# The Naked Scientists Forum

### Author Topic: On what principle does a weighing balance operate?  (Read 39661 times)

#### Bored chemist

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##### On what principle does a weighing balance operate?
« Reply #75 on: 11/12/2011 14:44:46 »

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.

Well, try doing it again until you get a better answer.

#### JP

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##### On what principle does a weighing balance operate?
« Reply #76 on: 11/12/2011 15:32:38 »
You're dividing 9.8 by 9*1016.  The answer has to be something times 10-16.

#### syhprum

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##### On what principle does a weighing balance operate?
« Reply #77 on: 11/12/2011 16:53:23 »
Do you think we have the answer to the Neutrino anomaly here .

#### Geezer

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##### On what principle does a weighing balance operate?
« Reply #78 on: 11/12/2011 20:38:35 »
I'll add it to the poll.

#### MikeS

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##### On what principle does a weighing balance operate?
« Reply #79 on: 12/12/2011 08:36:19 »
Looking back through my last post it looks like I made two completely separate mathematical mistakes.

The first being 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)
I was thinking kilometers not meters so squared 300,000 not 300,000,000.

Working out the bucket weight difference with one bucket dropping one meter whilst the other bucket rose one meter, the difference in weight due to the difference in GPE (using my wrong figure) was  1.563500000579e-7 kg

My second mistake
“M(earth) X G /(6,400,401^2)
So the ratio of them is (6,400,000^2 ) to (6,400,001^2)”
For some reason I read ˆ as multiply not square.
This resulted in a weight difference of the buckets due to height, of 1.563600000587e-7 kg

That’s one heck of a coincidence.  One digit difference in the 11 decimal place.
I need to change my glasses, just noticed one digit difference in the fourth decimal place, oh well.
« Last Edit: 12/12/2011 08:53:17 by MikeS »

#### MikeS

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##### On what principle does a weighing balance operate?
« Reply #80 on: 12/12/2011 08:48:34 »
I wasn't sure whether to start this in a new thread or not, as I seem to have worn this one out.

If you weigh an object within a gravitational gradient (at different heights) you get different weights.  The object weighs more the deeper it is within the gravity well.

Likewise the object has different GPE depending upon its height within the gravity well.

As the object is moved lower within the gravity well it looses some of its GPE but gains weight (mass).

The question is why aren’t these the same?  Why does the objects weight plus GPE at one height not equal its weight plus GPE at another height?  Surely, because of the equivalence principle, E=mc2, they should be the same?

If GPE is much less over a given distance than weight difference (by many orders of magnitude) then why is dropping a 1kg weight on your head from 1m noticeable whereas its weigh difference over 1m is not?

#### Bored chemist

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##### On what principle does a weighing balance operate?
« Reply #81 on: 12/12/2011 19:53:19 »
"The question is why aren’t these the same?  "
Because one of them is much bigger than the other.
He would be able to calculate the change in weight with altitude but not the change in mass with energy.
They are simply different things.
Why should they be the same?

#### syhprum

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##### On what principle does a weighing balance operate?
« Reply #82 on: 12/12/2011 20:17:28 »
To keep this bizarre thread going even longer perhaps we should consider the case where we have a very long string and the lower bucket is lowered down the gravity train tunnel.
I rather worry for the rabbit, firstly irradiated by the Polonium now subjected to the Earth centre temperatures and the effects of zero Gravity (at the centre).
We have not yet considered the effects of centrifugal Centripetal force ! No doubt the shades of Newton, Einstein, and Mach will have to be invoked.
« Last Edit: 12/12/2011 20:38:30 by syhprum »

#### MikeS

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##### On what principle does a weighing balance operate?
« Reply #83 on: 14/12/2011 09:08:37 »
Quote Bored chemist.

"The question is why aren’t these the same?  "
"Because one of them is much bigger than the other.
He would be able to calculate the change in weight with altitude but not the change in mass with energy.
They are simply different things.
Why should they be the same?"

You say “they are simply different things.  Why should they be the same?”
As I see it, a change in weight with altitude should be equivalent to a change in GPE with altitude.  Mass and energy being equivalent.  What are the factors to consider here?  The gravitational gradient, which in turn leads to a time dilation gradient and mass/energy.  GPE and weight are both affected by the gravitational gradient (caused by a change in height).  When you change the height you change the weight.  Why does the GPE not change by the same amount?  GPE is dependent upon weight and height.  GPE and weight seem to look like ‘different faces of the same coin’.  However, the difference in weight due to a change in height is not equivalent to the change in equivalent mass of the change in GPE.

For an object to ‘weigh’ more deeper within a gravity well it must have gained mass which is equivalent to a gain of energy.  This seems to make sense, as it requires more energy to do anything the deeper you go within the gravity well.  In other words, gravity ‘ties up’ energy rendering it unusable.

The same argument seems to apply to GPE.  The deeper the object is within the gravity well the less GPE it has.  Energy has been ‘tied up’ rendering it unusable.

"He (Newton) would be able to calculate the change in weight with altitude but not the change in mass with energy."
Surely,"the change in weight with altitude", should be equivalent to "the change in mass with energy"  But the change in mass due to a change in height is many orders of magnitude greater than the change in mass due to the change in GPE.  I still don’t understand why?
« Last Edit: 14/12/2011 09:17:55 by MikeS »

#### JP

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##### On what principle does a weighing balance operate?
« Reply #84 on: 14/12/2011 14:55:28 »
Mike you're mixing your theories.  You want to use general relativity, because that's the theory that tells you that energy effects gravity, but in general relativity, gravitational potential energy isn't a thing, so your arguments don't hold.

But there are two effects in GR, similar to to "position effects gravity" and "GPE effects gravity."  If a small mass is near a big mass, the big mass curves space-time, which influences how the small mass will move under gravity.  This is how position effects gravity.  However, the small mass also has a very small effect on the space-time around it, which alters the total way space-time curves around the big mass by a very tiny bit and in turn effects how the small mass feels gravity.  Since this effect is tiny, it will mostly be unimportant, but if you really want to do the calculations of how this tiny distortion in space-time effects its overall motion under gravity, you can do so.

#### Bored chemist

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##### On what principle does a weighing balance operate?
« Reply #85 on: 14/12/2011 19:31:46 »
"As I see it, a change in weight with altitude should be equivalent to a change in GPE with altitude.  "
The real world doesn't see it like that so nor should you.

#### ajitharidas

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##### Re: On what principle does a weighing balance operate?
« Reply #86 on: 11/05/2014 16:22:14 »
A balance requires a restoring torque. The restoring torque is provided by a centre of mass of the balance being below than the horizontal plane of the beam knife edge. When a pan is pushed down, there c.m. moves away, on the opposite side, out of the vertical plane of beam knife edge, but remaining below the horizontal plane of the beam knife edge. This creates restoring torque.

#### ajitharidas

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##### Re: On what principle does a weighing balance operate?
« Reply #87 on: 12/05/2014 09:12:20 »
To make it clearer, think of a balance beam with no pan - say a straight edge. Pass a pin through its centre of mass. This balance is stable at any angle. If you hang equal masses on either end, it becomes a balance with a restoring torque. The centre of mass shifts below the pivot. On the other hand, if you stick equal masses at ends of the straight edge, on the line of symmetry, you will not change the centre of mass, (it still passes through the pivot), and you will have no restoring torque.

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##### Re: On what principle does a weighing balance operate?
« Reply #87 on: 12/05/2014 09:12:20 »