On what principle does a weighing balance operate?

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Offline MikeS

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A weighing balance (jewellers balance etc.) operates through gravity comparing the torque of the weighed object with a known mass.
The balance arm comes to rest where the acting forces presumably balance.  But what are the forces and why do they balance?  As one end of the balance drops it gets nearer to the Earth's centre of gravity where gravity is stronger.  So why does it not keep dropping?

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Offline syhprum

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On what principle does a weighing balance operate?
« Reply #1 on: 28/11/2011 19:25:38 »
In addition to the two pans there is normally a pointer arm at right angles to the beam that points down to the centre of the Earth when the pans are equally loaded.
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Offline MikeS

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On what principle does a weighing balance operate?
« Reply #2 on: 28/11/2011 19:52:02 »
In addition to the two pans there is normally a pointer arm at right angles to the beam that points down to the centre of the Earth when the pans are equally loaded.

True, but that's just a technicality of how the balance is made and does not address the question.
« Last Edit: 28/11/2011 19:55:32 by MikeS »

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Offline syhprum

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On what principle does a weighing balance operate?
« Reply #3 on: 28/11/2011 20:09:39 »
The weight of the pointer produces a restoring force that tends to maintain the bar of the balance horizontal, this restoring force is much greater than any differential gravity effects.
The balance suspension point may also be vertically above the centre of the beam which has the same effect.
if you design your balance to avoid these restoring forces it will be truly unstable and either of the equally weighted pans can stay down.
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Offline MikeS

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On what principle does a weighing balance operate?
« Reply #4 on: 28/11/2011 20:44:36 »
The weight of the pointer produces a restoring force that tends to maintain the bar of the balance horizontal, this restoring force is much greater than any differential gravity effects.
The balance suspension point may also be vertically above the centre of the beam which has the same effect.
if you design your balance to avoid these restoring forces it will be truly unstable and either of the equally weighted pans can stay down.

I don't think this is true.  The balance will work equally well without the pointer (but maybe more difficult to read).
I can't see this being true either.  If the pointer (above the beam) is off centre its weight would tend to make it go further off centre, not restore it.

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Offline Bored chemist

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On what principle does a weighing balance operate?
« Reply #5 on: 28/11/2011 21:18:18 »
The weight of the pointer produces a restoring force that tends to maintain the bar of the balance horizontal, this restoring force is much greater than any differential gravity effects.
The balance suspension point may also be vertically above the centre of the beam which has the same effect.
if you design your balance to avoid these restoring forces it will be truly unstable and either of the equally weighted pans can stay down.

I don't think this is true.  The balance will work equally well without the pointer (but maybe more difficult to read).
I can't see this being true either.  If the pointer (above the beam) is off centre its weight would tend to make it go further off centre, not restore it.
No it won't.
Have a look at pages 21 et seq here
http://books.google.co.uk/books?id=hYZC-k4mo-YC&pg=PA23&lpg=PA23&dq=%22sensitivity+of+a+balance%22+knife&source=bl&ots=BLB1Qa5EqB&sig=jKzHvhGBb_VWFf4WbhmncMI3zrM&hl=en&ei=JvrTTpXZNMmd-waYu8z6Dg&sa=X&oi=book_result&ct=result&resnum=1&ved=0CBwQ6AEwAA#v=onepage&q=%22sensitivity%20of%20a%20balance%22%20knife&f=false
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Offline Soul Surfer

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On what principle does a weighing balance operate?
« Reply #6 on: 28/11/2011 23:26:52 »
The basic principle of the balance is that the centre of gravity of the beam and pans is below the point of suspension so that as one pan goes down there is a slight restoring force that allows equally loaded pans to Sit in the centre. the change in gravitational attraction as one pan goes down a centimetre or two is far smaller than this and does not have any effect
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Offline Geezer

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On what principle does a weighing balance operate?
« Reply #7 on: 29/11/2011 00:36:57 »
Are the fulcrums of the pans slightly lower than the centre fulcrum? (I think they are, but I can't remember!) If so, the the pans will contribute a small restoring torque.
There ain'ta no sanity clause, and there ain'ta no centrifugal force Šther.

