is increased. Crucially, this force has no privileged membership to either my foot, or the ground - it is an interactive force between them.

Yet, I get the impression that when Newton's law is first taught, it is not taught in terms of (fundamental) force pairs (whose magnitude depends upon distance). Rather, it is taught in the standard "If you push on a wall, the wall pushes back". Parity at this high level description no doubt confuses many minds, as it seems to impute a physical agency to the wall. Trying to resolve this confusion by simply saying that things come in force pairs seems to be an arbitrary explanation that has no deeper meaning.

Yes, I do understand that on some level, even the deepest explanation may seem arbitrary and meaningless, but for some reason, I at least find it much easier to accept the idea of force pairs when it is presented in the context of fundamental forces and distance between objects.

So, two questions:

1) Is my understanding of the law correct?

2) Is there a reason that it is not usually taught this way?

• I'm voting to close this question as off-topic because you seem to be asking about how we are teaching physics in high school. That's a question you have to take to the folks who teach high school or who make the guidelines about how it is being taught. As it's formulated it does not seem to be a question about physics. – CuriousOne Dec 25 '15 at 5:00
• I'm sure there are many educators who participate in this forum who may have insights to share here. I did include "education" as one of the tags. – spacediver Dec 25 '15 at 5:42
• There is absolutely no doubt that this is an interesting topic, it's just not about physics. The site is focused very narrowly on actual physical concepts and if you make it a question about Newton's third law I will gladly retract my vote. – CuriousOne Dec 25 '15 at 6:01
• I'm relatively new to these parts, so my question may be wholly inappropriate. I did, however, carefully read the education tag before posting. Here is an excerpt: "How is physics taught and learned. Teaching strategies, class examples and demonstrations;" I reckon that leaves room for pedagogical considerations? – spacediver Dec 25 '15 at 6:09
• To all of you who want to close this question: Just go away. If you want a site that is closed to anything but graduate level physics and beyond, go to physicsoverflow.org . – David Hammen Dec 25 '15 at 15:59

Spacediver, I DO teach physics at the high school level, so I will "take a shot" at an answer.

I have done demonstrations whereby two students interact with each other. Each student has a spring scale in their hand, and they link the two spring scales together. When each student pulls on their spring scale and reads it, they each see the same reading on their scale, indicating that the forces between them are equal in magnitude and opposite in direction. I also have had pairs of students push their hand against the hand of another student. When I ask them who is pushing, they realize that they both have to push to feel a resistance.

Often, these demonstrations do not seem to "stick" in students' minds, probably because they have misconceptions regarding how the world works. This isn't a good thing, but in the final analysis, there are some ideas in physics that just have to be accepted as facts, and I consider Newton's 3rd law to be one of those things. So to answer one of your questions, ANY TIME I apply a force to some object, there HAS to be an equal and opposite force applied to me, and that is just a fact. It doesn't matter how far apart the object is from me, as I could apply a contact force, or a magnetic force, or assuming that I was a planet (a ridiculous assumption, but bear with me) a gravity force. For all three cases, there just IS an equal and opposite force applied to me.

As a final note on this issue, I am continually amazed that when students have a misconcept that they have probably acquired from some Hollywood special effect, it is usually ALMOST impossible to get them to let go of that misconcept, and accept physical evidence that is right in front of their own eyes. If seeing is believing, and they see some physical effect with their own eyes, and STILL revert back to their misconcept on test day, it is obvious that they are not ready to think about the world around them in new and different ways.

