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polaris12
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title says it all
I don't really like that - I don't think it addresses the OP's question and I'm not really sure it is correct anyway. The definition of "conserve" is "to hold (a property) constant during an interaction or process". What I tried to convey is that this word doesn't really apply to force, which the OP already instinctively knows, which is why the question was asked.Phrak said:I hadn't really thought about it. Excuse me if the mathematics is too advanced for you. It's a very thoughtful question.
Where conservation of momentum over a region might be expressed as
[tex]\sum \frac{d\textbf{p}}{dt} = 0 \mbox{~or~} \sum \textbf{F} = 0[/tex]
then the conservation of force is already implicit in the conservation of momentum.
[tex]\sum \frac{d^2\textbf{p} }{dt^2} = 0 [/tex]
We could go on and on with this and say that impulse, and so forth, are conserved.
Correct. This has nothing to do with Newton's third law, however.Andy Resnick said:There are 'conservative' forces, but not all forces are conservative forces- friction, for example. Conservative forces are derivable from a potential.
The Earth and Moon are not in contact with one another, yet the gravitational force exerted by the Earth on the Moon is equal but opposite to the gravitational force exerted by the Moon on the Earth.Newton's third law F12 = -F21 should be considered a definition of *contact* forces, not as a general property of 'force'- confusing the two is what leads to the example of pulling a cart and finding that no matter how hard you pull, the cart can't move.
Sorry, I've missed this point.The weak form of Newton's third law follows from conservation of linear momentum. Add in conservation of angular momentum and you get the strong form of Newton's third law. The derivations implicitly assume that no momentum is stored in the fields that generate these forces. This is not always true; Newton's third law does not hold in such domains.
D H said:<snip> I'm going to side with Russ, "The word 'conserved', though, doesn't really apply."
<snip>
Andy Resnick said:My mistake.
Force is not a conserved quantity, for the reasons enumerated above.
The only hand waving was in that post. You assumed Newton's third law to prove Newton's third law. Newton's third law does not always hold. The Biot-Savart law, for example, violates Newton's third law. That shouldn't be all that surprising; Maxwell's equations are inconsistent with Newtonian mechanics. Aside: The original intent of the Michelson Morley experiment was to disprove the claims of those upstart E&M physicists. As we all know, that was not the outcome of that experiment.Phrak said:How do you justify this wand waving without showing that the mathematical proof I presented above to be false or not appicable?
Phrak said:How do you justify this wand waving without showing that the mathematical proof I presented above to be false or not appicable?
The sum of the force vectors is equal and opposte, but not conserved. Equal and opposite doesn't include the concept of invariant over time - as I pointed out, the forces do vary over time.Phrak said:In common usage a conservation law is something invariant over time.
Consider your collision of two billiard balls. During every collision dp/dt of one billiard ball is equal and opposite to the dp/dt of the other. That is to say, the sum of the force vectors is conserved.
Again, the concept of "over time" doesn't appear in that equation and without it, the word "conserved" doesn't apply. What you are really saying is just that that equation is always true over a period of time - as opposed to 'this time-dependent quantity is always constant'.Phrak said:Well, I'm not in agreement with some posters. Force really is conserved. It's just not very interesting to say that in homogeneous space
[tex]\frac{d}{dt}\sum 0 = 0 \ .[/tex]
russ_watters said:The sum of the force vectors is equal and opposte, but not conserved. Equal and opposite doesn't include the concept of invariant over time - as I pointed out, the forces do vary over time.
Studiot said: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.
D H said:But what they are saying is wrong. Newton's third law is not a universal law. It can fail in electromagnetism.
If force is conserved, what is the symmetry of nature that is responsible for this?
Dadface said: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?
Studiot said:There is no balance of force for a body falling freely under gravity.
[tex]\sum {F \ne } 0[/tex]
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".