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Offline MikeS

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On what principle does a weighing balance operate?
« Reply #8 on: 29/11/2011 08:30:16 »
I still can't see the thing about restoring forces.
I came across this http://en.wikipedia.org/wiki/Roberval_Balance.  A Roberval balance is frequently used in the retail trade for weighing fruit, veg etc.  It's essentially a balance beam scale that is not suspended.  Quote "Since the vertical beams are always exactly vertical, and the weighing platforms always horizontal, the potential energy lost by a weight as its platform goes down a certain distance will always be the same, so it makes no difference where you put the weight."
"the potential energy lost by a weight" is presumably referring to gravitational potential energy.  So a balance beam weighing machine is actually comparing the GPE of an object in comparison to a known weight (mass). 
But this leads back to my original question. "   As one end of the balance drops it gets nearer to the Earth's centre of gravity where gravity is stronger.  So why does it not keep dropping?"  In other words if the weights are slightly unequal, the heaviest end of the balance will tip down slightly until equilibrium is established.  But why is equilibrium established?  Why does the beam not continue to tip?  Can anyone give me a non-mathematical answer to this?

Let me just add this in order to try to clarify what I am getting at.
A simple beam balance can be made from a strip of wood suspended by thread at the centre.  If coffee cans are suspended from either end by adjusting the suspension (fulcrum) points, the scale can be made to balance.  Any very slight discrepancy in weight distribution will cause the beam to rotate a certain amount around the centre fulcrum until it reaches a point of balance.  Why does it reach a point of balance?

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Offline MikeS

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On what principle does a weighing balance operate?
« Reply #9 on: 29/11/2011 08:37:24 »
I have just realised I think I have answered my own question.
Say the left hand side of the beam is slightly heavier, the beam will tilt down on the left until equilibrium is established.  The decreased GPE of the left hand (heavier) mass is equaled by the increased GPE of the right hand (lighter) mass.
So the balance beam scale is actually comparing minute differences in GPE over potentially very small distances.
« Last Edit: 29/11/2011 09:50:31 by MikeS »

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Offline Geezer

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On what principle does a weighing balance operate?
« Reply #10 on: 29/11/2011 08:54:54 »
Mike,

I think it's all about "stable" and "unstable" equilibrium. If the centre of mass of the system happens to be below the fulcrum, the system will be stable, meaning it will self-correct.

If the centre of mass happens to be above the fulcrum, the system will be unstable, and it will simply fall over.

The trick with the balance is to arrange for the system to be just stable enough that a very small difference between the masses on the pans is amplified by the pointer.
There ain'ta no sanity clause, and there ain'ta no centrifugal force Šther.

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Offline MikeS

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On what principle does a weighing balance operate?
« Reply #11 on: 29/11/2011 09:47:58 »
Mike,

I think it's all about "stable" and "unstable" equilibrium. If the centre of mass of the system happens to be below the fulcrum, the system will be stable, meaning it will self-correct.

If the centre of mass happens to be above the fulcrum, the system will be unstable, and it will simply fall over.

The trick with the balance is to arrange for the system to be just stable enough that a very small difference between the masses on the pans is amplified by the pointer.

Geezer

Exactly, that accounts for how to make the balance stable and easy to read but doesn't really answer the question.  I am pretty sure  I gave the correct answer in my last post.
"Say the left hand side of the beam is slightly heavier, the beam will tilt down on the left until equilibrium is established.  The decreased GPE of the left hand (heavier) mass is equaled by the increased GPE of the right hand (lighter) mass ."

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Offline MikeS

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On what principle does a weighing balance operate?
« Reply #12 on: 29/11/2011 10:06:03 »
"Say the left hand side of the beam is slightly heavier, the beam will tilt down on the left until equilibrium is established.  The decreased GPE of the left hand (heavier) mass is equaled by the increased GPE of the right hand (lighter) mass ."

