How do Newton's laws of motion relate to conservation of energy?

In summary: Your trying to equate physical law to an axiom is fallacious.It's equivocating,not fallacious.In other words,there are no differences,they are the same thing... Daniel.Starting with the definitions of momentum and force, we can derive the laws of motion. But in order to derive the laws of conservation of momentum and energy, we need to use the laws of motion as axioms. So yes, the conservation laws are more fundamental in that sense.However, this does not mean that the laws of motion are not fundamental or that they are just a result of the conservation laws. They are all interconnected and play important roles in understanding the behavior of physical systems. In summary, the impulse momentum theorem and
  • #1
UrbanXrisis
1,196
1
how does the impulse momentum theorem and conservation of momentum show the existence of the third law of motion?

impulse momentum theorem- the force of an object a that hits object b will create a force. The force that object b exerts back on object a should be the same as the force object a exerts on object b. So the impulse should be equal in magnitude.

conservation of momentum-since the sum of the initial velocities of both objects are equal to the sum of the final velocities. Therefore, there is the same amount of force exerted back on each objects.

did I explain this right?
 
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  • #2
any suggestions?
 
  • #3
Force is the derivative of momentum...so... conservation of momentum has no different from Newtons 3rd law
 
  • #5
What Vincent is saying but more formally.

Consider a closed system of two bodies A and B, with no other forces acting on the system. Let the momentum of A be [itex]\vec{p_A}[/itex] and that of B be [itex]\vec{p_B}[/itex].

Now let us say the two bodies interact such that the momentum of A changes by [itex]\Delta \vec{p_A}[/itex] and that of B by [itex]\Delta \vec{p_B}[/itex].

By the law of conservation of linear momentum,

[tex]\Delta \vec{p_A} + \Delta \vec{p_B} = 0[/tex] since no net force acts on the system.

Hence [tex]\Delta \vec{p_A} = - \Delta \vec{p_B}[/tex]

Take the first differential with respect to time.

[tex]\frac{d}{dt}(\Delta \vec{p_A}) = - \frac{d}{dt}(\Delta \vec{p_B})[/tex]

But by Newton's second law, the derivative of momentum w.r.t. time is equal to force.

Hence [tex]\vec{F_A} = - \vec{F_B}[/tex]

and we've proved Newton's third law.
 
  • #6
what about the impulse momentum theorem?
 
  • #7
Don't be mislead.U cannot prove the thord law...It is an axiom.The theorems regarding the conservation of total energy and momentum in isolated systems are proved via the three laws.So what the previous posters tried to show is conceptually and logically garbage.

Daniel.
 
  • #8
It is an axiom.The theorems regarding the conservation of total energy and momentum in isolated systems are proved via the three laws.
What is axiom? and what is fundamental law?
if you DEFINE conservation of momentum is more FUNDAMENTAL than 3rd law.. you can say 3rd law can PROVED by conservation of momentum.. however, if you DEFINE 3rd law is more FUNDAMENTAL.. sure, conservation of momentum can proved by 3rd law..
In mathematics, this relation is called equalvance.. none of them are more fundamental, they are the same thing which appears differently..
In physics, we usually called the conservation law is more fundamental..
 
  • #9
I surely as hell resent those pleonastic expressions.Things are fundamental and that's it.No more,no less.
Conservation laws are not fundamental.They appear in ideal situations,usually unencountered in nature.I'm sure u weren't aware of that,else u would have deleted your post.
While principles/postulates/axioms,well,they are the basis.Newton's laws go along with the principles of QM,SR,GR,Thermodynamics,Statistical Physics,QFT into the axiomatic structure of physics,of major theories in physics.

One cannot have equivalence between a consequence seen a fortunate particular case of an axiom and the axiom...Elementary logics...I believe science is based on logics... :rolleyes:


Daniel.
 
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  • #10
impulse momentum theorem:
I=Ft
I/t=F
F=F

This shows the relationship between the 3rd law and the theorem correct?
 
  • #11
dextercioby said:
Don't be mislead.U cannot prove the thord law...It is an axiom.The theorems regarding the conservation of total energy and momentum in isolated systems are proved via the three laws.So what the previous posters tried to show is conceptually and logically garbage.

Daniel.

It's not "garbage" as you so eloquently put it. There is a logical dependence of the third law on the law of conservation of momentum and the second law. Of course, you can argue the other way, saying the three laws came first and conservation of momentum is a consequence. But that's just the chicken and the egg.

