# The Naked Scientists Forum

### Author Topic: On what principle does a weighing balance operate?  (Read 38540 times)

#### MikeS

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##### On what principle does a weighing balance operate?
« Reply #50 on: 02/12/2011 08:55:54 »
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?

(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.)

I like it!

Let's suppose the wheel is perfectly balanced, has no bearing friction and has no restoring force, the buckets perfectly balanced, the string has no mass and is very long.

If we pull one of the buckets almost as far down as possible the other bucket will be almost as high as possible.  The lower bucket will now weigh marginally more than the higher bucket.  If you bring the bucket to a stop and release hold of the bucket will it continue down or will it remain stationary?
« Last Edit: 02/12/2011 11:07:50 by MikeS »

#### syhprum

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##### On what principle does a weighing balance operate?
« Reply #51 on: 02/12/2011 14:52:30 »
May I refer you to my calculation of the differential gravitational effect (post 2307), provided the lower bucket is still above the surface of he Earth there is a very small additional gravitational attraction to it so as you have specified that there is zero friction in the system presumably it would continue down but you would be hard put to realise such a system in practice.

PS are you a member of the legal profession ?
« Last Edit: 02/12/2011 14:55:34 by syhprum »

#### imatfaal

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##### On what principle does a weighing balance operate?
« Reply #52 on: 02/12/2011 15:34:14 »
PS are you a member of the legal profession ?

No, that would be me!  And we only ask silly questions when we are being paid to do so  :-)

I think Syhprum is quite correct - I estimated it to be in the order of 10^-7 to 10^-8N

#### Geezer

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##### On what principle does a weighing balance operate?
« Reply #53 on: 02/12/2011 18:08:14 »

I think Syhprum is quite correct - I estimated it to be in the order of 10^-7 to 10^-8N

If we had a really long piece of string we might even be able to observe the effect.

« Last Edit: 02/12/2011 19:29:39 by Geezer »

#### syhprum

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##### On what principle does a weighing balance operate?
« Reply #54 on: 02/12/2011 18:12:54 »
the difficulty is finding string of zero mass

#### Bored chemist

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##### On what principle does a weighing balance operate?
« Reply #55 on: 02/12/2011 18:19:13 »
You could use neutrally buoyant string and set the rig up underwater.
Of course, the variation of water density with depth...

The fact is that balances are actually built so that they come to rest with the beam horizontal.
The means by which this is achieved are simple enough to understand.

#### Geezer

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##### On what principle does a weighing balance operate?
« Reply #56 on: 02/12/2011 18:24:23 »
the difficulty is finding string of zero mass

It might be even harder to find a skyhook to hang the wheel from.

#### syhprum

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##### On what principle does a weighing balance operate?
« Reply #57 on: 02/12/2011 18:47:46 »
Eureka, use a loop of string then it cancels out.
A convenient place to carry out the experiment would be the Kreigmarine memorial in Laboe.
« Last Edit: 04/12/2011 08:50:10 by syhprum »

#### Geezer

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##### On what principle does a weighing balance operate?
« Reply #58 on: 02/12/2011 19:00:20 »
Maybe they'd let us use that giant wheely thing they built beside the Thames?

#### syhprum

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##### On what principle does a weighing balance operate?
« Reply #59 on: 02/12/2011 19:02:08 »
we would be shielded from the wind in Laboe

#### imatfaal

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##### On what principle does a weighing balance operate?
« Reply #60 on: 02/12/2011 19:27:02 »
We could use the Monument: one of its design parameters was for a astronomical and gravitational experiments (it has a secret(ish) underground lab at the bottom) and it is still used to this day.

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

#### Geezer

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##### On what principle does a weighing balance operate?
« Reply #61 on: 02/12/2011 19:37:45 »

Looks like we might have to recalibrate the lower bucket.