• thanks for the reply David. Don't you feel that if things were presented in terms of distance dependent forces, things would make more sense? The way you've described it (and indeed, the way I feel it is often taught), the reactionary force arises directly as a result of the "applied" force. While this is technically true, there is a missing step here: that of the role of distance. Wouldn't it make more sense to say that when I apply a force, the distance between molecules decreases, and this results in a reactionary force from the other object? – spacediver Dec 25 '15 at 6:02
• @spacedriver: With regards to the physics part of your question: Newton's third law is a special case of the conservation of momentum. It has absolutely nothing to do with the details of the dynamics but follows trough Noether's theorem directly from the homogeneity of space and this is how we teach it to professionals. That David White isn't teaching it that way is a trivial consequence of the inability of the average high school student to understand the necessary level of calculus and abstraction. You would loose 99 of 100 students (or more) if you tried to teach "the full truth". – CuriousOne Dec 25 '15 at 6:11
• While I can accept that my rendition is not the "full truth", is it at least an accurate rendition? If so, I don't see why a 10 year old could not grasp it if presented well. If my rendition is not accurate, can you explain how it isn't? – spacediver Dec 25 '15 at 6:13
• I would not call it an accurate rendition and I can assure you that a ten year old will, unless exceptionally gifted, not profit from "the truth". If you already have a mathematical genius of a kid, gift him a copy of "Mechanics" by Landau and Lifshitz. If you don't... let science teachers explain it hands on with force gauges (that has its own problems, but it's better than what you are proposing). – CuriousOne Dec 25 '15 at 6:22
• If it's not an accurate rendition, then is RocketMagnet's answer also inaccurate? – spacediver Dec 25 '15 at 6:34

Yet, I get the impression that when Newton's law is first taught, it is not taught in terms of (fundamental) force pairs (whose magnitude depends upon distance). Rather, it is taught in the standard "If you push on a wall, the wall pushes back".

That is the right way to teach it. Newton's third law is an abstraction. Whether it's a hammer striking a nail, the interaction between air and an airplane's wings that generates lift, or two stars interacting gravitationally, it doesn't matter how the force arises. You don't (and shouldn't) need to care what makes the force between two objects arise.

Things get even more abstract when one starts looking to the conservation laws. Newton's third law addresses the concept of "force". Even that is a bit much in the context of the conservation laws.

• Fair enough. I appreciate that the 3rd law is independent of the first two laws of motion and the fundamental forces (i.e. if you were to create a computer simulation, you'd need to explicitly include the conservation of momentum in order to observe the 3rd law in action). I still feel that an explanation in terms of microscopic contact forces is a powerful "intuition pump", however. While by itself it doesn't account for the beautiful result that the opposite force exactly equals the applied force, it does provide an intuition of the most proximal cause behind the opposite force – spacediver Dec 25 '15 at 16:34

If it helps let me put my grain of sand.

You can view Newton's 3rd law from a more general view as the statement that:

All interactions between 2 bodies must be symmetric.

If you think carefully about it, the violation of this simple and intuitive? statement would mean to see an effect over some body with minimal or no cause at all!!! (Something more like 'magic'!!!)

The causal attibute of our existence would vanish and the random chaos would reign instead. This law guarantees or rules out that scenario...

Hope this helps.

• This form is not true of magneto-dynamic (or general electromagnetic) forces, which absolutely requires you to include the fields in order to have proper momentum conservation. It is, of course, a reasonable first statement of the principle, but it fails fairly early in the students continuing education. – dmckee --- ex-moderator kitten Dec 27 '15 at 22:24
• @dmckee, thanx for the ilustration, it is interesting!. May you please elaborate a little more in order to understand?. – fante Dec 29 '15 at 23:36

As far as I am aware, there is no theoretical proof that forces must exist in pairs. However, all fundamental forces that we are aware of exhibit this property to the most basic levels.

Newton's third law never says anything about forces existing in pairs. It says,

To every action, there must be an equal and opposite reaction

When you say your foot applies force, you are exerting electromagnetic and gravitational forces (mainly) on the ground, and the ground is doing the same. Both the foot and the ground are pushing each other. And if the ground and the foot were light years away (they can still exert forces on each other), you can talk about who pushed first!

The key mistake that you are making is your understanding that since forces here are coming in pairs, then both the foot and the ground are equivalently doing the work.

The correct answer is that it is indeed the muscles that are doing the heavy lifting, not the floor. This is because the amount of effort exerted (called work) is related to energy spent, not force.

Here's how to analyse Newtons Law of motion to the law of jumping from the ground. You coil your muscles by spending chemical energy. Then you push on the ground. By Newtons third law. The ground pushes back on your feet, your feet the rest of your body. Since your foot is stationary when in contact with the ground, the ground didn't do any work, and hence, since you spent the energy, you pushed!

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