Paradox of balance scales

[DimaMazin]

Why' after change of balance on scales , balance happens again? How space/time works here?

[Strange]

What do you mean by "balance happens again"?

If you are referring to the fact that the scales can find a stable, but unbalanced, position then my guess is that this is due to imperfections in the mechanism, friction, rotational forces, etc. Trying to use GR to explain this is probably overkill.

[Lord Antares]

I have a feeling he's asking something like this: ''if you have an old-school balance scale and put two objects of different masses on it, why does it go back to equal level once you remove them?''

 

Simply because, once you remove the objects, the weight on both sides is equal, so having nothing on the scale would be the same as having two objects of the same mass. Except, the force of gravity is weighing it down (equally on both sides), rather than a solid object.

 

Forgive me if I misenterpreted your question, but this is how I understood it.

[DimaMazin]

What do you mean by "balance happens again"?

If you are referring to the fact that the scales can find a stable, but unbalanced, position then my guess is that this is due to imperfections in the mechanism, friction, rotational forces, etc. Trying to use GR to explain this is probably overkill.

You have changed ideal balance by your hand.. One bowl has lowered downwards, the second has risen upwards.After the disbalance they came back in balance again.Why? If you solve it with Newton then please.I can't understand why lowered bowl has less force than risen bowl.

[Manticore]

I think the central pivot is normally above the beam - this means that when it is tilted, the upwards end of the beam must move outward slightly (and the lower end inwards), giving a greater torque from the upper arm around the pivot.

Edited July 14, 2017 by Manticore

[Lord Antares]

You have changed ideal balance by your hand.. One bowl has lowered downwards, the second has risen upwards.After the disbalance they came back in balance again.Why? If you solve it with Newton then please.I can't understand why lowered bowl has less force than risen bowl.

 

See what I said above + Manticore's engineering explanation. But if you want it explained simply with gravitation, it's simple as that.

[DimaMazin]

 

See what I said above + Manticore's engineering explanation. But if you want it explained simply with gravitation, it's simple as that.

Do you think point of the support is accelerating relative to the beam, and then force of inertia of the bowls is force of the balance?

[J.C.MacSwell]

Do you think point of the support is accelerating relative to the beam, and then force of inertia of the bowls is force of the balance?

Not sure exactly what you are describing but his sounds like the equivalency principle. You could use a balance scale without the use of gravity (say, in outer space somewhere) based on that principle and accelerating the scale, if that is what you are wondering.

 

The scale would (generally) be designed to have just one point of stable equilibrium for any given weighted condition, including empty, and will tend to those/that points.

Edited July 14, 2017 by J.C.MacSwell

[DimaMazin]

Thanks.

[studiot]

Why' after change of balance on scales , balance happens again? How space/time works here?

 

My apologies DM.

 

When I first read this I thought it was just so much nonsense but I understand your point and it is a good one that demonstrates some deeper than usual thought.

 

+1

 

 

The answer is that a plain beam will not return but remain in its tilted position.

 

Manufacturers of scales, such as post office scales, chemical scales etc are aware of this and mechanically articulate the beam and pans to ensure that the high side is heavier than the low side, without anything on the pans.

 

As the (empty) high side drops, the articulation brings both sides of the mechanism into rebalance at horizontal.

 

The mechanism is different for post office and chemical type scales.

 

In modern times electromagnetic compensators are used instead of mechanical articulation.

Edited July 14, 2017 by studiot

[DimaMazin]

The answer is that a plain beam will not return but remain in its tilted position.

 

Are force of gravitational acceleration and force of gravitational attraction different forces?

[DimaMazin]

Are force of gravitational acceleration and force of gravitational attraction different forces?

Excuse me. The question was from delusion.

[studiot]

Are force of gravitational acceleration and force of gravitational attraction different forces?

 

Excuse me. The question was from delusion.

 

 

No worries, but you should consider this.

 

Any object rotating with the Earth eg a set of balance scales on the surface measures a different value of g, depending upon where on surface it is.

This is called apparent g.

 

The easist way to understand this is to understand to realise that any rotating observert will observe an outward centrifugal force, reducing force of attraction due to gravity.

This is much smaller than gravity itself.

So the value of apparent g at the poles, where the centrifugal reduction is zero is 9.83.

and the value at the equator where the reduction is maximum is 9.78.

 

Note the following.

 

The weight of an object is its true mass multiplied by the apparent gravity i.e. the total force betwen the Earth and the object.

This is what is measured by a spring balance, which measures Force.

 

A beam balance reports a different weight from a spring balance because both the weights and the weighed object are equally affected by the rotational reduction and they cancel out.

