How come there is no conservation of force?

[Dadface]

How does Newtons third law fail in electromagnetism?When we put Biot and Savarts law to the test, for example with two parallel current carrying conductors we find that the force on conductor A is equal and opposite to that on conductor B.Are there any conductor geometries where this is not the case?

 

[mikeph]

How does Newtons third law fail in electromagnetism?When we put Biot and Savarts law to the test, for example with two parallel current carrying conductors we find that the force on conductor A is equal and opposite to that on conductor B.Are there any conductor geometries where this is not the case?

If an electron radiates, it has a force on it, but where is the opposing force? Either (1) you attribute this to the radiation, and I don't see how, or (2) you assume the radiation ultimately interacts with a second electron, but the radiation has a finite travel time so you no longer have that net force is instantaneously conserved.

With the Biot-Savart law, what if the two conductors are moved apart?

 

[Studiot]

Conservation means the same total before and after.

There are forces acting before, there are none after I cut the string.
These forces have suddenly been removed from the universe.

There is no balance of force for a body falling freely under gravity.

\sum {F \ne } 0

Nobody need violate Newton or dream up complicated examples.

 

[mikeph]

There is no balance of force for a body falling freely under gravity.

\sum {F \ne } 0

Nobody need violate Newton or dream up complicated examples.

That's only half the system- there must be at least two bodies interacting with the gravitational field or nothing will "fall".

 

[Studiot]

That's only half the system- there must be at least two bodies interacting with the gravitational field or nothing will "fall".

Where in Newtons first or second law does it say that there have to be two bodies?

 

[mikeph]

Where in Newtons first or second law does it say that there have to be two bodies?

Newton's law of Gravitation, there must be at least two bodies for one to feel a gravitational force.

 

[Dadface]

If an electron radiates, it has a force on it, but where is the opposing force? Either (1) you attribute this to the radiation, and I don't see how, or (2) you assume the radiation ultimately interacts with a second electron, but the radiation has a finite travel time so you no longer have that net force is instantaneously conserved.

With the Biot-Savart law, what if the two conductors are moved apart?

1.Because the electron is charged it is an integral part of the field it interacts with.If it decelerates and radiates due to it approaching a positively charged metal plate then during the event the plate repels the electron and the electron repels the plate

2.The force on each one decreases by the same amount.

 

[mikeph]

The force on each one decreases by the same amount.

But if they are 1 light year apart and one cable is cut the current stops and there is no force, but the other one is still feeling the force for another year. Newton's third law fails during that year.

 

[Studiot]

Newton's law of Gravitation, there must be at least two bodies for one to feel a gravitational force.

C'mon we are talking about Force, for which Newton had three laws.

My version of the first two does not mention the number of particles and the third is usually applied via a free body diagram in which the interaction with the rest of the universe is summed to one force acting across the boundary.

I can successfully apply any or all of these laws to a free body system comprising my particle, and the force due to gravity acting across the boundary.
I do not need to consider the effect on the other end or the source of that force.

This is fundamental to Newtonian mechanics.

This is really very simple, why make it complicated?

 

[mikeph]

My version of the first two does not mention the number of particles and the third is usually applied via a free body diagram in which the interaction with the rest of the universe is summed to one force acting across the boundary.

You would never use Newton's third law in such a way because that gives you no information.

Of course the conservation is violated locally. This is like me saying "energy conservation is violated inside a beaker of water when water evaporates out of it". Take a step back and the problem goes away.

You are talking about a particle falling in a gravitational field. Well I am saying the second part of the force which completes the conservation is outside your realm of consideration- but it must exist somewhere in the universe for there to be a gravitational field! So let's consider that as well and the conservation is sustained.

 

[Dadface]

But if they are 1 light year apart and one cable is cut the current stops and there is no force, but the other one is still feeling the force for another year. Newton's third law fails during that year.

This is such an interesting point and it is connected with fields in general.

 

[Studiot]

Mikey,
I get the impression you are just arguing for the sake of it.

When responding to my comments, you either only address part (1) or address a different statement from the one made (2) or simply state an inaccuracy (3)

(1)

If I pump up a bicycle tyre I am adding to its internal energy.
This energy is still there when I stop pumping and can be recovered at some later time.

That is what is meant by conservation of energy.

If I whirl a stone around my head on a string, there are forces acting and there is euqilibrium in the balance of tension and inertial force.
If I cut the string the forces cease and cannot be recovered.

There is no conservation of force.

By the way what about D'Alembert's principle and moments?
Forces have both direct and indirect effects.
Would you also conserve these?
There is no coresponding pair for energy.

my statement

Adding all the forces together you arrive at 0 N before and after you cut the string,
d/dt of the sum of forces = 0 so the net force is conserved.

your reply

(2)

Where in Newtons first or second law does it say that there have to be two bodies?

my statement

Newton's law of Gravitation, there must be at least two bodies for one to feel a gravitational force.

your reply

(3)

……….Newton had three laws.……….. I can successfully apply any or all of these laws to a free body system comprising my particle…………

my statement

You would never use Newton's third law in such a way because that gives you no information.

your reply

Why would I never use it in that way?

Surely even schoolboys doing junior high physics use Newton's third law in a free body analysis when they discuss the reaction acting on a weight sitting on a table.

You are talking about a particle falling in a gravitational field. Well I am saying the second part of the force which completes the conservation is outside your realm of consideration- but it must exist somewhere in the universe for there to be a gravitational field! So let's consider that as well and the conservation is sustained.

What exactly do you mean by this? Are you saying that forces have “second parts” somewhere in the universe?

Or are you saying we have to consider the entire universe every time we calculate a force balance for a free body?

Bear in mind that although I gave a purely gravitational example the body cannot determine the source of its acceleration as per the famous lift or elevator example.