This seems to be saying that the heavier mass weighs less deeper within the gravity well and the lighter mass weighs more higher within the gravity well.

If this is correct then it could be tested by weighing a mass at different heights in the gravitational field using a very accurate type of 'spring' (not balance beam) weighing machine.  I understand observation confirms this.

So to re-phrase the answer.
A simple balance beam comes to rest at the angle where equilibrium is reached.  That is, where both objects have the same weight within the gravity well.

Edit
The part of this post that has strike through is completely wrong, please ignore it.
« Last Edit: 29/11/2011 14:51:04 by MikeS »

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Offline syhprum

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On what principle does a weighing balance operate?
« Reply #13 on: 29/11/2011 13:18:40 »
I cannot believe that you really believe this nonsense about gravity wells, at least four senior correspondents have explained in words of one symbol how and why balances work as they do.
I think you are just practicing as a devils advocate to see if you can convince anyone of your ridiculous idea.
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Offline MikeS

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On what principle does a weighing balance operate?
« Reply #14 on: 29/11/2011 14:47:38 »
syphrum

I realised my last post was wrong almost immediately after posting it but I was not near a computer so couldn't delete it.

I cannot believe that you really believe this nonsense about gravity wells, at least four senior correspondents have explained in words of one symbol how and why balances work as they do.
I think you are just practicing as a devils advocate to see if you can convince anyone of your ridiculous idea.

I don't believe it has been explained how a balance works.  Perhaps you would be good enough to explain in words of one syllable how they work.

If a balance does not work through the effects of differential gravity in a gravity well (field) then I would certainly like to know how they work.  Please enlighten me.
« Last Edit: 29/11/2011 14:52:35 by MikeS »

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Offline syhprum

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On what principle does a weighing balance operate?
« Reply #15 on: 29/11/2011 14:59:25 »
May I refer you to the posts by Geezer, Soul Surfer, and myself also the article cited by Bored Chemist.
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Offline Geezer

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On what principle does a weighing balance operate?
« Reply #16 on: 29/11/2011 18:09:44 »
Mike,

As Syhprum pointed out in his second post, any differential gravitational effect is negligible. In fact, the beam balance operates on the basis that gravitational effects are uniform.

The restoring torque is simply a consequence of the fact that the system is stable when it is at, or nearly at, equilibrium. If it was an unstable system in equilibrium (meaning all the forces summed to zero) there would be no restoring force and any "noise" in the system would cause one of the pans to hit the deck.
There ain'ta no sanity clause, and there ain'ta no centrifugal force Šther.

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Offline syhprum

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On what principle does a weighing balance operate?
« Reply #17 on: 29/11/2011 18:49:20 »
It is not difficult to do a calculation of the net rotational forces acting on the beam  taking in the effect of various positions of the fulcrum and the differential gravitational effect.
scientific arguments always look more convincing if accompanied by a mass of calculations.
to work out the differential gravitational effect (which is infinitesimal) I will have to make the assumption that the Earth is flat and of infinite extent so if MikeS considers this invalidates the argument I will not bother or perhaps some more competent mathematician will take over the task
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Offline yor_on

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On what principle does a weighing balance operate?
« Reply #18 on: 30/11/2011 00:33:15 »
It's a quite nice question Mike. Seems it has to do with where the 'centre of gravity' is placed with the scale you use, at least when using equal arm balances. If it is under the pivot you will be able to to have unequal weights and see it tilt without it losing its balance.

This one shows some different balance instruments. Types of Mechanical Scales.
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Offline MikeS

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On what principle does a weighing balance operate?
« Reply #19 on: 30/11/2011 09:05:33 »
Thank you all for your replies but I still don't think the original question has been answered.

A lot of the answers concentrate on how to make a balance beam stable, not why "The balance arm comes to rest where the acting forces presumably balance."
The articles referred to by Bored chemist and Geezer are of no help.