A beam balance measures mass.

 

https://en.wikipedia.org/wiki/Gravity_of_Earth

Edited July 16, 2017 by studiot

[TakenItSeriously]

You have changed ideal balance by your hand.. One bowl has lowered downwards, the second has risen upwards.After the disbalance they came back in balance again.Why? If you solve it with Newton then please.I can't understand why lowered bowl has less force than risen bowl.

Ahh, I think I understand. You are wondering what is allowing the two sides to communicate and find an equilibrium point.

 

The Paradoxical effect is created by a common mistake of forgetting about changes that we assume subconsciously due to repeatedly cancelling out L. we arent aware of anything our subconscious does which is why we say it's a hidden assumption the professor does without even knowing it.i

 

So the origional problem is two levers that meet at the focal point with forces applied at each end.

 

M₁ x L ₁ x Y₁ = M₂ x L₂ x Y₂

 

where

M₁, M₂ are the two masses

L₁, L₂ Are the horizontal distances from each mass to the focal point in the middle.

Y¹, Y₂ Are the vertical offsets of eash plate.

 

However, instead of writing the problem as shown above he subconsciously cancells out L without even being aware that he did it so we call it a hidden assumption.

M₁ × Y₁ = M₂ x Y₂

.

 

This form seems weird where the equation that models two mases that balance at equilibrium but the plates seem to be hovering in mid air and the information has no mechanism to cross from one plate to the other.

 

Another form of the kind of mistake that follows from hidden assumptions the hidden L may cause a person to ignore the offset Y. since it no longer seems to be relavent without the crossbar.

 

So you end up with

M₁ = M₂

 

the illusion is completed because the absent minded professor isn't aware that he just made these mistakes, but students are left to wonder if he's being serious about the paradox where unequal masses seem to be equal.

 

to answer the origional question the information travels accross the cross bar to get to the other side as infinitessimal stresses that exist across the cross bar.

Edited July 16, 2017 by TakenItSeriously

[studiot]

Ahh, I think I understand. You are wondering what is allowing the two sides to communicate and find an equilibrium point.

 

The Paradoxical effect is created by a common mistake of forgetting about changes that we assume subconsciously due to repeatedly cancelling out L. we arent aware of anything our subconscious does which is why we say it's a hidden assumption the professor does without even knowing it.i

 

So the origional problem is two levers that meet at the focal point with forces applied at each end.

 

M₁ x L ₁ x Y₁ = M₂ x L₂ x Y₂

 

where

M₁, M₂ are the two masses

L₁, L₂ Are the horizontal distances from each mass to the focal point in the middle.

Y¹, Y₂ Are the vertical offsets of eash plate.

 

However, instead of writing the problem as shown above he subconsciously cancells out L without even being aware that he did it so we call it a hidden assumption.

M₁ × Y₁ = M₂ x Y₂

.

 

This form seems weird when L is canceled outand yes the cause and effect is no longer clearly defined.

 

Another kind of mistake that is a common result of hidden assumptions. the absence of L may cause a person to ignore the vertical offsets of Y since it no longer seems to be relavent when L is missing.

 

So you end up with

M₁ = M₂

 

the illusion is completed because the absent minded professor isn't aware that he just made these mistakes, but students are left to think strange thoughts and no one will be comfortable to ask the obvious question at the end of the lechture.

 

to answer the origional question the information travels accross the cross bar to get to the other side. Think of it as infinitesimally small stress loops that propagate across the cross bar.

 

 

On the side: A note about hidden assumptions:

 

 

Some may doubt that hidden assumptions are real.

 

The subconscious mind is always working in the background doing a ton of tasks that you stopped thinking about a long time ago. For example, ever drive to work and realize you have no recolection of the drive because you were thinking about some upcomming meeting. So who drove? Your subconscious mind did, it was fully aware so it could break for pedestrians its only the conscious mind that is unaware.

 

The subconscious mind does everything your conscious mind can do, only it can work a whole lot faster because it doesnt have to take time translating every thought into English.

 

This is commonly experienced in poker through a gut feeling. Whenever i had a strong gut feeling at the poker table I would logically analyze the hand range and inevitably the range reduced to a single hand that verrified the warning.

 

Is it definitive? I used to play poker professionally both live and online which added up to a lot of poker at fairly high stakes. So yeah, it always worked out to show a single hand that beat me. Given that a river decision cuold be worth thousands in cash, I never took this warning lightly.

 

Besides that I once was able to exploit my subconscious to solve a logic test in record time.

 

it was a strange test that repeated the same kind of set theory problems hundreds of times in different permutations and it never deviated.

