Difference of weight with altitude

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Offline fgt55

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Difference of weight with altitude
« on: 02/04/2012 14:32:29 »
Hi,

Gravity change with altitude, when 2 masses of 1kg are at h=0 m we have 2*g N like weight. Now, if we turn these 2 masses with radius of 1 m when we turn of 90°, one masse is at h=1m and another massis at h=-1m. Like the formula for gravity is like g = G*Mt/r², it's not possible to have the same weight when 2 masses was at h=0m. The weight is greater when we have turned, why ?

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Offline imatfaal

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Re: Difference of weight with altitude
« Reply #1 on: 03/04/2012 09:48:39 »
fgt - firstly the amounts we are talking about are so insignificant that in reality who cares?  secondly, at present we just cannot do the numerical calculation - newtons constant is accurate to about 1 part in 10000, whereas you are introducing a change that will manifest at around 1 part in a million million. and lastly, why would this be a problem - it is not as if the change (if there actually is one) in force occurs without effort being made to change the system.  why don't you, for the moment assume G is well known to huge accuracy and actually do the sums
There’s no sense in being precise when you don’t even know what you’re talking about.  John Von Neumann

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Offline Nizzle

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Re: Difference of weight with altitude
« Reply #2 on: 03/04/2012 10:58:49 »
:o
I remember you telling me (and Aethelwulf and probably others too) not to be condescending imatfaal ;)
Roses are red,
Violets are blue.
Most poems rhyme,
but this one doesn't

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Offline MikeS

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Re: Difference of weight with altitude
« Reply #3 on: 05/04/2012 08:10:12 »
The lower mass is heavier by the same amount that the higher mass is lighter.  Together they both weigh the same as they did when horizontal.

And just for the record I care.

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Offline imatfaal

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Re: Difference of weight with altitude
« Reply #4 on: 05/04/2012 11:04:20 »
Mike - what is wrong with this calculation
1/5999999^2+1/6000001^2-2/6000000^2

or even more accurately ( ie setting fulcrum at 6*10^6 and modelling realistically)
1/5999999^2+1/6000001^2-2/sqrt(36000000000001)^2

There’s no sense in being precise when you don’t even know what you’re talking about.  John Von Neumann

At the surface, we may appear as intellects, helpful people, friendly staff or protectors of the interwebs. Deep down inside, we're all trolls. CaptainPanic @ sf.n

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Offline MikeS

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Re: Difference of weight with altitude
« Reply #5 on: 05/04/2012 11:27:45 »
imatfaal

The figures may seem insignificant.  It's the theory that interests me and its implications in explaining time and gravity.  The figures may seem minute but the Universe takes them into account.  If it did not then gravity and time would not exist.

Or are you suggesting that my reply was wrong?

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Offline Æthelwulf

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Re: Difference of weight with altitude
« Reply #6 on: 05/04/2012 11:30:57 »
fgt - firstly the amounts we are talking about are so insignificant that in reality who cares?  secondly, at present we just cannot do the numerical calculation - newtons constant is accurate to about 1 part in 10000, whereas you are introducing a change that will manifest at around 1 part in a million million. and lastly, why would this be a problem - it is not as if the change (if there actually is one) in force occurs without effort being made to change the system.  why don't you, for the moment assume G is well known to huge accuracy and actually do the sums

Certainly the post that brought the sword to the heart!

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Offline imatfaal

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Re: Difference of weight with altitude
« Reply #7 on: 05/04/2012 12:01:32 »
Mike - Please click on those links to (simplified) sums that are important
If you don't see what they represent - here goes

let G and M_earth = 1  we can do that without loss of precision or meaning (it just means the units are no longer SI)

you then end up with [tex] F = \frac{1}{r^2}[/tex]

The OP is asking if [tex] \frac{2}{r^2} [/tex] is equal to [tex] \frac{1}{(r+1)^2} +\frac{1}{(r-1)^2} [/tex]  Now I might have got something wrong with my interpretation - but I see that as a fairly simple sum and a definite No. 

 
There’s no sense in being precise when you don’t even know what you’re talking about.  John Von Neumann

At the surface, we may appear as intellects, helpful people, friendly staff or protectors of the interwebs. Deep down inside, we're all trolls. CaptainPanic @ sf.n

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Offline MikeS

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Re: Difference of weight with altitude
« Reply #8 on: 05/04/2012 15:20:28 »
imatfaal

Point taken I was wrong and fgt55 was correct.

The question still has not been answered though. 

I suspect that my answer should have been correct but relativistic effects have not been accounted for.  Does this make sense?

If not what does account for the difference?

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Offline Æthelwulf

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Re: Difference of weight with altitude
« Reply #9 on: 05/04/2012 16:14:46 »
Why has my post been censored, and why when I click it I cannot see it?