"A weighing balance (jewellers balance etc.) operates through gravity comparing the torque of the weighed object with a known mass.  The balance arm comes to rest where the acting forces presumably balance."
Please ignore for a moment that most balance arm scales are designed to be balanced with the beam in the horizontal position.
If the weight to be measured is slightly heavier than the known weight the beam will reach stable equilibrium with the heavier end slightly lower.  The beam is at an angle not horizontal. "But what are the forces and why do they balance?"

Agreed that a balance beam scale works by comparing an unknown weight to a known weight when the beam is horizontal. But what is it telling us when it reaches stable equilibrium at an angle?

I phrased it like this in a previous post.
"A simple beam balance can be made from a strip of wood suspended by thread at the centre.  If coffee cans are suspended from either end by adjusting the suspension (fulcrum) points, the scale can be made to balance.  Any very slight discrepancy in weight distribution will cause the beam to rotate a certain amount around the centre fulcrum until it reaches a point of balance.  Why does it reach a point of balance?

This was the explanation that I posted.
"Say the left hand side of the beam is slightly heavier, the beam will tilt down on the left until equilibrium is established.  The decreased GPE of the left hand (heavier) mass is equaled by the increased GPE of the right hand (lighter) mass ."

A few of you have said that the differential gravitational effect is negligible.  But is it?  How else can a balance reach stable equilibrium with the beam at an angle.  If it's not a differential gravity effect what is it?

The difference in the strength of gravity at that scale, if difficult to measure, is certainly not insignificant.
The latest atomic clocks can measure gravitational time dilation down to about one centimetre in height.  Therefore how can you say the differential gravitational effect is negligible?  It must be significant.
« Last Edit: 30/11/2011 09:38:19 by MikeS »

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Offline syhprum

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On what principle does a weighing balance operate?
« Reply #20 on: 30/11/2011 09:53:54 »
For the purpose of calculation we will take an idealised scale of the following dimensions and calculate the rotational forces operating on the beam

The beam will have a length of two meters and height of four centimetre's and will have a suspension point in the dead centre for the fulcrum and similar suspension points precisely in line at each end for the pans .

The beam mass will be zero and the mass of the pans will be 1/9.82 Kg.

The beam will be suspended at the fulcrum point so that the pans are 10cm above the working surface.

Let us next push the left hand pan down to the surface, the right hand pan will rise and exert a torque of

(1-(.1^2))^.5 = 0.99498 newton meters tending to rotate he beam clockwise while the left hand pan will exert a similar torque tending to rotate the beam anti clockwise hence the system will be stable and the left hand pan will remain down.

Now let us calculate the effect of gravity, taking the radius of the Earth as 6,366,197.8 meters the left hand pan will be this distance from the centre of the Earth while the right pan will be 6,366,197.6 meters away.

Applying Newton's inverse  square law the gravitational attraction on the right pan will be reduced by one part in (6,366,197.8/6,366,197.6)^2 =1.0000000631 hence there will be a net force of 0.99498*0.0000000631=0.0000000628 Newton's tending to hold the left hand pan down.

Now we come to the effect of raising the fulcrum point as it would normally be on any practical set of scales, If the fulcrum point is raised by one cm relative to the line of the pan suspension points when the left hand pan is pushed down the effective length of the left hand side the beam is reduced by one part in a ten thousand  while that of the right hand beam is increased by the same amount hence a restoring force tending to move the beam to a horizontal position  of 0.0002 Newton meters is generated vastly more than any gravitational effects.

 
« Last Edit: 30/11/2011 12:02:42 by syhprum »
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Offline Bored chemist

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On what principle does a weighing balance operate?
« Reply #21 on: 30/11/2011 18:33:08 »
Here's a thought experiment for you.
I'm going to build a balance.
In a rather unorthodox way, I'm going to start with just the pointer.
Obviously, with nothing else there, it hangs straight downwards.
If I push it to one side and let go, it swings back and to, but it settled down to being vertical.
Now I put the beam on the balance and fix it to the pointer.
The pointer still wants to point downwards so, if I set the beam swinging it still ends up settling down with the beam horizontal, and the pointer vertical.
I can hang pans from the beam- the pointer still does its job and the beam is only stable when it's horizontal.