 

I'm certain that the premise of the test was to simulate a speed test for number of problems we could solve. kind of like operations per second for a computer.

 

I hated IQ Types of tests because of my disability with short term memory which would force me to be a slow reader. Therefore my clock would always run out rducing my score to be something in the average range.

 

I tried to focus on key words but there wernt any words that repeated. I tried to do some kind of speed reading trying to defocua my eyes to read the problem a page at a time but that never worked for me.

 

However I started getting the same gut feeling that I knew so well in poker. I just stared at a problem for a fraction of a second and new the right button to select with no conscious awareness of the problem.

 

Its not some psyocic power as something crazylike that though I think the professor monitoring the test live was thinking exactly that based on the shocked expression that was the most genuine expression I ever sow. I swear He was scared witless.

 

Everyone could probably duplicate the process but they couldnt duplicate the results. I knew I had the highest score because I capped the results which probably invalidated the test. I have no idea about how much faith to put in the test but lets just say I have the confidence to solve any solvable problem given enough time and I've yet to prove that feeling wrong. I also challenged my brother to find a problem I couldnt solve and he had no limits while he attended college majoring in math and physics which was a key part of the challenge.

 

He graduated suma cum laude in four years but conceeded the challenge in two years after a dozen attempts his last attempt was the Monty hall problem which I solved and proved in maybe 15 minutes. He and a biochem major were the ones who taught me QM, SR, and GR when I was 7, my earliest memory was an arguement with dad about the proper way to solve a particular problem I was the youngest of seven boys and two brothers plus dad were all very gifted in my opinion. SATs were perfect but none of us ever took an IQ test. In fact I had the results of the logic test from the public for 25 years and only meantion it now because I need to build crediblity through any possible means with a terrible academic record.

 

Solving the most important engineering problem of the century apparrently holds no influence over the math and science crowd.

 

My ultimate goal is a series of proofs that cant be denied including infinite compression, Quantum Teleportation and then...? if you noticed a pattern, when the theory converged I was overwhelmed with a flood of epiphanies.

 

I decided to test it and chose a problem that I thought was absolutely rediculous which was teleportation as in Star Treck.

 

The fact that I saw the first two solitions immediately after I asked the hypothetical question even threw me off balance.

 

BTW The TOE really is a TOE and is it provides all proper analogs in the universe. I could see analogs for problems in chemistry, biology, psychology, economics, and politics with an emphasis on the last two since those need to be solved immediately because its guaranteed to fail soon ith all the signs of divergence that means failure is imminent without taking some action to divert it. Think of the Universe as being pre-deterministic except when free will intercedes. Theirs always a diminishing chance for a solution as long as one person is left to solve the problem.

 

You only need to know all of the information which takes some normal reading time but then the analog just pops like an epiphany and you can see the answer

 

I completely ignored the 50:50 solution since it seemed intuitively right so that ment that it couldnt possibly actually be right, but the proof for 1/3:2/3 answer didnt skip any steps based on assuming it was correct by elimination which felt too much like cheating to over exploit the strategy. I really wanted to find my limits but you could say that is the second problem I never solved.

 

The first was proving odd prime numbers which I believe is unsolvable based upon the law that you cant prove non-existence when given an infinite system. its not a valid law for math and debatable for logic, but it kind of rings true I covered every clever method I could think of and some solutions came very close but endud up proving the wrong problem which had already been solved. e.g. proving perfect exclude all perfect squares.

 

I checked the next three of rour resultss and it was real. So given the 12 years of academic torture I decided to get some payback and went to town solving problems faster and faster. I have no idea about my pace but I calculated some possible results though my memory isnt going to be that accurate. I'm guessing that I may have reached a pace of several questions per second.

 

I could do that becuse I wasnt reading the problems I was only staring at the page and another gut signal in the form of a letter told me what the answer was.

 

Again its the fully functional subconscious mind that I am speaking of though it could be the unconscious mind which always seemed confusing to me. The homogenious problems were ideal for training my subconscious to solve a repeateable task just like typing is an action that it could do very fast while we dont need to be conscious of.

 

I'm afraid that I over did it and solved all problems in roughly half the alloted time.

 

The professor who was monitoring the test in a one on one session at 7:00 AM on a Saturday morning while all other students who were taking the same logic class were distributed to time slots which filled the computer room every time. so I was clearly being targeted and they didnt mind letting me know it.

 

I was only a freshman when it happend so the NSA was not nearly as bad back in theearly eighties but youd be surprised how evil they could be.

 

Why am I bringing it all up now? call it a desperate plea to stop hacking me.

 

Its tough enough to solve the problems and even tougher to get anyone to accept them. My goal is to stop the human species from comitting its own self extinction event.