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Offline imatfaal

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Re: Difference of weight with altitude
« Reply #10 on: 05/04/2012 17:09:19 »
Why has my post been censored, and why when I click it I cannot see it?
  Cos it was completely off the point. We are having a problem with shrunk posts not unshrinking with the new forum software
There’s no sense in being precise when you don’t even know what you’re talking about.  John Von Neumann

At the surface, we may appear as intellects, helpful people, friendly staff or protectors of the interwebs. Deep down inside, we're all trolls. CaptainPanic @ sf.n

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Offline imatfaal

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Re: Difference of weight with altitude
« Reply #11 on: 05/04/2012 17:15:12 »
imatfaal

Point taken I was wrong and fgt55 was correct.

The question still has not been answered though. 

I suspect that my answer should have been correct but relativistic effects have not been accounted for.  Does this make sense?

If not what does account for the difference?

It is not really something I had thought a great deal about.  Relativistic effects? - possibly but which? if you got an idea I will number-crunch it.  Perhaps ask why it is assumed they should be the same, are there any consequences for them not being the same, are there positives for them not being the same.

This sort of the problem exemplifies why I always harp on about going back to the math
There’s no sense in being precise when you don’t even know what you’re talking about.  John Von Neumann

At the surface, we may appear as intellects, helpful people, friendly staff or protectors of the interwebs. Deep down inside, we're all trolls. CaptainPanic @ sf.n

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Offline Æthelwulf

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Re: Difference of weight with altitude
« Reply #12 on: 05/04/2012 17:40:17 »
Why has my post been censored, and why when I click it I cannot see it?
  Cos it was completely off the point. We are having a problem with shrunk posts not unshrinking with the new forum software

I am sorry, but I think censoring posts is more of a time-waste unless there is a serious problem, afterall, how much bandwidth has it caused now?

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Offline Æthelwulf

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Re: Difference of weight with altitude
« Reply #13 on: 05/04/2012 18:57:25 »
Why has my post been censored, and why when I click it I cannot see it?
  Cos it was completely off the point. We are having a problem with shrunk posts not unshrinking with the new forum software

I am sorry, but I think censoring posts is more of a time-waste unless there is a serious problem, afterall, how much bandwidth has it caused now?

All I am saying, as a moderator, you should not waste time for time.

Ironic yes? Considering I don't think time exists yes? :) But do not waste my time either. I will quickly leave this place if all it has in mind to censor my posts.

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Offline MikeS

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Re: Difference of weight with altitude
« Reply #14 on: 07/04/2012 07:10:05 »
imatfaal

Point taken I was wrong and fgt55 was correct.

The question still has not been answered though. 

I suspect that my answer should have been correct but relativistic effects have not been accounted for.  Does this make sense?

If not what does account for the difference?

It is not really something I had thought a great deal about. Relativistic effects? - possibly but which? if you got an idea I will number-crunch it.  Perhaps ask why it is assumed they should be the same, are there any consequences for them not being the same, are there positives for them not being the same.

This sort of the problem exemplifies why I always harp on about going back to the math

imatfaal
I wish I was a mathematician but I'm not and I'm too long in the tooth.

Gravitational time dilation
The gravitational constant is approximately
6.67300 × 10-11 m3 kg-1 s-2

What this does not seem to take into account is that a second at a lower altitude is longer than a second at a higher altitude so the formula can only be an approximation to reality.

It's a poor answer I know but it just seems logical.

Yes, it seems to show the inadequacies of using Newtonian gravity where relativistic effects are present.

The positives are, if I am correct, another confirmation of the correctness of GR.

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Offline fgt55

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Re: Difference of weight with altitude
« Reply #15 on: 08/04/2012 00:02:23 »
What do you think with a fixed column of water with a left fixed mass under it ? The pressure is different ? So the water move ?

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Offline MikeS

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Re: Difference of weight with altitude
« Reply #16 on: 08/04/2012 05:34:24 »
No, that would be perpetual motion.

Your reasoning is only taking into account a difference in weight due to gravity.  It is not allowing for the difference in gravitational time dilation which effectively cancels what may appear at first sight, to have been a gain. 

It would be interesting if someone did the math using Newtonian gravity to see whether or not it would predict perpetual motion?
« Last Edit: 08/04/2012 08:10:56 by MikeS »

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Offline MikeS

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Re: Difference of weight with altitude
« Reply #17 on: 08/04/2012 08:05:36 »
imatfaal

Previously I assumed they would be the same as it seemed logical but could not offer any reasoning.

Here is the reasoning.
Going back to the original experiment.
It seems to me that if the gain in weight were real it could be used as the basis for a perpetual motion machine.
That's another reason for me thinking that relativistic effects need to be taken into consideration.

