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-7Both 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-7That’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 =mc

^{2}Unless you know differently of course.

Added

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