There are no true axioms in physics, because it is an empirical system. Physical "laws" are statements we make based on inductive reasoning to try and explain the observations of many, many repeated experiments. Just because it is a "law" does not mean it cannot be disproved by a completely unexpected observation 10 years down the line. Contrast this with a mathematical axiom which is truly unfalsifiable because it is simply defined that way and the logical structure is built from the ground up. Your trying to equate physical law to an axiom is fallacious.
 
  • #12
UrbanXrisis said:
impulse momentum theorem:
I=Ft
I/t=F
F=F

This shows the relationship between the 3rd law and the theorem correct?

No.I'll say it again and will say it whenever necessary:there are rules imposed by logics.The only valid methods would imply determining the laws of momentum and energy conservation starting with the fundamental laws of Newton...

Daniel.
 
  • #13
dextercioby said:
No.I'll say it again and will say it whenever necessary:there are rules imposed by logics.The only valid methods would imply determining the laws of momentum and energy conservation starting with the fundamental laws of Newton...

Daniel.

And why should the conservation laws not be the "fundamental" ones and the laws of Newton derive thereof ?
 
  • #14
Curious3141 said:
It's not "garbage" as you so eloquently put it. There is a logical dependence of the third law on the law of conservation of momentum and the second law.

It's true.There is:the three laws imply everything at classical macroscopical level.




Curious3141 said:
But that's just the chicken and the egg.

Let's leave analogies and collateral discussions to the phylosophers,okay??They have to make a living,right??



Curious3141 said:
There are no true axioms in physics,because it is an empirical system.

False is the conclusion,true is the hypothesis...I would advise you to read more.Science needs theory.Theory is logics and mathematically based.Axioms are a part of both...

Curious3141 said:
Physical "laws" are statements we make based on inductive reasoning to try and explain the observations of many, many repeated experiments.

True,however modern theoretical physics doesn't have the empirical basis anymore.Yet it's unanimously accepted,simply because it lack the only the only way of falsifying...

Curious3141 said:
Just because it is a "law" does not mean it cannot be disproved by a completely unexpected observation 10 years down the line.

True,science in general is full of theories overturned...

Curious3141 said:
Contrast this with a mathematical axiom which is truly unfalsifiable because it is simply defined that way and the logical structure is built from the ground up.

Really??Compare that to the fact:by definition,force is the time derivative of momentum.Is there any difference??Definitions are in a sense axioms... :wink: You mean physics does not have "logical structure (...) built from the ground up"? What planet have you been living on??

Curious3141 said:
Your trying to equate physical law to an axiom is fallacious.

Nope.It's irrefutable.If experiment falsfies the results of a theory,then its axioms were wrong.However,we can find a new theory...New axioms,new theorems,new sylogisms and this time confirmation of results... :cool:


Daniel.
 
  • #15
Curious3141 said:
And why should the conservation laws not be the "fundamental" ones and the laws of Newton derive thereof ?

Logics??One of them is a consequence of the other,seen a restriction?Particular case,perhaps??I believe i said that before...Can u derive Schroedinger's equation using the equation of continuity for the localization probability density?

Daniel.

PS.Read more physics...
 
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  • #16
dextercioby said:
It's true.There is:the three laws imply everything at classical macroscopical level.

OK, derive the principle of conservation of energy from Newton's three laws of motion.

Not just conservation of kinetic energy, but of all forms, including the first law of thermodynamics.

Conservation of energy IS a fundamental proposition in Physics. It is not logically dependent on Newton's three laws for its truth.

So you see, there are other fundamental propositions upon which Physics rest, it's not just Newton's three laws.

BTW, "fundamental" is a rather nebulous word, especially when we're trying to grade it. Conservation of momentum is to me, just as fundamental as Newton's three laws. As I think I have shown, conservation of momentum is actually equivalent to the 2nd and third law of Newton. The major reason for splitting up the law into two in Newton's formulation is to define the concept of a force as a rate of change of momentum. Force is no more fundamental than momentum, the former is just the first differential of the latter wrt time.

Let's leave analogies and collateral discussions to the phylosophers,okay??They have to make a living,right??

We ARE discussing the philosophy of science. You opened the door, remember ?

False is the conclusion,true is the hypothesis...I would advise you to read more.Science needs theory.Theory is logics and mathematically based.Axioms are a part of both...

A mathematical axiom is FUNDAMENTALLY DIFFERENT from a physical "axiom". A mathematical axiom can exist with totally *no* reference *whatsoever* to the "real world" of physical objects. A physical "axiom" or law or principle absolutely NEEDS to say something about something in the real world. Don't you see this very basic difference ?