#### MikeS

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##### On what principle does a weighing balance operate?
« Reply #62 on: 03/12/2011 08:04:46 »
To answer syphrums question, no I am not a member of the legal profession although it has been suggested, more than once that I think like one.  (I still haven't worked out how to take that.)  My primary background was as an engineer troubleshooting for BT.  My brain seems to be wired that way, if you'll excuse the pun.
« Last Edit: 03/12/2011 09:45:32 by MikeS »

#### MikeS

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##### On what principle does a weighing balance operate?
« Reply #63 on: 03/12/2011 08:05:20 »
Mmmm rabbit in a bucket, tasty.

Continuing with 'Geezers wheel and bucket balance' (less rabbit).

The lower bucket, as measured by a 'spring balance' weighs more than the higher bucket so we expect it to continue down to the full extent possible.
Both buckets when in the same horizontal plane weighed the same.  The lower bucket now weighs more because it is deeper within the gravity well but has lost a certain amount of gravitational potential energy (GPE).  The higher bucket has correspondingly lost weight but gained the same amount of GPE.  Therefore both buckets still contain the same amount of mass/energy through the mass/energy equivalence principle.

The question is if both buckets have in effect the same mass would the lower bucket continue its journey down or would they both balance regardless of position?

« Last Edit: 03/12/2011 08:12:15 by MikeS »

#### syhprum

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##### On what principle does a weighing balance operate?
« Reply #64 on: 03/12/2011 20:37:50 »
Even if you position the two buckets so that the gravitational attraction is the same on each the system is inherently unstable any infinitesimal disturbance could set them moving,rather like a pencil standing on its point.
Re-reading your post it would seem that you want to bring special relativity into the problem, I regret being only a retired technician lacking even "O" levels such mathematics are beyond me, perhaps one of the better educated correspondents will be able to take the matter further.
« Last Edit: 03/12/2011 22:03:27 by syhprum »

#### MikeS

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##### On what principle does a weighing balance operate?
« Reply #65 on: 04/12/2011 08:45:02 »
The maths are beyond me as well unfortunately but it's still interesting to consider thought experiments.  I tend to agree that the system is 'probably' inherently unstable.  The instability presumably being due to the differential effects of gravity.

I hope someone will answer the question in my last post above.

#### Bored chemist

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##### On what principle does a weighing balance operate?
« Reply #66 on: 04/12/2011 11:13:14 »
My maths isn't that good, but I have seen lots of adverts from balance makers.
A while ago (maybe 15 or 20 years) one of them produced an ad that was a picture of a gold bar next to a picture of a tall building with the caption something like
1.000000 grams on the ground floor 0.999997 grams on the 30th floor.
I forget what the numbers were but the point was that you could measure (just) the difference in the force of gravity between the top and bottom of a tall building.
Now imagine that I take that gold bar and drop it from the top of the building to the ground.
Most of the energy released will be turned into heat. The bar will warn up- but only very slightly.
So the gravitational energy is equivalent to a small rise in temeperature.
On the other hand, I know that it's still (15 or 20 years on) impossible to measure the change in mass due to changes in temperature that arise from relativity.

I conclude that the change in weight due to differential gravitation is much bigger than the change in mass due to potential energy.

I'm sure the calculation would confirm this.

#### MikeS

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##### On what principle does a weighing balance operate?
« Reply #67 on: 04/12/2011 12:44:00 »
Thanks but.

Say you dropped it in a vacuum, there would be no warming on the way down.  When it hits the ground it has gained kinetic energy (by converting GPE into kinetic) and that energy is converted into sound and heat upon contact.  The energy gained is substantial.  You wouldn't want it to drop on your head.  Is it simply that a very large amount of energy is required to produce even a slight increase in mass hence it is difficult to measure the increase, or is there some other explanation?

I conclude that the change in weight due to differential gravitation is much bigger than the change in mass due to potential energy.

But isn't this the same thing?
At the top of the building the bar weighs less but has a higher GPE.  At the bottom of the building the bar weighs more but has a lower GPE.  The two being equal due to the energy/mass equivalence principle?

#### MikeS

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##### On what principle does a weighing balance operate?
« Reply #68 on: 04/12/2011 12:49:16 »
Aaaah I've just realised the two probably arn't equivalent.  I hadn't taken into account the energy lost in slowing the bar down to stationary.  Does that make sense?