Also bear in mind what I said about D’Alembert, which you did not respond to.

 

[mikeph]

This is taking too long, I am sorry. I shortened your posts because I was trying to focus on what I felt was the error, but responding to multi-quotes is not what I had in mind when entering this debate.

I don't know how I have been so unclear to you.

 

[Studiot]

Mikey perhaps you would like to consider a 'conservation law' system of forces that posseses zero resultant, yet does work?

(D'Alembert again)

 

[mikeph]

For example two masses moving toward each other?

The potential energy decreases as work is done by the gravitational field on the masses. But the sum of the net forces is once again zero. It is always zero. Therefore it is conserved.

 

[Studiot]

Don't you like D'Alembert?

I was thinking of couples and moments.

 

[mikeph]

How is the sum of forces not conserved? That is the question in the title: "how come there is no conservation of force?".What do couples and moments have to do with it?

 

[Phrak]

I just want to mention I lost track of what you guys were talking about a while ago. Yea, I don't get what you guys are debating anymore.

To be blunt Nearly everyone is either agreeing that conservation of force is a part of Newton's three laws--and it is, or protecting the all-important ego.

Anyway, at face value it's a fairly uninteresting fact that conservation of force is a direct result of Newton's three laws that you have been studying.

It might be more interesting to discover if this rather unintersting thing as it stands has more interesting consequences when examined in the light of modern ideas, but that ain't gunna happen here in PF.

 

[gabbagabbahey]

Phrak, you haven't addressed my question yet: what happens when there are momentum carrying fields involved?

If \sum_i\textbf{p}_i represents the sum of the momenta of all particles in a closed system, it needn't be constant, since fields can transfer momentum to particles. Momentum for the system will still be conserved, but only when you include the momentum in the fields (which will be an integral of a momentum density). However, when fields are present (even if you include their sources in your system), the sum of the forces on all the particles in a system need not by zero, even if momentum is conserved .

Consider a field propagating at finite speed (like light) towards a stationary particle. Prior to the interaction of the field and the particle, there are no forces acting on either and the only momentum is stored in the field. After the two interact, some momentum may be transferred to the particle, and hence some force was exerted on it. Momentum is conserved in this interaction, but force is not since there is no equal and opposite force exerted on the field (which is presumed massless).

 

[Studiot]

The conservationists need to answer several questions.

1) Non concurrent forces acting on a system may well have

\sum {F = 0}

However there may also be a resultant moment which would be non existent for concurrent forces.
In this situation since there is no resultant force the system does not translate, but it will rotate. Henece there will be a vector associated with this rotation. How is this cosnerved?

2) A system in say an accelerating elevator cannot distinguish between inertial forces, which are not balanced by any Newtons third law force and a field force such as gravity which they say is.

My analogy between the tyre/balloon and a whirling weight has not been properly answered either.

The plain fact is that the conservations seem to think all thay have to do to prove their policy is to declare it so.

This is not good enough.

No personal criticism is meant by any of this.

 

[russ_watters]

The forces vary but their sum does not.


Applying Newton's 3rd law at every instant should give sum(Force vectors) = 0 at every time. Isn't this a stronger statement than normal conservation?

I don't know if it is a "stronger" statement, but it is a different statement.

 

[Phrak]

Phrak, what if the system contains momentum-carrying fields? What happens to \sum_{i} \textbf{p}_i when momentum is transferred from a field to a particle?

Phrak, you haven't addressed my question yet: what happens when there are momentum carrying fields involved?

If \sum_i\textbf{p}_i represents the sum of the momenta of all particles in a closed system, it needn't be constant, since fields can transfer momentum to particles. Momentum for the system will still be conserved, but only when you include the momentum in the fields (which will be an integral of a momentum density). However, when fields are present (even if you include their sources in your system), the sum of the forces on all the particles in a system need not by zero, even if momentum is conserved .

Consider a field propagating at finite speed (like light) towards a stationary particle. Prior to the interaction of the field and the particle, there are no forces acting on either and the only momentum is stored in the field. After the two interact, some momentum may be transferred to the particle, and hence some force was exerted on it. Momentum is conserved in this interaction, but force is not since there is no equal and opposite force exerted on the field (which is presumed massless).

I'd like to know the premises you are using. I am assuming Newton's three laws. From the OPs second post, this is the context in which the question was being asked. It should go without saying that all the other peripheral premises such as homogeneity of space should be assumed, right?

 

[Studiot]

Let us review what we mean by conservation, in the light of conservation of energy which we are all agreed on, and see how the concept can or cannot be applied to force.

Energy is a positive definite scalar quantity that can be simply aggregated. An energy change may be given a positive or negaive sign, but that is merely an accounting. The energy is always positive. It is definite because equality to zero implies no energy at all.

Energy conservation implies the statement "energy can be neither created nor destroyed". The total energy before, during and after a process never changes. Energy is merely transformed from one form to another or moved from one location to another.

So one thing I cannot do with this type of conservation is to deploy a law that allows the total energy to vary ie to be turned on or off.

Now consider the implication of applying this to a vector quantity.

Let us consider an athlete exercising in a gym on a running platform.
The forward velocity of the runner exactly matches the backwards velocity of the platform so the net velocity of the runner is zero. If it does not the runner moves forwards or backwards.

What is conserved in this situation?
It is certainly not velocity. It is location.
Can I justify the statement the total velocity does not change, whether the runner moves forwards, backwards or is stationary? Obviously not.
Nor can I justify the statement that zero net velocity means the absence of velocity - ask the runner how fast he is running.
And what of the total velocity in the universe if he runs or goes down the pub instead and does not run?

I think situation with force is more akin to the situation with velocity than with energy.

That is why I originally simply said that the concept was not applicable to force.