Does Newton's Third Law Hold in the Presence of Gravitational Fields?

[Swapnil]

Newton's third law states when two bodies interact they exert equal but opposite forces on each other. Now we apply this concept to gravitational attraction between, say, the Sun and the Earth. Sun exerts a gravitational force on Earth, and thus Earth also exerts a gravitaional force on the Sun. Now say that somehow, we can block the gravity of the Sun. So now since Sun doesn't exert a gravitational force on Earth, Earth shouldn't exert a force on the Sun as well according to Newton's third law. But we didn't block Earth's gravitational force, and thus, technically, Earth should still pull on the Sun!

How can one resolve this apparent paradox?

 

[Janus]

If you could block gravity (unlikely), and if you could make this blocking effect one-way(extremely unlikely; It would be like saying that object A can touch object B without object B touching object A), Then it would simply mean that Newton's 3rd law doesn't hold.

 

[GotMex?]

My understanding is that there is no gravitational force in the abscence of another mass to interact with. F = Gm1m2/r^2 (Unless there are two masses, then this force is 0). In other words, gravitational force is not a property a mass exhibits constantly, but rather when it is interacting with another mass.

Now assuming you were to be able to block the gravitational force of the Sun, my guess is that you would indirectly be blocking the gravitational force of the Earth as well so the law would still hold.

 

[Danger]

I'm not sure where that came from. Gravity is an intrinsic component of mass. It doesn't matter whether or not there's anything for it to interact with, except that it's the only way we can detect it.

 

[Tomsk]

What you should do, is use Newton's 3rd law to show that you can't block the pull from one mass without blocking the pull from the other (ie separating them to infinity). You can't assume that you can block the pull from one mass only, and say that Newton's 3rd law still holds. You could say that if Newton's 3rd law wasn't true, then you could block the pull from one without blocking the pull from the other. But that wouldn't accurately describe reality.

 

[rbj]

Now say that somehow, we can block the gravity of the Sun. So now since Sun doesn't exert a gravitational force on Earth, Earth shouldn't exert a force on the Sun as well according to Newton's third law. But we didn't block Earth's gravitational force, and thus, technically, Earth should still pull on the Sun!

How can one resolve this apparent paradox?

there is no paradox for a hypothetical situation that is impossible. why waste your time on it? i can also dream up a pile of other paradoxes based on fantasy. here's one:

If Gandalf can summon giant eagles to fight the Nasgool in an air battle at the end, why couldn't he summon them earlier when needed in battle?

 

[Swapnil]

What you should do, is use Newton's 3rd law to show that you can't block the pull from one mass without blocking the pull from the other (ie separating them to infinity). You can't assume that you can block the pull from one mass only, and say that Newton's 3rd law still holds. You could say that if Newton's 3rd law wasn't true, then you could block the pull from one without blocking the pull from the other. But that wouldn't accurately describe reality.

That's a sweet move.

 

[sdemjanenko]

It would be impossible to selectively block gravity. You cannot selectively block EM radiation so why is this different

 

[xAxis]

I think this question theoreticaly makes sence.
Here is what I think would happen. As Sun's gravitational field is blocked, the Earth's would act on Sun. And because Earth acts with force on Sun, the Sun must act on Earth too with equal but opposite force. The only difference would be the magnitude of force. It would be Gm/r, where m is Earths mass.
Thus - no paradox

 

[rbj]

I think this question theoreticaly makes sence.
Here is what I think would happen. As Sun's gravitational field is blocked, the Earth's would act on Sun. And because Earth acts with force on Sun, the Sun must act on Earth too with equal but opposite force. The only difference would be the magnitude of force. It would be Gm/r, where m is Earths mass.
Thus - no paradox

none of the above makes any sense whatsoever. not sure it's not a troll.

"Gm/r" is not a force. nor is it a force per unit mass (which is what you might be implying). it is energy per unit mass (so i think it would have the same dimension as c²). but i have no idea where this 1/r form comes from in the context of this discussion.