This still works in the case of a perfectly uniform gravitational field.
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Offline syhprum

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On what principle does a weighing balance operate?
« Reply #22 on: 30/11/2011 20:40:08 »
MikeS
"If it's not a differential gravity effect what is it?"

Let me answer this specific point as I think it is something you have not considered.
When the beam is pivoted at a point above the line of the pan suspension points if for instance the left hand pan tends to drop the beam moves to the right reducing the effective length of the beam on the left hand side and increasing it on the right hand side.
This produces a negative feedback effect causing the beam to stabilise in the horizontal position if the masses in the two pans are equal.

« Last Edit: 30/11/2011 20:43:06 by syhprum »
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Offline syhprum

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On what principle does a weighing balance operate?
« Reply #23 on: 30/11/2011 20:51:08 »
Bored Chemist

If we have a pointer the beam can be pivoted exactly in line with the pan suspension points and it will serve to stabilise the beam in a horizontal position but if the beam is pivoted above the line of the pan suspension points the system is still stable without a pointer.
PS although the matter is trivial and of little scientific interest I find this a good writing exercise
« Last Edit: 30/11/2011 20:53:31 by syhprum »
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Offline Geezer

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On what principle does a weighing balance operate?
« Reply #24 on: 30/11/2011 20:56:15 »
If we have a pointer the beam can be pivoted exactly in line with the pan suspension points and it will serve to stabilise the beam in a horizontal position but if the beam is pivoted above the line of the pan suspension points the system is still stable without a pointer.

I agree. The pointer is, well, a pointer to tell you when the pans are balanced. Even if the pointer had zero mass, the balance would still work.

A diagram is necessary - stay tuned!
There ain'ta no sanity clause, and there ain'ta no centrifugal force Šther.

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Offline syhprum

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On what principle does a weighing balance operate?
« Reply #25 on: 30/11/2011 21:03:20 »
I resisted  the temptation add diagrams thinking it was a challenge to clarify the matter with text alone.
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Offline Bored chemist

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On what principle does a weighing balance operate?
« Reply #26 on: 30/11/2011 21:20:44 »
In the next development of the thought experiment I explain that my pointer is of a non-traditional shape.
Specifically it is exactly the same shape as the beam. It just has a little arrow drawn on it  labelled "Down".

There's nothing magical about what you call the mass that hangs downwards below the suspension point. A pointer will clearly do the job of ensuring that the beam comes to rest horizontal.
But the beam itself will also do that job.
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Offline Geezer

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On what principle does a weighing balance operate?
« Reply #27 on: 30/11/2011 21:23:36 »
Look mum! No pointer.

[attachment=15584]


The forces (F) on the pan pivots are equal but the beam is not level. L1 is greater than L2, so the counter-clockwise torque is greater than the clockwise torque. The net torque is zero when L1 and L2 are equal, at which point the beam will be horizontal.

EDIT: BTW, this works when the pointer has zero mass, but it works just as well when the beam has no mass either.

« Last Edit: 30/11/2011 22:39:32 by Geezer »
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Offline MikeS

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On what principle does a weighing balance operate?
« Reply #28 on: 01/12/2011 08:18:47 »
For the purpose of calculation we will take an idealised scale of the following dimensions and calculate the rotational forces operating on the beam

The beam will have a length of two meters and height of four centimetre's and will have a suspension point in the dead centre for the fulcrum and similar suspension points precisely in line at each end for the pans .

The beam mass will be zero and the mass of the pans will be 1/9.82 Kg.

The beam will be suspended at the fulcrum point so that the pans are 10cm above the working surface.

Let us next push the left hand pan down to the surface, the right hand pan will rise and exert a torque of

(1-(.1^2))^.5 = 0.99498 newton meters tending to rotate he beam clockwise while the left hand pan will exert a similar torque tending to rotate the beam anti clockwise hence the system will be stable and the left hand pan will remain down.

