[MikeS (OP)]

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?

[syhprum]

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.

[MikeS (OP)]

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.

[syhprum]

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.

[MikeS (OP)]

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.

[Bored chemist]

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

[Soul Surfer]

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

[Geezer]

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.

[MikeS (OP)]

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?

[MikeS (OP)]

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.

[Geezer]

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.

[MikeS (OP)]

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 ."

[MikeS (OP)]

"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.

[syhprum]

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.

[MikeS (OP)]

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.

[syhprum]

May I refer you to the posts by Geezer, Soul Surfer, and myself also the article cited by Bored Chemist.

[Geezer]

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.

[syhprum]

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

[yor_on]

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.

[MikeS (OP)]

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.