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Offline fgt55

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Re: Difference of weight with altitude
« Reply #18 on: 08/04/2012 10:51:11 »
Quote
It seems to me that if the gain in weight were real it could be used as the basis for a perpetual motion machine.
not at all because when you move down a reverse torque appears and you lost energy. The sum of energy is always 0 in this case like forever ;)

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Offline MikeS

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Re: Difference of weight with altitude
« Reply #19 on: 08/04/2012 12:05:51 »
You may well be right.  It obviously can't work but I can't seem to get my head around why.

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Offline fgt55

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Re: Difference of weight with altitude
« Reply #20 on: 08/04/2012 17:43:01 »
When a mass move down it lost energy because it never move up with the same gravity (it move down).

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Offline MikeS

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Re: Difference of weight with altitude
« Reply #21 on: 09/04/2012 10:48:41 »
No that's not it.  There are two masses about a fulcrum.  Assuming the fulcrum to remain an equidistant from the Earth.  The system weighs more when the weights are in vertical alignment than when they are in horizontal alignment. 
When they rotate one mass moves down the other moves up so they balance and the energy of the system should remain constant.  In the vertical alignment the system weighs more which represents an increase in energy of the system.  The gravitational potential energy of the system remains the same.  As far as I understand it there should not be an increase of weight when the masses are vertically aligned.  The discrepancy, I believe is caused by not taking into account gravitational time dilation.

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Offline fgt55

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Re: Difference of weight with altitude
« Reply #22 on: 09/04/2012 12:52:28 »
Quote
When they rotate one mass moves down the other moves up so they balance and the energy of the system should remain constant.
why ?

Quote
In the vertical alignment the system weighs more which represents an increase in energy of the system. 
it's normal for me, because one mass is lower and other upper. Don't forget there is a torque.

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Offline MikeS

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Re: Difference of weight with altitude
« Reply #23 on: 10/04/2012 07:43:47 »
Let me re-phrase the question to get rid of problems to do with torque and inertia.
Lets have your original system but two identical ones.  One vertical and one horizontal, both with the fulcrum the same height above the Earth.
Why is the vertical one heavier using Newtonian gravity?

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Offline fgt55

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Re: Difference of weight with altitude
« Reply #24 on: 10/04/2012 10:31:11 »
I don't understand could you make drawings ? and explain step by step ?

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Offline MikeS

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Re: Difference of weight with altitude
« Reply #25 on: 10/04/2012 11:12:03 »
Just imagine your original drawing and one rotated through 90 degrees.
Both having the fulcrum points the same distance above the Earth.
The system where the weights are in vertical alignment weighs more as pointed out by yourself (at least that's what I thought you meant) and confirmed by imatfaal (at least that's what I think he meant).

I believe that they should weigh the same but the maths appear to say differently.  That is the vertical system weighs more than the horizontal system.

I believe the discrepancy arises because Newtonian laws of gravity are being used where relativistic laws of gravity should have been used.  I may be wrong.
« Last Edit: 10/04/2012 11:13:49 by MikeS »

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Offline fgt55

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Re: Difference of weight with altitude
« Reply #26 on: 10/04/2012 12:39:40 »
Quote
I believe that they should weigh the same
for me no, the distance of the center is the same (center of masses) but the center of gravity is different (and physics say it can be different). Think with energy, the sum is always 0. Make calculations and maybe you'll find your error.

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Offline MikeS

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Re: Difference of weight with altitude
« Reply #27 on: 10/04/2012 15:48:33 »
You assume I have an error, interesting.
When you say center of gravity what do you mean?  The center of the gravitational potential or the center of gravitational potential energy.

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Offline fgt55

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Re: Difference of weight with altitude
« Reply #28 on: 10/04/2012 17:00:49 »
Quote
You assume I have an error, interesting.
In fact, I don't understand all your problem...Have you a problem with sum of energy or what ? For me, the system has more weight when the masses are vertical. And what ? If you move down you lost potential energy. If you turn and move down you lost energy too and win, the sum is always 0. Make a calculation and I can help you to find the error.


Quote
When you say center of gravity what do you mean?  The center of the gravitational potential or the center of gravitational potential energy.
I'm not fluently in english. I don't understand these 2 differences.

Like you seem to like this problem. Maybe you'll like this another. Take a fixed container full with water. An object O like the drawing show is empty (air inside for example with small pressure). There isn't other mass around water or object O. The pressure at right is bigger than at left, so the object must turn with torque and give energy ? I'm sure not, but where is the solution ? How to calculate pressure in water even it's evidence the pressure at right is bigger than at left ?

