I’m teaching some fifth graders a super-intro lesson on Newton’s Laws of Motion. I got the first law and second law pretty well down (on an intro level), and I understand reasonably well why they work and they make intuitive sense.
And “equal and opposite reaction” make perfect sense to me in the context of things like a rocketship or a balloon flying across the room.
What I struggle with is the classic example of a glass set on a table, how the force of the glass pushing down is matched by the table’s equal force pushing up. Something about the table pushing up just bothers me.
Forgive my very stupid question, but how does the table “know” what level of force to apply to the glass so that the glass neither sinks through the table nor flies into the sky? If I pour water into the glass, how does the table adjust the amount of force it applies to the glass so that the glass remains on the table?
I am obviously misunderstanding something here, and worry that I’ll teach this aspect of the third law poorly to my fifth graders. I’m happy to tell them I’m confused, that’s a valuable part of their education to see that their teacher is trying to learn; but I’d be happier still if I could intuit this aspect of the law well enough that I can explain it to them.
Any help on understanding this–not on a mathematical level, but on an intuitive, “oh, that makes sense” level? Bonus points for fifth-grade-appropriate demonstrations, either that I can perform or that I can show videos of.
This may not be the proper way to explain it, but I’ve always thought of the table as a spring. The atomic bonds that keep the table together shift microscopically when the force of the glass interacts with them. The table deforms microscopically if the glass is small and actually bends if the glass is heavy enough or the table is weak enough.
Since the table is acting as a spring, the more a weight deforms it, the more force it projects upwards.
The force that keeps two rigid objects pushing against each other is electromagnetism.
So, when the glass gets heavier, and it tries to push its way into the table, the electrons in the neighboring atoms get pushed into a higher energy position, which causes them to push back against each other harder.
One way to thing about this is it’s a little like pushing on a (fairly rigid) spring. When you push on a spring, how does the spring know how much to push back? It doesn’t, it’s just that it takes more energy to compact the spring into a smaller space, so the harder you push, the more the spring pushes back.
ETA: Bah! Ninjaed by Yllaria. Obviously this is the most intuitive way to think about it
Oh my gosh, y’all–the spring metaphor absolutely makes sense to me, makes sense out of something that’s been bothering me for a few decades now. Thank you!
(My physics education was incredibly spotty, as you can maybe tell).
Exactly. Perhaps for fifth graders, the simplest analogy is this - Instead of a table, consider an apple (or something Newtonian) put on a foam cushion. The cushion deforms until the stretch (being pulled in from around the sides) and compression (springiness) aspects of the foam are resistive enough to stop the apple sinking any further into the cushion.
The apple exerts downward force and the cushion exerts an upward force. A first, the weight of the apple (force of gravity times mass) is greater and the apple moves downward. As the springiness of the foam being deformed builds up, the upward force resisting that movement increases. when the apple stops moving, the forces are in equilibrium.
The same would apply with any material. It’s just that some deform a lot less under weight than others. Put the same apple on a thin plastic table, you can see the deforming as the table gives slightly. Glass or metal, less so. Balsa wood, maybe - walnut or oak, not so visible.
Or consider some idiot sitting on the hood of your car. The metal will give until the tension from the edges and attach points of the hood matches his weight. Baby - no dent. Big Bobby - dent.
If you want to make a demonstration, you can do it with a wooden yard stick, balanced at its ends. If you put a weight on it, you can see the deformation.
Thinking of it as an engineer, you would model the system with vector arrows. Then you’d say that if there’s an arrow pointing down, there has to be an arrow pointing up or else the weight would be in motion. Being an engineer, you don’t have to explain what is causing the upward arrow, you just know it has to be there.
I think “pushing” is maybe the wrong way to describe it- it implies some sort of action on the part of the glass and the table, when it’s not really quite like that. I think you probably have to touch on the idea of equilibrium as well- that’s why nothing’s moving, sinking, deforming, etc…
But does this really address the fundamental question in the OP? At all stages of deformation, the force exerted by the apple on the foam exactly equals the force exerted by the foam on the apple.
It isn’t obvious to most people but all real world solid objects have elasticity, e.g. they compress (or stretch in tension) when loaded. Even if this compression is not measurable in terms of macroscopic displacement it will result in “strain energy” stored within the structure right down to the molecular or metallic structure, analogous to how a spring stores energy by changing length. It is helpful intuitively as thinking of solid objects as just really, really stiff springs.
Although this is well beyond the grasp of a class of fifth graders, but the whole idea of “force” is actually an abstraction that is used to formulate physics problems (e.g. free body diagrams). Forces are fundamentally interactions between two continua (or within a flowing field) and while the forces we interact with on a daily basis are all fundamentally electrostatic and electrodynamic in nature, there are also the ‘residual’ strong and weak nuclear forces which are interactions that control atomic nuclei binding and decay processes. Although we often colloquially talk about the ‘force of gravity’, General Relativity actually says that such forces are a result of deformation of the underlying plenum of space-time caused by the presence of mass; in other words, what we observe as a force is an emergent property of distortions in the ‘floor’ of the universe.
Now go out and fry some fifth grade minds with that!
If the apple is moving (while the cushion deforms), it’s a dynamics problem, not a statics problem. You then have to account for the velocity of the apple/cushion and the acceleration of the apple/cushion. You use calculus instead of algebra & geometry.
But Newton’s Third Law does not apply only to static systems. So if you’re only able to obtain intuition about the Law from a static system, it seems to me that’s not good intuition.
Newton’s Third Law of Motion is equivalent to Conservation of Momentum. That is, if one body changes its momentum, there must be an equal and opposite change in momentum elsewhere, so that the total momentum remains constant.
One possibly useful explanation would go like this:
Science has concluded that nothing is perfectly rigid, and thus the table - or anything else - on which we place a glass deforms a little bit, like a strong spring. But we don’t have to take anyone’s word for that. Instead, we can place something less rigid between the glass and the table, and watch whether it is deformed by this claimed force between them.
One possibility would be a piece of soft foam, which we can watch to see if it gets squeezed. Another would be a scale, which is a device that deforms when a force is applied and also reports on the magnitude of that force.
