Thread: Questions regarding Newtonian mechanics

This is the first of a two part question. (possibly more, depending on your answers) Please restrict your answers to Newtonian mechanics only. Please participate even if someone else has already posted your answer.



For this thought experiment, the universe consists only of the two magnets illustrated above. No other outside forces are involved. Both magnets have the same inertial mass. Which of the following is true?

1) The meeting point of the two magnets will depend on the strength of the magnetic fields. If the fields are equal in strength, then they will meet at the center of mass. If magnet A has the greater field strength then they will meet to the left side of the center of mass. If magnet B has the greater field strength then they will meet to the right of the center of mass.

2) Same as above except reversed. If the field strengths are equal then they will meet at the center of mass. If the magnetic field strength of A > B then they will meet to the right of the center of mass. If the magnetic field strength of B > A then they will meet to the left of the center of mass.

3) The magnets will always meet at the center of mass regardless of the difference in magnetic field strengths.

4) Other. Please explain.

The center of mass of this system should not move under any circumstances, by conservation of momentum.

Originally Posted by MagiMaster

The center of mass of this system should not move under any circumstances, by conservation of momentum.

correct.

And since the two magnets will meet they will meet at that center of mass.

All of this is quite independent of the field strength of either magnet, so long as it is not zero.

It in fact applies if one of the magnets is simply replaced by a magnetic material, like iron, with no intrinsic magnetic field.

This sort of problem gets somewhat dicey if one replaces the magnets with moving electric charges since then the forces are not directed linearly away from the bodies involved. See for instance the cautions in Goldstein's Classical Mechanics.

MagiMaster and DrRocket are correct. The correct answer is number 3.

Here is the second question.



For this thought experiment, the universe consists only of the two planets illustrated above. No other outside forces are involved. Both planets have the same inertial mass. But their active gravitational mass is variable. Active gravitational mass is a measure of the strength of an object’s gravitational flux. Even though this universe assumes that the equivalence principle is not valid for active gravitational mass, there is a correct answer to this question using currently accepted Newtonian methodology. With that in mind, which of the following is true?

1) The meeting point of the two planets will depend on the strength of the gravitational fields. If the fields are equal in strength, then they will meet at the center of mass. If planet A has the greater field strength then they will meet to the left side of the center of mass. If planet B has the greater field strength then they will meet to the right of the center of mass.

2) Same as above except reversed. If the field strengths are equal then they will meet at the center of mass. If the gravitational field strength of A > B then they will meet to the right of the center of mass. If the gravitational field strength of B > A then they will meet to the left of the center of mass.

3) The planets will always meet at the center of mass regardless of the difference in gravitational field strengths.

4) Other. Please explain.

again, the center of mass in a closed system never changes if there are no outside forces. it's the exact same situation as the first one, save it's gravitational forces instead of electromagnetic.

Originally Posted by Osby

MagiMaster and DrRocket are correct. The correct answer is number 3.

Here is the second question.



For this thought experiment, the universe consists only of the two planets illustrated above. No other outside forces are involved. Both planets have the same inertial mass. But their active gravitational mass is variable. Active gravitational mass is a measure of the strength of an object’s gravitational flux. Even though this universe assumes that the equivalence principle is not valid for active gravitational mass, there is a correct answer to this question using currently accepted Newtonian methodology. With that in mind, which of the following is true?

1) The meeting point of the two planets will depend on the strength of the gravitational fields. If the fields are equal in strength, then they will meet at the center of mass. If planet A has the greater field strength then they will meet to the left side of the center of mass. If planet B has the greater field strength then they will meet to the right of the center of mass.

2) Same as above except reversed. If the field strengths are equal then they will meet at the center of mass. If the gravitational field strength of A > B then they will meet to the right of the center of mass. If the gravitational field strength of B > A then they will meet to the left of the center of mass.

3) The planets will always meet at the center of mass regardless of the difference in gravitational field strengths.

4) Other. Please explain.

You have to be more careful with definitions here.

So long as Newton's third law holds, that forces exerted by the bodies are equal and opposite, then the bodies will meet in the center of of inertial mass.

This requires that the ratios of active to passibe gravitational mass for the two bodies be the same.

I am getting weary of third-grade tests. Do you have a point to make ?

Originally Posted by DrRocket

So long as Newton's third law holds, that forces exerted by the bodies are equal and opposite, then the bodies will meet in the center of of inertial mass.

This requires that the ratios of active to passibe gravitational mass for the two bodies be the same.

It was clearly stated that the equivalence principle for active gravitational mass was not true for this universe. So your answer is invalid. As stated, there is a correct answer to this question (1, 2, or 3) using currently accepted Newtonian methodology. (I will provide links).