#### Bored chemist

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##### On what principle does a weighing balance operate?
« Reply #69 on: 04/12/2011 15:29:22 »
OK lets do the maths.
Assume the gold bar is 1Kg because it makes the maths easy. Similarly, it falls 1 metre.
It lands at ground level and that is 6400Km (exactly) from the centre of the Earth where I choose to do the experiment and the local value of g is 9.8 m/s/s

It falls 1 metre so it converts potential energy =Mgh into kinetic energy just before it hits the ground and it converts that into thermal energy when it hits.
The energy released is 9.8J
From E=MC^2 we get a change in mass of
9.8=300,000,000* 300,000,000 M.
M= 1.1E-16 Kg

On the other hand, the change in weight (and an apparent change in mass) is given by the change in g

g= M(earth) X G/ (6,400,000^2)
whereas the value 1 metre further up is
M(earth) X G /(6,400,401^2)
So the ratio of them is (6,400,000^2 ) to (6,400,001^2)
So a 1 Kg mass would apparently weigh 3.125 E-7 Kg less

Since the two mass changes are different by a factor of about 3 billion, they are not the same.

#### syhprum

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##### On what principle does a weighing balance operate?
« Reply #70 on: 04/12/2011 16:18:08 »
I could of course have made these simple calculations despite zero "O" levels but I think this question has been flogged to death.
« Last Edit: 04/12/2011 16:20:00 by syhprum »

#### syhprum

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##### On what principle does a weighing balance operate?
« Reply #71 on: 04/12/2011 17:06:38 »
With gold at £25,000 per kilo the loss in value on the thirtieth floor would have been only a few pennies but if it had been Polonium or anti matter or some real expensive stuff it would be real serious
« Last Edit: 04/12/2011 18:49:35 by syhprum »

#### Geezer

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##### On what principle does a weighing balance operate?
« Reply #72 on: 04/12/2011 19:17:23 »
I'm revising the diagram to include a polonium rabbit.

#### MikeS

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##### On what principle does a weighing balance operate?
« Reply #73 on: 11/12/2011 10:42:18 »
Like a phoenix from the grave, some things just wont die.

From an earlier post.
"Continuing with 'Geezers wheel and bucket balance'" (less rabbit, polonium or otherwise).

"The lower bucket, as measured by a 'spring balance' weighs more than the higher bucket so we expect it to continue down to the full extent possible.
Both buckets when in the same horizontal plane weighed the same.  The lower bucket now weighs more because it is deeper within the gravity well but has lost a certain amount of gravitational potential energy (GPE).  The higher bucket has correspondingly lost weight but gained the same amount of GPE.  Therefore both buckets still contain the same amount of mass/energy through the mass/energy equivalence principle.

The question is if both buckets have in effect the same mass would the lower bucket continue its journey down or would they both balance regardless of position?"

From an earlier post.
Quote from: Bored chemist on 04/12/2011 11:13:14

”I conclude that the change in weight due to differential gravitation is much bigger than the change in mass due to potential energy.”

From an earlier post.
"But isn't this the same thing?
At the top of the building the bar weighs less but has a higher GPE.  At the bottom of the building the bar weighs more but has a lower GPE.  The two being equal due to the energy/mass equivalence principle?"

Let’s do the maths for the above experiment.

From an earlier post by Bored chemist.
“Assume the gold bar is 1Kg because it makes the maths easy. Similarly, it falls 1 metre.
It lands at ground level and that is 6400Km (exactly) from the centre of the Earth where I choose to do the experiment and the local value of g is 9.8 m/s/s

It falls 1 metre so it converts potential energy =Mgh into kinetic energy just before it hits the ground and it converts that into thermal energy when it hits.
The energy released is 9.8J
From E=MC^2 we get a change in mass of
9.8/300,000,000* 300,000,000 M.
M= 1.1E-16 Kg”

I work it out to be M=1.088888888889e-10 not the above figure.