Now let us calculate the effect of gravity, taking the radius of the Earth as 6,366,197.8 meters the left hand pan will be this distance from the centre of the Earth while the right pan will be 6,366,197.6 meters away.

Applying Newton's inverse  square law the gravitational attraction on the right pan will be reduced by one part in (6,366,197.8/6,366,197.6)^2 =1.0000000631 hence there will be a net force of 0.99498*0.0000000631=0.0000000628 Newton's tending to hold the left hand pan down.

Now we come to the effect of raising the fulcrum point as it would normally be on any practical set of scales, If the fulcrum point is raised by one cm relative to the line of the pan suspension points when the left hand pan is pushed down the effective length of the left hand side the beam is reduced by one part in a ten thousand  while that of the right hand beam is increased by the same amount hence a restoring force tending to move the beam to a horizontal position  of 0.0002 Newton meters is generated vastly more than any gravitational effects.

But the left hand pan wont stay down.  The beam will go back to horizontal.

If all three fulcrum points are in-line the balance will still work despite the fact that both arms remain the same length regardless of the beams inclination.

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Offline MikeS

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On what principle does a weighing balance operate?
« Reply #29 on: 01/12/2011 08:24:17 »
MikeS
"If it's not a differential gravity effect what is it?"

Let me answer this specific point as I think it is something you have not considered.
When the beam is pivoted at a point above the line of the pan suspension points if for instance the left hand pan tends to drop the beam moves to the right reducing the effective length of the beam on the left hand side and increasing it on the right hand side.
This produces a negative feedback effect causing the beam to stabilise in the horizontal position if the masses in the two pans are equal.


It's true that I hadn't originally thought of the effective lengths of the arms changing due to the geometry of the fulcrum points.
But
If all three fulcrum points are in-line the balance will still work despite the fact that both arms remain the same length regardless of the beams inclination. 
I think I am right in believing in this design torque is always equally balanced and therefore plays no part.
« Last Edit: 01/12/2011 08:58:37 by MikeS »

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Offline MikeS

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On what principle does a weighing balance operate?
« Reply #30 on: 01/12/2011 08:44:57 »
This is the question that still hasn't been answered.

Let's consider a simple balance beam with all three pivot points in line.  One pan is slightly heavier than the other.  The beam will come to stable equilibrium with one pan lower than the other.  Why?

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Offline syhprum

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On what principle does a weighing balance operate?
« Reply #31 on: 01/12/2011 09:06:41 »
But it will not with all three pivot points in line and one pan heavier than the other the heavier pan will descend until it meets a stop.
This of course assumes their is no friction in the system and an equal mass of beam above or below the fulcrum points
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Offline MikeS

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On what principle does a weighing balance operate?
« Reply #32 on: 01/12/2011 09:21:34 »
Mmmmm.  Do you have any evidence for that?

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Offline syhprum

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On what principle does a weighing balance operate?
« Reply #33 on: 01/12/2011 10:00:02 »
No I thought this was a theoretical discussion and I have not had access to any laboratory type balance since I left school seventy years ago.
Perhaps our Bored Chemist could confirm it.
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Offline MikeS

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On what principle does a weighing balance operate?
« Reply #34 on: 01/12/2011 10:03:25 »
syphrum

"Practical balances are constructed with the central knife-edge lying a little
below the plane of the terminal knife-edge."

http://books.google.co.uk/books?id=hYZC-k4mo-YC&pg=PA23&lpg=PA23&dq=%22sensitivity+of+a+balance%22+knife&source=bl&ots=BLB1Qa5EqB&sig=jKzHvhGBb_VWFf4WbhmncMI3zrM&hl=en&ei=JvrTTpXZNMmd-waYu8z6Dg&sa=X&oi=book_result&ct=result&resnum=1&ved=0CBwQ6AEwAA#v=onepage&q=%22sensitivity%20of%20a%20balance%22%20knife&f=false

This is the opposite of the way that most of you have described the pivot points of a balance and the opposite of
Geezers diagram.  L2 is greater than L1.