Originally Posted by DrRocket

I am getting weary of third-grade tests. Do you have a point to make ?

In that case, you should have no problem answering the question. Yes, there is a point, which will be my next question.

Originally Posted by Osby

It was clearly stated that the equivalence principle for active gravitational mass was not true for this universe. So your answer is invalid. As stated, there is a correct answer to this question (1, 2, or 3) using currently accepted Newtonian methodology. (I will provide links).

Sorry Charlie.

The constant ratio that is needed :

1) Is between active and passibe gravitational masses and has nothing to do with inertial mass , which is the subject of the equivalence principle.

2) Does not require the ratio to be 1.

Originally Posted by DrRocket

I am getting weary of third-grade tests. Do you have a point to make ?

In that case, you should have no problem answering the question. Yes, there is a point, which will be my next question.[/quote]

Sorry again Charlie. I am not willing to play your stupid games. If you have a point then make it. You are not going to get anywhere playing games with questions and answers that you apparently don't understand.

Thank you MagiMaster, DrRocket, and Arcane_Mathematician for your participation. My intention is not to test you but to learn something from your answers. It is true that I already know the answers to the first two questions. But they were necessary to help you understand what it is that I don't understand.

The correct answer to the second question is number 1. This is the basis of the Newtonian equivalence principle as it relates to active gravitational mass. In this Wikipedia entry you will find the following equations:





Notice that if:



Or if:



then



This would result in a third law violation. In 1986 David F. Bartlett and Dave Van Buren used this methodology as the basis for a non-laboratory experiment using the moon http://prl.aps.org/abstract/PRL/v57/i1/p21_1. Because of the moons unusual distribution of two metals, iron on one side and aluminum on the other, they surmised that if the force that Fe exerts on Al differed from the force that Al exerts on Fe, then the moon would self accelerate and would be in a different orbit than the one predicted by classical physics.

So my third question is, why should Arcane_Mathematician's answer to the second question be incorrect? What makes gravity unique in this respect? If the uneven force pairs in the gravitational thought experiment produces a third law violation, why doesn't the same happen with uneven force pairs in the magnet thought experiment? Wouldn't it be more logical for the gravitational thought experiment to obey the laws of motion the same way the magnet thought experiment does?

Originally Posted by Osby

Thank you MagiMaster, DrRocket, and Arcane_Mathematician for your participation. My intention is not to test you but to learn something from your answers. It is true that I already know the answers to the first two questions. But they were necessary to help you understand what it is that I don't understand.

The correct answer to the second question is number 1. This is the basis of the Newtonian equivalence principle as it relates to active gravitational mass. In this Wikipedia entry you will find the following equations:





Notice that if:



then



This would result in a third law violation. In 1986 David F. Bartlett and Dave Van Buren used this methodology as the basis for a non-laboratory experiment using the moon http://prl.aps.org/abstract/PRL/v57/i1/p21_1. Because of the moons unusual distribution of two metals, iron on one side and aluminum on the other, they surmised that if the force that Fe exerts on Al differed from the force that Al exerts on Fe, then the moon would self accelerate and would be in a different orbit than the one predicted by classical physics.

So my third question is, why should Arcane_Mathematician's answer to the second question be incorrect? What makes gravity unique in this respect? If the uneven force pairs in the gravitational thought experiment produces a third law violation, why doesn't the same happen with uneven force pairs in the magnet thought experiment? Wouldn't it be more logical for the gravitational thought experiment to obey the laws of motion the same way the magnet thought experiment does?

Wrong.

You preserve Newton's third law if the ratio of active to passive gravitational mass is a constant.

Either do the simple algebra yourself or go read the Wiki article that you linked.

The equivalence principle would require that passive gravitational mass equal inertial mass. But that is not required for Newton's third law to hold, and it is only Newton's third that is need for the meeting point to be the center of inertial mass.

Originally Posted by DrRocket

Wrong.

You preserve Newton's third law if the ratio of active to passive gravitational mass is a constant.

Either do the simple algebra yourself or go read the Wiki article that you linked.

The equivalence principle would require that passive gravitational mass equal inertial mass. But that is not required for Newton's third law to hold, and it is only Newton's third that is need for the meeting point to be the center of inertial mass.

Sorry about the error. I edited the post. The questions are still valid.

Repeating my questions.

So my third question is, why should Arcane_Mathematician's answer to the second question be incorrect? What makes gravity unique in this respect? If the uneven force pairs in the gravitational thought experiment produces a third law violation, why doesn't the same happen with uneven force pairs in the magnet thought experiment? Wouldn't it be more logical for the gravitational thought experiment to obey the laws of motion the same way the magnet thought experiment does?

