Physics

[DMTsurel]

This is probably stupid, but can someone explain this?
According to Newton's third law "For every action, there is an equal and opposite reaction."
So why don't they cancel each other?

[extropalopakettle]

Maybe they do, if you look at the big picture.

[i_h8_evil_stuff]

Reaction: I push a rock.
Equal but opposite reaction: The rock pushes me.

I might not move, but the rock still pushes me.

Another example: I, standing on the earth, jump.
Reaction: My feet push the earth.
Opposite Reaction: The earth pushes my feet.

[This message has been edited by i_h8_evil_stuff (edited 03-20-2004 03:33 PM).]

[Antrax]

Disclaimer: I suck at physics, and failed my SIVUG exam in the Technion.
In any case, I believe the idea is that the reaction does necessarily apply to the same object the action was applied on. The most chewed up example is firing a rifle - the bullet flies forward, and the gun hits you in the shoulder. The reason the gun hits you is Newton's third law - the same amount of force that acted on the bullet acts on the gun, in the opposite direction. Because the gun is more massive (or so I should hope), it moves slower than the bullet (Newton's first law).
Antrax


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"Look, that's why there's rules, understand? So that you think before you break 'em" - Lu-Tze, Thief of Time

[lurker]

IMO the action and reaction always apply to different things. I don't think one object can act (exert an action) on itself, and even if it did, the reaction need not be in the exact same spot. So in most cases, the object doing the action is acted upon itself by the reaction. The two forces apply to different things so they won't add up and cancel each other.

I know i basically agreed w/ what Antrax just said, but i wanted to add my 2c...

[Antrax]

You also failed your SIVUG exam? How terrible. Wanna study with me this semester?
Antrax

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"Look, that's why there's rules, understand? So that you think before you break 'em" - Lu-Tze, Thief of Time

[Dr. Borodog]

quote:

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According to Newton's third law "For every action, there is an equal and opposite reaction."

So why don't they cancel each other?

---

Extro's answer, while not being very enlightening, is the most correct, in my opinion.

The answer is that the forces do indeed cancel each other out, when the system you are interested in includes both masses being acted upon. Newton's second law states that F = ma, or Force equals Mass times Acceleration. Imagine an astronaut working on a satellite in space. If he pushes the satellite away, it experiences a force, and will hence accelerate. But the astronaut experience a force of the same magnitude, but in the opposite direction. Hence he will also accelerate, in the opposite direction from the satellite.

But if we look at the whole system of satellite + astronaut, these two forces cancel out, and hence the center of mass of the system does not accelerate.

Since all forces are essentially created by the interaction of two masses (gravitationally, electromagnetically, etc) then all forces leave the center of mass of the interacting bodies un-accelerated.

Someone before gave the example of pushing on a rock, and said "Even if you don't move, the rock is still pushing on you." While true this is incomplete. The reason that you can push on the rock, and move it, but not appear to move, is that the force is transfered through your feet to the ground; hence the rock moves, as does the whole Earth (just not very much), leaving the center of mass of the two undisturbed.



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You will respect my philosophai.

[zeek]

I disagree Borodog. Or at least I disagree with your terminology.

The phrase “two forces canceling each other out” applies when two forces of equal magnitude and opposite direction, coming from different sources, act on a single object to produce a net acceleration of zero on that object.
In short: one central object between two sources of force.

The question asked about Newton’s third law, which describes a single source of two opposite forces that operate on two different objects as a result of the interaction between those objects.
In short: one central source of forces, between two objects.

To use the given example, suppose a man is standing on an earth of infinite mass pushing on a light rock.
Define
Force A: force applied to rock by man = +X.
Force B: force applied to man by rock = -X.
Force C: force applied to man by earth = +X.

Forces B and C cancel each other out to give the man a net acceleration of 0.
Forces A and B (the forces in question) do not cancel each other. Ever.
(If there is a force ‘D’ on the other side of the rock pushing back, then that might cancel A.)

The bottom line answer to the original question is this - the two forces don’t cancel out because they act on different objects.

[Dr. Borodog]

Your semantics are pedantic. Internal forces acting between interacting bodies may be individually applied to the single "object" that is the system including both masses. These force net to zero, leaving the center of mass unaccelerated.



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You will respect my philosophai.

[zeek]

[casinopete]

I don't think you're giving Newton enough credit. The man invented calculus - I'm quite sure his concepts of "action" and "reaction" were quite well developed.

[zeek]

Is that directed at me?
Where am I taking credit from Newton? I'm sure he did have a good concept of action and reaction. Furthurmore, I think I understand what his concept was. What's your point?