True,however modern theoretical physics doesn't have the empirical basis anymore.

Of course it does ! Just because QM involves a lot of fancy mathematics doesn't mean the conclusions can stand unsupported by empirical verification. Why do you think so much money is spent building humongous particle accelerators and colliders, if not to verify the fruits of mathematical searching ?


Yet it's unanimously accepted,simply because it lack the only the only way of falsifying...

Even the most abstruse theory, like the ones that talk about superstrings and what not, are constructed to lend mathematical coherence to a greater model that CAN be verified in the real world. If a theory makes absolutely no predictions that can either directly, or through ramifications thereof, be falsified, then it is not a scientific theory and has no merit.


Really??Compare that to the fact:by definition,force is the time derivative of momentum.Is there any difference??

1st proposition : F = dp/dt

2nd proposition : 1 is a natural number.

The 1st proposition defines Force. It depends on the concept of momentum for its definition. However, forces can be measured by physical instruments, as can momentum, so they are both "real world entities". It is remotely possible that 50 years from now, an extremely subtle physical effect becomes apparent that changes this relationship. This would negate the proposition.

This is not so far fetched. If one were to look back to the 19th Century and question the validity of "F = ma = m(dv/dt)", one would be made a laughing stock. Of course, now we know that isn't correct, since mass alters with motion. Even though F = dp/dt is still correct at the moment, can you really rule out another paradigm shift in thought in the future ? :biggrin:

The 2nd proposition is Peano's first axiom. It relates two concepts : "1" and "natural number". Neither of these has any real meaning in the "real world". Although we can define the cardinality of a real world set using the naturals, the mathematical definition does not depend on the nature of the physical world for its veracity. The whole Universe can dissolve away tomorrow, leaving only one self aware particle and the particle can still cognize the successor of one, two, even though it cannot find anything to count using this new number.

Definitions are in a sense axioms... :wink: You mean physics does not have "logical structure (...) built from the ground up"? What planet have you been living on??

Let's not assume airs here. Physics is much more bread and butter than mathematics, and is far more pragmatic. This need not be pragmatic in the sense of inventing new machines to do stuff, but can also be the pragmatism of needing to tie up observations of the physical world into a coherent theory. Mathematics can exist solely for the pleasure of an arbitrary game of the imagination.

Nope.It's irrefutable.If experiment falsfies the results of a theory,then its axioms were wrong.However,we can find a new theory...New axioms,new theorems,new sylogisms and this time confirmation of results... :cool:

You've just proved my point ! Your physical "axioms" are simply tentative truisms that can be falsified ! Mathematical axioms can NEVER be falsified. They can be undecidable in a theoretical framework (like the Axiom of Choice in ZF set theory) but cannot be proven "wrong", simply because they are by definition "right". Always and forever.

PS.Read more physics...

I'll get right on it. In the meantime, read more formal logic. :biggrin:
 
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1. What is the Third Law of Thermodynamics?

The Third Law of Thermodynamics states that the entropy of a perfect crystal at absolute zero temperature is zero. In other words, as the temperature of a perfect crystal approaches absolute zero, the disorder or randomness of its molecules also approaches zero.

2. How is the Third Law of Thermodynamics related to the other laws?

The Third Law of Thermodynamics is closely related to the First and Second Laws of Thermodynamics. The First Law states that energy cannot be created or destroyed, only transferred or converted. The Second Law states that the total entropy of a closed system can never decrease. The Third Law provides a baseline for measuring entropy, as it states that the minimum possible entropy is zero at absolute zero temperature.

3. What is the significance of the Third Law of Thermodynamics?

The Third Law of Thermodynamics has several important implications in the field of thermodynamics. It allows for the calculation of absolute entropies, which are useful in determining the stability and spontaneity of reactions. It also helps to explain why certain substances, such as noble gases, have such low melting and boiling points.

4. Can the Third Law of Thermodynamics be violated?

No, the Third Law of Thermodynamics is a fundamental principle of thermodynamics and has been shown to hold true in countless experiments. However, there are some exceptions in certain systems, such as supercooled liquids, where the Third Law may not hold exactly.

5. How does the Third Law of Thermodynamics relate to the concept of absolute zero?

The Third Law of Thermodynamics defines the concept of absolute zero, which is the lowest possible temperature that can be reached. At absolute zero, the entropy of a perfect crystal is zero, meaning that there is no disorder or randomness in its molecules. This is the only temperature at which the Third Law holds true.

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