« Last Edit: 10/04/2012 17:29:47 by fgt55 »

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Offline MikeS

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Re: Difference of weight with altitude
« Reply #29 on: 12/04/2012 08:14:43 »
I think what you are suggesting above is similar to an experiment carried out by Richard Feynman.  He was trying to find out if the thrust of a fluid emitted through a nozzle worked in reverse.  That is if fluid were admitted by the nozzle would it generate thrust.  The result of the experiment was it did not but he blew up a carboy in the process.

See
http://en.wikipedia.org/wiki/Feynman_sprinkler
« Last Edit: 12/04/2012 08:49:48 by MikeS »

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Offline MikeS

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Re: Difference of weight with altitude
« Reply #30 on: 12/04/2012 08:46:26 »
Going back to the original problem as I understand it.
With the two weights horizontal they both weigh the same and both have the same gravitational potential energy.

With the weights vertical about the same fixed fulcrum point.  The higher weight now weighs less but has more GPE.  The lower weight now weighs more but has less GPE.

As I understand it the total weight of the system as obtained by using the Newtonian law of gravity when the weights are horizontal is less than the same system when the weights are vertical.  That's what I understand.

My question is, if you weighed the two systems would they weigh the same or not?  If not, would taking a relativistic approach predict that they should weigh the same?

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Offline imatfaal

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Re: Difference of weight with altitude
« Reply #31 on: 12/04/2012 10:55:07 »
Mike - bit rushed, but this is worth bearing in mind.- I know maths is not your favourite but here goes

Force due to gravity falls of inverse square
[tex] F = \frac{GM_1M_2}{r^2}[/tex]
Ignoring all the constants and units etc - just the maths
Initial State with horizontal bar [tex]F=\frac{1}{x^2}+\frac{1}{x^2} = \frac{2}{x^2}[/tex]

Final state with vertical bar [tex] F=\frac{1}{(x-1)^2}+\frac{1}{(x+1)^2} = \frac{2(x^2+1)}{(x^2-1)^2[/tex]

sorry gonna have to go - will try and pickit up
There’s no sense in being precise when you don’t even know what you’re talking about.  John Von Neumann

At the surface, we may appear as intellects, helpful people, friendly staff or protectors of the interwebs. Deep down inside, we're all trolls. CaptainPanic @ sf.n

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Offline fgt55

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Re: Difference of weight with altitude
« Reply #32 on: 12/04/2012 11:07:37 »
Quote
My question is, if you weighed the two systems would they weigh the same or not? 
not the same

Quote
If not, would taking a relativistic approach predict that they should weigh the same?
I don't know, but relativistic is not here for me

Quote
With the weights vertical about the same fixed fulcrum point.  The higher weight now weighs less but has more GPE.  The lower weight now weighs more but has less GPE.

You're right, there is a problem with GPE and weight. Example with masses at radius of 3m from the center. The center is at 10 m from the object which attrack (like Earth, but closed). The weight in vertical position is 1/13²+1/7²=0.0263 and the weight in horizontal position is 2*1/(10²+3²)=0.0183. (I cancel constant). The weight in vertical position is bigger than in horizontal position.

For the GPE (from 1 to the position of the mass), we have mgh, in vertical position this is: (1-1/13)*13+(1-1/7)*10 = 18 compared with horizontal position (1-1/13.34)*13.34+(1-1/7.6)*7.6 = 18.94, the GPE in horizontal position is bigger, that's normal but not in this proportion !

This is strange for me.

Edit: it's ok, it's because we can move with the same length so energy is the same.
« Last Edit: 12/04/2012 11:19:50 by fgt55 »

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Offline fgt55

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Re: Difference of weight with altitude
« Reply #33 on: 12/04/2012 16:51:42 »
edit more later
« Last Edit: 12/04/2012 17:08:00 by fgt55 »

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Offline MikeS

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Re: Difference of weight with altitude
« Reply #34 on: 13/04/2012 05:50:54 »
I think I have got my head around it at last. 
With the weights in vertical alignment the center of the gravitational potential is below the fulcrum point.  This is because the gravitational potential and hence weight varies by the square rule.  The bottom weight has gained more weight than the top weight has lost.  So, in vertical alignment the system weighs more than in horizontal alignment.

My thinking was wrong.  It's obvious, I don't know how I missed it. I was stuck in a rut and considering it in terms of energy, in which case I believe I would have been correct and it would need to be considered from a relativistic viewpoint to make the energies balance.

fgt55 sorry this has been such a long and hazardous uphill trek. ;-)

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Offline fgt55

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Re: Difference of weight with altitude
« Reply #35 on: 21/04/2012 14:53:10 »
I'm thinking about a problem with pressure when I calculate the pressure under water. I put a conic volume under pressure under gravity. The pressure at left or at right is lower thn the pressure in the center, so if we remove parts of the volume for have a helicoid like the drawings show, the volume turn in water ? because the pressure seems to be differents ! The vertical surface is closer to the center than the horizontal surface, so each surface see a different torque ?