If a balance can work with the central pivot point either above or below the terminal pivot points then I see no reason why it should not work with all three pivot points in line.

In which case this is wrong
But it will not with all three pivot points in line and one pan heavier than the other the heavier pan will descend until it meets a stop.

« Last Edit: 01/12/2011 10:06:17 by MikeS »

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Offline syhprum

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On what principle does a weighing balance operate?
« Reply #35 on: 01/12/2011 10:40:39 »
The balance will certainly work with all pivot points in line but with equal weights in each pan it will not automatically restore its self to a horizontal beam state if either pan is pushed down it will stay down.
As far as I recall our school balances had a lever to lift the central post after the pans were loaded, if they were equally loaded the beam would come up horizontal but of course they had some self restoring force built in.
Even in the absence of this feature they would still would still have come up in this manner but this state would have been unstable and if either were pushed down the would have stayed down.
Reading the article you quoted I notice that the central pivot is placed below the line of the pan pivots which in effect gives a positive feedback making the balance point unstable but stability is restored by the use of a pointer which gives a negative feedback effect to counteract this.
This combination is done to increase the sensitivity at small deflections.
We have of course been discussing the most basic form of balance but commercial designs are a little different
 
« Last Edit: 01/12/2011 10:58:04 by syhprum »
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Offline MikeS

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On what principle does a weighing balance operate?
« Reply #36 on: 01/12/2011 11:26:30 »
syphrum

Ok so let's consider a simple balance beam with all three pivot points in line and the balance beam incorporates some kind of restoring force.  One pan is slightly heavier than the other.  The beam will come to stable equilibrium with one pan lower than the other.

Do you agree?

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Offline syhprum

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« Reply #37 on: 01/12/2011 11:44:16 »
With some sort of restoring force ? a pointer perhaps as your postioning of the pivots gives none.
In this case yes
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Offline MikeS

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On what principle does a weighing balance operate?
« Reply #38 on: 01/12/2011 11:54:27 »
The question is why does the balance reach stable equilibrium with one pan lower than the other?  Why does the heavier pan not continue until it reaches the stop?

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Offline syhprum

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« Reply #39 on: 01/12/2011 12:17:31 »
It depends how stability has been achieved, in the original case where stability had been achieved by the positioning of the pivots the non linear change in apparent length of the arms with the deflection angle would limit how far the heavier pan drops, the restoring force exerted by a pointer is also not in a linear relationship to the deflection angle .
The mathematics of the situation would involve trigonometric functions into which I don't really wish to go.
syhprum

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Offline MikeS

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On what principle does a weighing balance operate?
« Reply #40 on: 01/12/2011 12:37:09 »
syphrum

Ok so let's consider a simple balance beam with all three pivot points in line.

Would you consider the pans to contribute a restoring force without the requirement of the mass of a needle?

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Offline syhprum

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« Reply #41 on: 01/12/2011 13:24:53 »
No in this case there would be no restoring force so the heavier pan would go down to limit or equally weighted pans would just sit where they were placed, but let me continue 
As stated by Bored Chemist there is no difference between a scale stabilised by the weight of a pointer to one stabilised by the positioning of the pivots so I will use the later to explain how trigmetric functions determine the deflection angle hence how far the weighted pan drops .
As the weighted pan drops the torque it develops varies as the cosine of the angle of the beam from the horizontal i.e starts high and falls away whereas the torque generated by the pointer being set at 90░ to the beam varies as the sine of the angle of the beam from the horizontal i.e starts low and climbs.
when these two sources cancel out that is the angle at which the beam rests.
« Last Edit: 01/12/2011 13:27:16 by syhprum »
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Offline Bored chemist

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On what principle does a weighing balance operate?
« Reply #42 on: 01/12/2011 19:05:37 »
"Ok so let's consider a simple balance beam with all three pivot points in line. "
Why should we?
It's not as if anyone would actually make a balance like that (unless they were relying on a pointer to keep it in check).
If they did that, it wouldn't work.
Please disregard all previous signatures.