Continuing the earlier post by Bored chemist

”On the other hand, the change in weight (and an apparent change in mass) is given by the change in g

g= M(earth) X G/ (6,400,000^2)
whereas the value 1 metre further up is
M(earth) X G /(6,400,401^2)
So the ratio of them is (6,400,000^2 ) to (6,400,001^2)
So a 1 Kg mass would apparently weigh 3.125 E-7 Kg less

Since the two mass changes are different by a factor of about 3 billion, they are not the same.”

Continuing the maths.
The two buckets have the same mass (1kg) when horizontal, so remain horizontal.  If we manually position one bucket (a) 1 meter lower then the other bucket(b) is one meter higher.

Bucket a now weighs 1.00000015625kg
Bucket b now weighs 0.9999998437500244kg
That’s a difference of 1.563600000587e-7

Both buckets are now stationary but bucket a is now heavier than bucket b so we would expect bucket a to continue to fall whilst bucket b continues to rise and thereby increasing the weight differential.

But this is only half of the story.  As bucket a falls and increases in weight it looses GPE.  Likewise as bucket b rises and looses weight it increases its GPE.  The buckets were positioned manually.  Any loss in GPE of bucket a is equaled by the equivalent gain in GPE of bucket b.

Continuing the earlier post by Bored chemist
"It falls 1 metre so it converts potential energy =Mgh into kinetic energy just before it hits the ground and it converts that into thermal energy when it hits.
The energy released is 9.8J
From E=MC^2 we get a change in mass of
9.8/300,000,000* 300,000,000 M.”"
=1.088888888889e-10 (my calculated figure)

Bucket a has lost 1.088888888889e-10kg so now weighs 0.9999999998911111kg less in GPE

Bucket b has gained 1.088888888889e-10kg so now weighs 1.000000000108889kg more in GPE
That’s a difference of 1.563500000579e-7

That’s a discrepancy of 1.000000080001e-11

Quote from earlier post.
"But isn't this the same thing?
At the top of the building the bar weighs less but has a higher GPE.  At the bottom of the building the bar weighs more but has a lower GPE.  The two being equal due to the energy/mass equivalence principle?"

You can’t get much closer than that.  The minute difference in results is probably due to the slight differences in the strength of gravity not being taken into account at the different heights.

From an earlier post.
"The question is if both buckets have in effect the same mass would the lower bucket continue its journey down or would they both balance regardless of position?"

From the above it seems obvious to me that any difference in weight of the buckets caused by differential gravity is equally balanced by a corresponding change in GPE thereby negating the effect caused by the change in weight.  In other words, the buckets will remain perfectly balanced, regardless of differences in height in any position.

Going back to previous posts a neutrally balanced, balance beam should remain stable (ignoring any instability caused by construction) in any position due to any differences in pan weigh due to differential gravity being balanced by a corresponding change in GPE.  The two being equivalent through E =mc2

Unless you know differently of course.

The figure given by Bored chemist is correct, I don't know how I managed to get it wrong using an on-line calculator.  I must have entered it wrongly I guess.  The strange thing is the wrong figure gave a result that when 'plugged' into everything else gave exactly the answer that I was expecting.  Guess that was why I didn't re check it.  Obviously I need to go over it all again.

Just gone over my figures and discovered I squared 300,000 not 300,000,000

« Last Edit: 11/12/2011 16:14:31 by MikeS »

#### syhprum

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##### On what principle does a weighing balance operate?
« Reply #74 on: 11/12/2011 13:24:39 »
"9.8/300,000,000* 300,000,000 M.”"
=1.088888888889e-10 (my calculated figure)"
No arithmetic error !!!

9.8/300000000^2 = 1.088888*10^-14 Wrong again back to infants school
Deduct another brownie point it should of course be 1.0888*10^-16
I think some maintenance on sliderules needs to be done.
« Last Edit: 11/12/2011 16:50:36 by syhprum »

#### The Naked Scientists Forum

##### On what principle does a weighing balance operate?
« Reply #74 on: 11/12/2011 13:24:39 »