 

[Danger]

xAxis, either you're a troll as rbj suggested, or you have no concept of gravity. Either way, please keep in mind that this is a serious science site intended to help people with their studies or projects in professional life. There's no room for baseless speculation. I speculate a lot, because of lacking an education, but never unless I have some basis for thinking that my speculation is valid. And at that, I always defer to those more knowledgeable. Any understanding of either Newtonian or Einsteinian gravitational theory should prevent someone from making the assumtion that you did in your post.

 

[sdemjanenko]

Newton's 3rd law will not be changed over time, it might be slightly modified like his law of gravity for all we know but its going to be generally true, for me i don;t believe that it will ever be overturned or modified.

 

[xAxis]

Yes, I've probably gone too far with my conclusions. I somehow wanted to point out that the third Newton's law is at least as universal as gravitation law.
Now let's consider another example. Let's put a boy and a girl somewhere in free space so that they are meter appart facing each other and holding each other hands. If he pulls her with constant forse of say 10N, and she pulls him with force of 5N, what will be the actual force with which he is pulling her?

 

[rcgldr]

Let's put a boy and a girl somewhere in free space so that they are meter appart facing each other and holding each other hands. If he pulls her with constant force of say 10N, and she pulls him with force of 5N, what will be the actual force with which he is pulling her?

This isn't possible. They will always pull with the same force. Imagine that they both are holding on to the ends of a rope. Assuming that the rope isn't accelerating (in the direction of the rope), then the tension in the rope will always be the same at both ends. If one of them initiates a 10N force in the rope, then once things stabilize (after the rope stops stretching), there will be 10N of tension in the rope, and at both ends of the rope. If they're not attached to anything else (other than the rope), then they are accelerating towards each other.

For a simpler example, connect two fishing weight scales (these measure tension and indicate the tension in order to weigh an object, usually a poor dead fish), in series. Have two people pull on each end of one of the scales. Can the two people generate forces so that the fishing scales show a different amount of tension (weight reading)?

Regarding your question about gravity from only one of two objects, it doesn't matter. Even if you ignore the gravitational field generated by one of a pair of bodies (which is quite often done in the case of relatively small objects interacting with much larger objects, say a bowling ball or a space station, and the earth), the gravitational field generated by the remaining object (for example the earth) still results in an attractive force between the two bodies (for example the Earth and bowling ball). In the case of a bowling ball and the earth, almost all of the gravitational force between the two objects is due to the mass of the earth. The Earth is pulled towards the bowling ball just as hard as the bowling ball is pulled towards the earth, because of the gravitational effects due to the mass of the earth. The increase in this pulling force due to the mass bowling ball is insignifcant.

 

[franznietzsche]

I think this question theoreticaly makes sence.
Here is what I think would happen. As Sun's gravitational field is blocked, the Earth's would act on Sun. And because Earth acts with force on Sun, the Sun must act on Earth too with equal but opposite force. The only difference would be the magnitude of force. It would be Gm/r, where m is Earths mass.
Thus - no paradox

Where do I start.


First off: A general rule in theoretical physics--fields are made up. Completely fabricated. They are a mathematical construct with no reality--you cannot measure fields (well, with one exception that I am aware of, but its not gravity). Fields are really just a bookeeping tool to simplify the descriptions of interactions--which are real.

So you cannot block the sun's gravitational field--it doesn't exist. Further, in General Relativity, gravity isn't even an interaction. So there isn't even an interaction to block. The situation suggested simply makes no sense.

 

[xAxis]

quote Jeff Reid:

"Even if you ignore the gravitational field generated by one of a pair of bodies (which is quite often done in the case of relatively small objects interacting with much larger objects, say a bowling ball or a space station, and the earth), the gravitational field generated by the remaining object (for example the earth) still results in an attractive force between the two bodies (for example the Earth and bowling ball). In the case of a bowling ball and the earth, almost all of the gravitational force between the two objects is due to the mass of the earth. The Earth is pulled towards the bowling ball just as hard as the bowling ball is pulled towards the earth, because of the gravitational effects due to the mass of the earth. The increase in this pulling force due to the mass bowling ball is insignifcant."

yes, that's exactly what I ment in my first post. I even wanted to take that same example, with Earth and pebble, but was scared out of it by rbj's and Danger's reply :)
As for general Relativity, gravitation is not even a force, and so I think there is no action and reaction.
As for my second example, here is how I calculate. The boy pulls on girl with the force of 10N. By reaction he is pulled by 10N force, plus the girls pull of 5N acting also on him, which makes 15N. The same goes for the girl.
So they are both acted on by the same force of 15N