[Dr. Borodog]

[casinopete]

I mean I'd bet that he didn't see "action" and "reaction" as limited to external forces.

[Dr. Borodog]

You are implying that I'm saying there's something wrong with identifying the two forces as operating on two the separate masses, which I'm not.

I think I'll concede the point though, since I said you could apply the forces "individually" to the system, and clearly you cannot; the one does not exist in absence of the other.

You win.


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You will respect my philosophai.

[Dr. Borodog]

Although I would like to hear why, exactly, not.


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You will respect my philosophai.

[zeek]

~returning back from work~

[Dr. Borodog]

Easily. I can define any system I like. I can put Pluto in my system if I want. I still don't get what you're trying to say. A force exerted on any mass is by definition exerted on any system defined to include that mass. By definition. Not to be redundant or repetitive.

Consider a system of masses m₁...m_N located at positions x₁...x_N. The center of mass of this system is given by:

x_CM = Sm_nx_n / Sm_n.

Taking the second derivative of both sides, we find:

a_CM = Sm_na_n / Sm_n.

But Sm_na_n is just the sum of the individual forces F_n, and Sm_n = M is simply the net mass of the system. So:

SF_n = Ma_CM.

Hence, any force exerted on an individual mass acts upon the entire system according to Newton's Second Law. Newton, I am quite certain, understood this. It's just that forces internal to a system must come in equal and opposite pairs, as stated in the third law, which thus exert no net force on the system.

Saying that I can't include the man and the rock in my system is tantamount to saying that I cannot include different molecules that make up the rock within the same system. The system is whatever I define it to be. Forces between elements of the system are internal. Forces between elements of the system and elements outside the system are external. Period.

Every molecule in a rock is constantly exerting forces on its neighbors. Because these forces are internal to the system, they all must come in equal and opposite pairs, and net to zero. Hence rocks do not go sailing off willy-nilly on their own.



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You will respect my philosophai.

[Zealot]

[edit] Never mind, I think I misunderstood Dr. Borodog's explanation.

[This message has been edited by Zealot (edited 03-25-2004 06:49 PM).]

[zeek]

Now this is getting absurd.

Yes of course you could define any system you want. For example you could define the “rock-Pluto” system if you want. Then you could say that Force A, which is being applied to the rock, is also being applied to the rock-Pluto system. But just because a force is applied to a system as a whole, it doesn’t mean it has an affect on every element of that system. Pluto doesn’t move when you push the rock. Pluto isn’t connected to rock. So it is pointless to include Pluto in the system. And the man doesn’t move when Force A pushes on the rock either. So it is just as pointless to include the man in the system. (The man may move because of Force B, but that’s beside the point.)

If you want to talk about rock molecules, then yes, indeed the rock is a system of molecules. And if I am going to be exact, then I should say Force A applied to the rock is really just applied to the molecules on the outer edge of that rock. Those molecules will then move slightly inward and apply another force to the next molecule layer in which is connected to the outer molecules. They in turn will move.

Considering all the molecules of the “man-rock” system, they can be divided into two groups. One group is all the molecules that move as a result of Force A (rock molecules). The other group is all the molecules that don’t move as a result of Force A (man molecules). If you define two systems based on this grouping, you get the “rock” system and the “man” system.

I fully understand what you are saying when talk about how the center of mass of the “man-rock” system does not accelerate when no external force is applied. But I really think this is a manifestation of Newton’s Second Law. This thread is supposed to be about the Third Law. I am quite confident that when Newton was describing his third law, that he was thinking more of the “rock” and “man” system rather than the “man-rock” system.
The Second Law is about the interaction between one force and one object "system” (as you call it). The Third Law is about the interaction between two object systems.

Hence, my answer in post 7.

[Dr. Borodog]

[Dr. Borodog]

And just to put to rest what Newton was or was not "thinking" :

"Thus Newton's third law . . . is sufficient to guarantee the conservation of linear momentum for a system of particles, and it was for this purpose that the law was introduced." Mechanics, Third Edition, Symon [emphasis mine].

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You will respect my philosophai.

[This message has been edited by Dr. Borodog (edited 03-25-2004 09:39 PM).]

[zeek]

Looking back, Extro’s post refers to the “man-rock” system-as-a-whole approach.
Lurker’s post refers to the "man" and "rock" as a separate systems.

Then you said:

[Dr. Borodog]

I had here a pithy remark about how I didn't say any system was better, but I see now that I did:

Originally posted by me:

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Extro's answer, while not being very enlightening, is the most correct, in my opinion.