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Offline Geezer

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On what principle does a weighing balance operate?
« Reply #43 on: 01/12/2011 19:13:25 »
Ok so let's consider a simple balance beam with all three pivot points in line.

Would you consider the pans to contribute a restoring force without the requirement of the mass of a needle?

Absolutely not. If the weights are equal there is no torque in any position.

Your question is the same as "what would happen if I picked up a perfectly balanced bicycle wheel by it's axle?" Obviously, it won't rotate because there is no reason why it should rotate.

If the fulcrums on a scale are in line, and the center of mass of the entire beam assembly (including the pointer) is conincident with point of rotation of the beam, there will be no restoring force. If the weights are equal, the balance will remain in any position it is put in. If the weights are unequal, the heavier one will tip the balance as far as it can go.

A scale must have a restoring force because a balance is actually comparing the the restoring force with the difference in the weights on the pans. The displacement of the pointer from center actually calibrates that amount on a graduated scale.
« Last Edit: 01/12/2011 19:16:12 by Geezer »
There ain'ta no sanity clause, and there ain'ta no centrifugal force Šther.

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Offline syhprum

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On what principle does a weighing balance operate?
« Reply #44 on: 01/12/2011 20:03:54 »
Bored Chemist

The balance in the article you directed us to actually had the fulcrum below the suspension points of the pans and relied on the weight of the pointer to provide stabilisation.
This combination of positive and negative feedback was done to increase the sensitivity to small deflections
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Offline syhprum

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On what principle does a weighing balance operate?
« Reply #45 on: 01/12/2011 20:16:20 »
Geezer

The wheel of an inverted bicycle could well be used as a model balance, a small weight could be placed say where the valve comes out to emulate the pointer and pseudo pans attached either in line with the axle or symmetrically above or below it for experiment.
A simple and readally available model
« Last Edit: 01/12/2011 20:18:28 by syhprum »
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Offline Geezer

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On what principle does a weighing balance operate?
« Reply #46 on: 01/12/2011 20:59:38 »
Geezer

The wheel of an inverted bicycle could well be used as a model balance, a small weight could be placed say where the valve comes out to emulate the pointer and pseudo pans attached either in line with the axle or symmetrically above or below it for experiment.
A simple and readally available model

Oh, you mean something like this?


[attachment=15605]


(The pseudo pans are calibrated galvanised buckets attached to a piece of string.)

(Astute correspondents will observe that the distance between the string and the axis of the wheel is constant.)

« Last Edit: 01/12/2011 21:33:34 by Geezer »
There ain'ta no sanity clause, and there ain'ta no centrifugal force Šther.

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Offline syhprum

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On what principle does a weighing balance operate?
« Reply #47 on: 01/12/2011 21:36:30 »
No I think the buckets should be attached to the spokes so that you can adjust the suspension points relative to the axle
« Last Edit: 02/12/2011 08:14:08 by syhprum »
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Offline Geezer

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On what principle does a weighing balance operate?
« Reply #48 on: 01/12/2011 21:46:13 »
No I think the buckets should be attached to the spokes so that you adjust the suspension points relative to the axle


Yes. That would make it more like a beam balance, but I like my version better!

The only thing that produces a restoring force is the weight of the valve which tends to prove that there are many ways to produce a restoring force, but you gotta have one.

We could even eliminate (or counterbalance) the unbalanced mass of the valve and replace it with a torsion spring and get the same result.
« Last Edit: 01/12/2011 21:55:01 by Geezer »
There ain'ta no sanity clause, and there ain'ta no centrifugal force Šther.

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Offline MikeS

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On what principle does a weighing balance operate?
« Reply #49 on: 02/12/2011 08:42:26 »
Thank you all for taking part you have convinced me.  A balance needs a restoring force.