 

[franznietzsche]

yes, that's exactly what I ment in my first post. I even wanted to take that same example, with Earth and pebble, but was scared out of it by rbj's and Danger's reply :)
As for general Relativity, gravitation is not even a force, and so I think there is no action and reaction.
As for my second example, here is how I calculate. The boy pulls on girl with the force of 10N. By reaction he is pulled by 10N force, plus the girls pull of 5N acting also on him, which makes 15N. The same goes for the girl.
So they are both acted on by the same force of 15N

No, opposite forces of 15 N.

Newton's third law is very poorly stated in that form, IMO. Much better the restate it as 'All internal forces in a system sum to zero', which is to say that the interactions of the elements of a system can change their positions relative to each other, but not change the position of the system's center of mass (relative to some external observer).

 

[Skhandelwal]

Since we are talking about Newton's 3rd law, I have got a question on it too. When I push a concrete wall(it is connected to nothing but the floor-no ceiling or neighbor walls) Is the force I am applying to it rebounding to me thus stating Newton's 3rd law? But if the force completely rebounds(which it does) where is the damage to the wall?(considering that if I push the wall forever, it will break sometime(just assume I won't break) Because if the force does damages the wall, it would be wasted there and wouldn't completely rebound, unless, when the force damages the wall, the energy released by the damage is equal to the energy required for it to damage. Which is why the rebound energy is equal. Am I right?

 

[xAxis]

You can't say force is rebounding. It's just there as long as you are pushing. Imagine you are pushing a car. Do you feel heaviness while doing that? Of course you do, and that's the force with which the car pushes you. The stronger you push, the hevier the car will push on you. So the reaction force is not rebounding, it is just there at the same moment as you start pushing.
The same with the wall. As you push against the wall, the wall pushes against you. It won't break because the strong intermolecular forces resist. When you break the wall, what happend? Some parts of the wall couldn't resist the push as it was strong enough to break the intermolecular forces. Let's say that you manage to break the part of the wall which is exactly one brick. At the moment of breaking, your push was probably the strongest. After that, that brick leaves the wall as it is not intermoleculary bound to it any more, and now you are pushing only the brick, which will quickly go forward. You will unwillingly reduce your pushing force, but at any time the force you are pushing, and the force you are pushed are equal but opposite.

 

[Skhandelwal]

Lets say that I am a bug and that my force against wall isn't enough to break it, but since I am keep pushing on it till infinity, wouldn't wall run out of energy to equal action to its reaction at some time? If it would, would that be same as breaking the wall by weaking its bonds or would it something else, like wall has used up all of its energy?

Also, the force I am applying, where does that force go? Does it work like this?

I apply a force on wall, that force weakens some bond, the energy released by the weakness is the reaction force.

 

[russ_watters]

No, it doesn't work that way. Force is not energy: look at the mathematical definitions of them.

A book sitting on a table exerts a constant force on that table for all of eternity with no energy consumption.

 

[Skhandelwal]

I read in dictionary and physics that force equals mass times acceleration and as far as I know, mass is energy. Therefore, the only way that book phenomenon made sense to me is if the table was keep rebounding the force of the book to the table and hence it was a cycle, but xaxis said no to that theory stating that the force applied from both side is their own, no cycle.

I am confused. I mean if force isn't energy, then what it is b/c I couldn't find the answer in the dictionary. All they described in dictionary is what it does, and gave its formula, not what it is.

 

[kmarinas86]

I read in dictionary and physics that force equals mass times acceleration

Correct, but energy is NOT just mass times acceleration. Work is measured in units of energy. Work = Force * Distance. Work/Distance = Force.

Distance matters. Distance matters. Distance matters. Distance matters.

 

[Skhandelwal]

So what is work...? I looked it up and on the dictionary, it states that work is transfer of energy. Which is exactly my point that when I apply force to something, I am transfering my energy to it from which russ watters disagrees. I am don't believe I am the one right here over him, b/c he is probably a professor and I am a high school senior. Can someone please clear this out for me?