Originally Posted by Osby

Repeating my questions.

So my third question is, why should Arcane_Mathematician's answer to the second question be incorrect? What makes gravity unique in this respect? If the uneven force pairs in the gravitational thought experiment produces a third law violation, why doesn't the same happen with uneven force pairs in the magnet thought experiment? Wouldn't it be more logical for the gravitational thought experiment to obey the laws of motion the same way the magnet thought experiment does?

Arcane's answer is based on Newton's second and third laws. The third law (equal and opposite forces) is the key.

The magnet example follows Newton's third law.

IF, and you have not done this, you require that inertial mass, active gravitational mass, and passive inertial massnot notall be equal, and you require that the ratio of active inertial mass to active gravitational mass not be a constant, then Newton's third law is violated and Newtonian mechanics pretty much goes out the window. You will lose conservation of momentum for instance, which is dependent on the third law. If the ratio of active gravitational mass to passive inertial mass is some constant, whether 1 or something else, then Newton's second and third laws hold and you get pretty much ordinary Newtonian mechanics with the exception that gravitational force is different.

What is "passive inertial mass" and "active inertial mass"? I have not encountered those terms before.

Ok, I'm going to assume that those terms are just typo errors on your part. But if they're not then please explain their meaning.

But it is the unequal force pairs in second thought experiment that causes the third law violation. The magnet thought experiment has unequal force pairs also. So why is there a third law violation in one and not the other? Are you saying that if the proportional equivalence of active gravitational mass and passive gravitational mass were not true for the first thought experiment that it also would have a third law violation?

Originally Posted by Osby

What is "passive inertial mass" and "active inertial mass"? I have not encountered those terms before.

Ok, I'm going to assume that those terms are just typo errors on your part. But if they're not then please explain their meaning.

But it is the unequal force pairs in second thought experiment that causes the third law violation. The magnet thought experiment has unequal force pairs also. So why is there a third law violation in one and not the other? Are you saying that if the proportional equivalence of active gravitational mass and passive gravitational mass were not true for the first thought experiment that it also would have a third law violation?

They are not typo errors at all.

I thought when you referred to a Wiki article you meant the one on the equivalence principle. Read the part near the bottom, it explains the ideas pretty well. It is differences between the two that can result ina violation of the third law.

http://en.wikipedia.org/wiki/Equivalence_principle

In the case of the magnets the forces do not arise from gravity or from mass so the differences between active and passive gravitational mass and between inertial mass and any sort of gravitational mass are completely irrelevant. You have a force that obeys Newton's third law and your have inertial mass, that is all you need for ordinary Newtonian mechanics to apply.

There is no third law violation in the magnet scenario.

There is third law violation in the gravitational scenario if and only if the ratio of active inertial mass to passive inertial mass is not a constant, the same for all bodies.

Originally Posted by DrRocket

They are not typo errors at all.

I thought when you referred to a Wiki article you meant the one on the equivalence principle. Read the part near the bottom, it explains the ideas pretty well. It is differences between the two that can result ina violation of the third law.

I searched the entire page and could not find reference to "passive inertial mass" or "active inertial mass". I have also searched elsewhere and have been unable to find a definition. Please explain.

Originally Posted by Osby

Originally Posted by DrRocket

They are not typo errors at all.

I thought when you referred to a Wiki article you meant the one on the equivalence principle. Read the part near the bottom, it explains the ideas pretty well. It is differences between the two that can result ina violation of the third law.

I searched the entire page and could not find reference to "passive inertial mass" or "active inertial mass". I have also searched elsewhere and have been unable to find a definition. Please explain.

Please read the paragraph entitled "Active, passive, and inertial masses" and the subsequent discussion in the Wiki article. I do not intend to reproduce it for you.
http://en.wikipedia.org/wiki/Equivalence_principle

I,m still searching for the experimental proove that chargedifferences (and thus radiation) plays no role in meassuring the gravitational constant with a torsionbalance.

It,s a common known fact that if you hang something on a thin wire it builds up "static" charge relative to things on the ground. Having a charge there would be radiation between the halter weigths and the other weigths. Thus gravitation not being a symmetric force. That would change such a discussion completely.

As I say there is no evidence for a zero charge difference (or I can,t find it) as long as that evidence is absent I would be carefull to see the torsionbalance (the gravitational constant connecting it with gravitation true Newtons formula) as proof for the symmetrie of gravitation.

It must be testible though if there are chargedifferences for instance using a carbonwire instead of glassfibre,

That it is done in a covering does not convince me of absence of this (common) phenomenum. The charge build up of something on a wire (especially when thin and isolating) also happens in houses ( also a covering) closing the door won,t help the charge difference disappear either.