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Poor choice of words. My apologies. I should have said "the most interesting."

But I still don't see what your point is. What, exactly, are you disputing about what I've said?

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You will respect my philosophai.

[This message has been edited by Dr. Borodog (edited 03-25-2004 09:51 PM).]

[zeek]

Apology accepted.

I found nothing objectionable in your physics. However your perceived arrogance was unpleasant. I won't call you a troll, but frankly, you do tend to sound like a soap box preacher sometimes. You may want to work on that.

To answer your earlier question, my degree is in electrical engineering. My background in physics is only that I always found it interesting, and I was quite good at it in school. I even considered a degree in physics except that I found quantum physics to be too weird.

I did always like astrophysics. I think it's cool how the planetary paths are conic sections. I remember computing them just for fun in high school. I was a nerd.
Two years ago when I was visiting Prague I went to see where Kepler lived while he was working his numbers. It was almost like a pilgrimage for me.

[Samadhi]

I find it difficult to understand how anyone can compartmentalize the two forces. They are essentially the same force. Whether it's gravity, mechanical action, or whatever there are two bodies sharing opposite sides of the same force.

[Dr. Borodog]

Samadhi,

I find your perceived arrogance unpleasant.

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You will respect my philosophai.

[zeek]

Originally posted by Samadhi:

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They are essentially the same force.

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Not by Newton’s defintion.

Originally posted by Isaac Newton in Principia:

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DEFINITION IV.

An impressed force is an action exerted upon a body, in order to change its state, either of rest, or of moving uniformly forward in a right line.

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Note what it says. A force is “an action”. Not “actions”. Singular. Not plural.
By Newton’s definition a force is ONE action.

Originally posted by Isaac Newton in Principia:

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LAW III.

To every action there is always opposed an equal reaction; or the mutual actions of two bodies upon each other are always equal, and directed to contrary parts.

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Note how it says “mutual actions”. “Actions” is plural. Not singular. That means there are two of them. And since a force is just one action, there must be TWO forces.

And Borodog, your arrogance isn’t just perceived. It’s actual.

[Aarondalf]

Two things:

1) Zeek, how pedantic can you possibly be?

2) You know that rock you moved? In actual fact, it did affect pluto

[zeek]

[Dr. Borodog]

You are really annoying me here, zeek-with-a-small-z. Where in this whole stupid thread did I say anything arrogant? The only one around here who is arrogant seems to be you. You argue endlessly about a simple point, refusing to tell me what you even disagree with, only to say you don't [dis]agree with it at all. After which, do you apologize for telling me I'm wrong for umpteen posts? No, you insult me.

By the way, that apology wasn't directed at you; it was directed to the people at the beginning of the thread who may have taken my comment that extro's post was the "most correct" to mean that theirs were incorrect; hence my apology to them and revising my comment to "most interesting." At that point in the thread you hadn't even posted. It was only AFTER I had posted that you jumped in to tell me how silly I am for pointing out the entire REASON NEWTON INVENTED THE DAMN THIRD LAW IN THE FIRST PLACE.

Get a grip.


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You will respect my philosophai.



[This message has been edited by Dr. Borodog (edited 03-28-2004 02:51 PM).]

[i_h8_evil_stuff]

[aside]What does "umpteen" mean? Just a number between 13 and 19?[/aside]

[DMTsurel]

Hmm. After all this arguing, I still don't understand.

[ZutAlors!]

Well, let me try. First, understand that when Newton says "action" and "reaction", he's talking about forces, right? So, to rephrase Newton, "For every force, there is, somewhere, a force equal in size in the opposite direction."

So: How about the force you exert on your chair when you sit down? The chair exerts an equal and opposite force on you. How about the force propelling a bullet from a gun? The gun exerts an equal and opposite force on your shoulder. The horizontal force you create against the ground when walking? The ground exerts an equal and opposite force on you.

Do those forces cancel each other? Depends on how you look at it. On the one hand, the force on the chair from your butt, and the force on your butt from the chair are pushing on two seperate objects: you, and the chair. If you look at these two objects seperately, then you need to account for all the forces: both action on the chair and reaction on you, butt-force and chair-force.

However, if you look at the objects together (and there's nothing wrong with doing this), then the force from your butt on the chair cancels the force from the chair on your butt. And, if you go farther, the force from the chair on the floor cancels the force from the floor on your chair. These forces are now internal to the entire object that you are considering.

So do they cancel? It's a matter of your perspective.

Also see this, for example.