 

[russ_watters]

mass is energy.

No. You are confusing these concepts. Mass can be converted to energy, but mass and energy are not the same thing.

I am confused. I mean if force isn't energy, then what it is b/c I couldn't find the answer in the dictionary. All they described in dictionary is what it does, and gave its formula, not what it is.

Again, look at the mathematical definitions. The units and the equations.

 

[russ_watters]

So what is work...? I looked it up and on the dictionary, it states that work is transfer of energy. Which is exactly my point that when I apply force to something, I am transfering my energy to it from which russ watters disagrees.

The dictionary definition is fine, but you need to stop attaching meanings to these words in your head. They don't mean what you think they do. You keep saying force is energy: it isn't, and the dictionary definition doesn't say it is. But to make it clearer, look at the mathematical definitions:

Energy is only transferred when there is motion: w=f*d

If you exert a force on something and it doesn't move, you are doing no work.

Also, don't allow your muscles to confuse you. Biological/chemical work is required to make your muscles do anything, but that doesn't have anything to do with the mechanical definition of work.

 

[kmarinas86]

So what is work...? I looked it up and on the dictionary, it states that work is transfer of energy. Which is exactly my point that when I apply force to something, I am transfering my energy to it from which russ watters disagrees. I am don't believe I am the one right here over him, b/c he is probably a professor and I am a high school senior. Can someone please clear this out for me?

Do you burn calories when pushing against the wall? Yes. Where does the energy go? It is mostly wasted in forms such as sound, heat, and infrared radiation. Not all energy fits neatly into the idea of "work" which equals force times distance. Force times distance doesn't necessarily mean acceleration provided that applied force (a vector) equals the drag force (a vector), which translates into constant velocity. In the case of pushing a wall, the forces on the ground, feet, limbs, joints, muscles, skin, organs, blood vessels, fingertips, wall, ceiling, etc. are all affected such that the net force is zero.

The force you apply on the wall is actually a repulsive electromagnetic force which prevents your atoms passing straight through the atoms of the wall. In fact, all pushing is short distance repulsion between things due to the repulsive electromagnetic force. All physical work is done by pushing, even if it is the back of the door handle which we are pulling. Pulling is simply a pushing force on an object towards you that is exerted on the opposite side of the object. It's still repulsion. All the attractive electromangnetic does in this case is provide the material stability that allows a net force to be applied while preventing the material from disintegrating. This "net force" is canceled out by the effect we have on the rest of the enviroment.

 

[Skhandelwal]

Specifically, that is known as normal force. I know about that. What I was wondering is taht if the energy is not transfered, meaning the object didn't move, then do I get my force back as appied it? Sort of like how you strech a rubberband, the rubberband gets back to its normal shape b/c it is the reaction, simply rebounding my force, however, if I apply too much force, then I break it and then, the force doesn't rebound, it transfers and never comes back. I don't know why I am having trouble understanding such a simple concept. I just think that when you push something, your energy still moves(as a force), but since the object doesn't move, it comes back to you. B/c if force is not energy than what is force? It has to be something, and if it is something then isn't it energy? I mean you gave me the formula for force by which I understood why force is zero but what is force made up of?

Also, if you smack a brick by the right technique, when you break it, your hand doesn't hurt(as in martial arts) but where is the action=reaction force there? However, if you are unable to break the brick, then your hand does hurt. It is like when you apply enough force, breaking something, there is no reaction back at you. B/c if there was, your hand was suppose to get hurt.

btw what does this statement mean, "In the modern view mass is not equivalent to energy. It is just that part of the energy of a body which is not kinetic energy" Does this mean that mass only acounts for potential energy since the kinetic is already being used?

 

[Chronos]

The operative concept to keep in mind here is that gravity is a conservative force. The Encyclopidia Brittanica sums it up nicely:

". . . The term conservative force comes from the fact that when a conservative force exists, it is possible to view the effects of the force in terms of a change in potential energy which keeps the mechanical energy conserved. . . ."

I think it is more appropriate to think of Newtons Laws as the laws of kinematic interactions [motion], not field interactions. It also important to keep in mind that a conservative force can NEVER do any [not even a single quanta] amount of work - much to the chagrin of aspiring perpetual motion machine inventors.

 

[jtbell]

What I was wondering is taht if the energy is not transfered, meaning the object didn't move, then do I get my force back as appied it?

Imagine yourself pushing hard against a wall for a couple of hours. How do you feel afterwards? Hot and sweating, right? The energy that you've expended has gone basically into heat, warming yourself up and evaporating some of your sweat.

Muscles are complex objects. I don't have any references handy, but I'm sure I've read about muscle fibers alternately contracting and relaxing, and "ratcheting" against each other. I can easily imagine them dissipating their work in the form of heat.

 

[Danger]

Moonbear can explain it more accurately if she becomes aware of this thread, but muscles do indeed 'ratchet'. I can't remember the specifics, but it's almost as if they are barbed, with one strand pulling the next along. This is from a SciAm article a year or two back that dealt with muscle regeneration, specifically in regard to how they grow in response to exercise. There was a reference to the same thing in an article somewhere about the development of artificial muscles for robotics and prosthetics.

 

[castaway]

there is no paradox for a hypothetical situation that is impossible. why waste your time on it? i can also dream up a pile of other paradoxes based on fantasy. here's one:

If Gandalf can summon giant eagles to fight the Nasgool in an air battle at the end, why couldn't he summon them earlier when needed in battle?

then the 3rd movie won't have won so many oscars lol

 

[Skhandelwal]

Ok, Imagine yourself pushing against a air(as if there a wall), after couple of hours, you will still be sweaty, the only reason not as much is b/c you have problem balancing.

 

[Tomsk]

Specifically, that is known as normal force. I know about that. What I was wondering is taht if the energy is not transfered, meaning the object didn't move, then do I get my force back as appied it? Sort of like how you strech a rubberband, the rubberband gets back to its normal shape b/c it is the reaction, simply rebounding my force, however, if I apply too much force, then I break it and then, the force doesn't rebound, it transfers and never comes back. I don't know why I am having trouble understanding such a simple concept. I just think that when you push something, your energy still moves(as a force), but since the object doesn't move, it comes back to you. B/c if force is not energy than what is force? It has to be something, and if it is something then isn't it energy? I mean you gave me the formula for force by which I understood why force is zero but what is force made up of?

When you stretch a rubber band, you do work on it, as the atoms in it have moved. It gains potential energy. Then when you release it, the rubber band converts the PE you put into it back into kinetic energy and some heat, returning it to its original state. If you put so much energy in it snaps, it releases the PE you put into it in the form of sound and KE.

Also, if you smack a brick by the right technique, when you break it, your hand doesn't hurt(as in martial arts) but where is the action=reaction force there? However, if you are unable to break the brick, then your hand does hurt. It is like when you apply enough force, breaking something, there is no reaction back at you. B/c if there was, your hand was suppose to get hurt.

The reaction force exists as the brick applying a force on your hand, but this doesn't mean you'll get hurt! Your hand will slow down while it is in contact with the brick. If you don't break it, the energy from your hand goes into the brick, and becomes sound or heat, but you haven't put enough into break it.

btw what does this statement mean, "In the modern view mass is not equivalent to energy. It is just that part of the energy of a body which is not kinetic energy" Does this mean that mass only acounts for potential energy since the kinetic is already being used?

This is quite hard to picture if you've not done relativity, it's best to think of mass and energy as different things. This is referring to the equation KE=mc^2(\gamma-1), with E=\gamma mc^2. You can see if the kinetic energy is zero, then the particle in question still has some energy! It's not potential energy, as PE depends on the particles' position relative to another particle, but a particle has E=mc^2 even if it's completely on its own.

I think it is more appropriate to think of Newtons Laws as the laws of kinematic interactions [motion], not field interactions. It also important to keep in mind that a conservative force can NEVER do any [not even a single quanta] amount of work - much to the chagrin of aspiring perpetual motion machine inventors.

I think I've missed something here. Why is that, exactly? I know that curl(F)=0 is the requirement for a conservative force, but how does this lead to it being unable to do work? If you integrate up surely you get KE+PE=E, E being constant. So if there's a change in potential, work is done. What have I missed?

 

[russ_watters]

Ok, Imagine yourself pushing against a air(as if there a wall), after couple of hours, you will still be sweaty, the only reason not as much is b/c you have problem balancing.

Huh? That's not even a complete sentence.

Look, we've explained how energy works. You aren't listening to the answers. All of the questions you are asking go right back to the definition of work/energy already given. So it is time for us to stop answering and start making you give the answers. So: Given the definition of mechanical work/energy (w=f*d), you tell us whether energy is involved in that scenario and explain why.

 

[Skhandelwal]

thats seems like a good idea,(btw, the reason I was still asking is that you never really told me what force is made up of) Whatever you told me makes sense mathematically, but doesn't quite fit in into my mind.(may be I am just dumb) Here is what I got so far, no matter how much force you apply, if there is no motion, there is no transfer of energy. I guess the problem I am having is the concept I had that force is always energy. But know I know that force is only energy when there is acceleration. Well, when there is no acceleration, what is force?(what is it made up of?)

 

[russ_watters]

f=ma just tells you how force causes (or is caused by) acceleration of a mass. But force can also come from gravity, a stretched rubber band, a magnetic field, etc. Forces like that come from stored potential energy and generally require energy to create the situation where the force exists. But once the potential energy is stored, there is no further transfer of energy.

 

[rcgldr]

Force and energy are not the same, just like torque and power are not the same. Mass and energy are not the same, but you can convert mass to energy and energy back to mass.

Here are some definitions:

work = force x distance

if the units are pounds and feet, then

work (pound-feet) = force (pound) x distance (feet)

Energy is one of the states of an object.

For mechanical physics one type of energy is kinetic:

kinetic energy = 1/2 x mass x speed^2

If there are no losses due to friction, then work done on an object changes it kinetic energy. If you apply a force of 1 pound for 10 feet, or 10 pounds for 1 foot, the kinetic energy changes by 10 pound feet.

Assume it's a 1 slug (32.174 pound) mass, and not moving. You apply a 1035.166 pound force for 10 feet, for a 10351.66 pound feet increase in kinetic energy. Redoing the math:

Acceleration = 1035.166 pound force / 32.174 pound mass = 32.174 feet / sec^2 = 1 g of acceleration

This amount of acceleration is applied for 10 feet:

d = 1/2 a t^2
t = sqrt (2 x d / a) = sqrt(2 x 10 feet / 32.174 (feet / sec^2) = .788429 sec

v = a t = 32.174 feet / sec^2 x .788429 sec = 25.3669 feet / sec

kinetic energy = 1/2 m v^2 = 1/2 x 32.174 pound x 25.3669^2 = 10351.66 pound feet

So the increase in kinetic energy does equal the work done.

Power = a rate of work:

Power = work / time = force x (distance / time) = force x speed

Horsepower = force (pounds) x speed (mph) / 375 (conversion factor)

 

[Skhandelwal]

So when you force an object to work, do you increase it's kinetic energy or unleash it's potential?

 

[Danger]

That last question is a bit backwards. You can't force something to do work. If you try, all that you're doing is using it as a transfer medium for the work that you're doing. For example, if you force one end of a lever downward in order to lift something with the other end, you are doing the work and the lever is transfering it to the load.
If you force something into a situation where it can do work, such as winding up a rubber band, then you are increasing its potential energy.
When you let it go to do whatever it's going to do, then you're unleashing its kinetic energy.

 

[Skhandelwal]

aah, I get it, thx. But by that def.,, You can't accelerate energy b/c then you get undef. by the formula f=ma. Right?

 

[loom91]

Of course the paradoxes presented here are false paradoxes, but unless I'm mistaken N3L has been disproved, hasn't it? When you have fields propagating at finite velocities instead of instantaneous action at a distance as envisaged by Newton, N3L need not hold, either in the strong or the weak form. Examples can be found even in Classical Electrodynamics, though conservation of linear momentum would still hold with the introduction of field momentum into the mixture. In quantum mechanics of course works with energies and momenta instead of forces, so there's no question of N3L holding, though PCLM is once again there.

At least, that is what I was told (we haven't yet covered EM in detail). Is that right?