 

If that's not enough to curb your agenda your potentially committing genocide just so you know. This brag fest is 100% against my character but I'm hoping a full disclosure about my ultimate agenda might slow down the abuse. Even if you'r a complete sociopath, how does our extinction benefit you? once it starts, the last man standing is the inevitable conclusion call it a gut feeling.

 

 

 

Twaddle.

 

 

Let's be clear.

 

The clever thing that DM noticed and is asking about is what returns the scale to the level position when you remove the load and the weights?

 

Here is one type that doesn't automatically return.

 

[Mordred]

Hence why beam scales have a balancing weight on a horizontal rod at the center of the perpendicular rod.

Edited July 16, 2017 by Mordred

[Mike-from-the-Bronx]

Good job studiot.

(and your assessment of TakenItSeriously is spot on too)

[TakenItSeriously]

Twaddle.

 

beam1.jpg

 

Let's be clear.

 

The clever thing that DM noticed and is asking about is what returns the scale to the level position when you remove the load and the weights?

 

Here is one type that doesn't automatically return.

 

beam2.jpg

OK, fine, so when he pushes down on one side he is doing the equivalent of imparting some of his own mass to one side so after removing his hand then:

 

m₁ = m₂

∴

y₁ = y₂

 

I should add that there should be a sine and cosine function involved with the m and y variables since the lever equation is the perpendicular force but movement is in an arc while the force of gavity is verticle but the fact remains that when both masses and both lever lengths are equal then the y offsets must be equal.

 

 

...edit to add:

Not that it matters because there are only three terms on either side of the equation in this problem, but I thought I should check what the accepted equation for a balance was.

 

After googling balance equation, I found no results other than accounting references. After googling balance paradox, I was surprised to see that there were some hits that seemed to try and show a paradox without any explanations.

 

Hasn't anyone ever formalised an equation for the balance yet?

Edited July 17, 2017 by TakenItSeriously

[Mike-from-the-Bronx]

Hasn't anyone ever formalised an equation for the balance yet?

 

Post #18 is again very confusing. But the last statement (question) is valid. No analysis has yet been presented to show that a restoring torque exists on a balance beam which has been displaced from its normal horizontal position. I can't find one.

[swansont]

 

Post #18 is again very confusing. But the last statement (question) is valid. No analysis has yet been presented to show that a restoring torque exists on a balance beam which has been displaced from its normal horizontal position. I can't find one.

 

 

 

This one has a restoring torque

 

https://1.bp.blogspot.com/-rU-uK-WMRWs/VrdExckiZ9I/AAAAAAAAA1k/uSTwavno-U4/s320/zc.jpg

[Mike-from-the-Bronx]

 

 

 

This one has a restoring torque

 

https://1.bp.blogspot.com/-rU-uK-WMRWs/VrdExckiZ9I/AAAAAAAAA1k/uSTwavno-U4/s320/zc.jpg

 

That works for me.

[studiot]

 

 

 

This one has a restoring torque

 

https://1.bp.blogspot.com/-rU-uK-WMRWs/VrdExckiZ9I/AAAAAAAAA1k/uSTwavno-U4/s320/zc.jpg

 

Yes, indeed the weight of the (displaced) red pointer provides this and is probably the simplest mechanism.

 

+1

[Tim88]

I have the impression that most people answered the question somewhat, but either incompletely or inaccurately. So, here's my try to finalize it

 

In contrast to the last picture here above by Studiot (thanks Studiot), a common balance scale has a bent horizontal arm. But also with a bent horizontal arm, both sides are equal in weight; what matters is the torque (likely Studiot meant with "heavier" not the weight but the torque).

Torque = L X F (this is a vector product). The lever effect is therefore not determined by the arm length but by the horizontal distance L*cosα (the effective arm length).

Consequently when one side is higher than the other side, the lever effect on that side is greater than on the other side, because the effective arm length is greater. That pulls the balance scale back to the point of equilibrium, where the effective arm lengths are equal.

PS and yes, the new picture added by Swanson has the red pointer doing that job instead.

Edited July 17, 2017 by Tim88

[DimaMazin]

OK, fine, so when he pushes down on one side he is doing the equivalent of imparting some of his own mass to one side so after removing his hand then:

 

m₁ = m₂

∴

y₁ = y₂

 

I should add that there should be a sine and cosine function involved with the m and y variables since the lever equation is the perpendicular force but movement is in an arc while the force of gavity is verticle but the fact remains that when both masses and both lever lengths are equal then the y offsets must be equal.

 

 

...edit to add:

Not that it matters because there are only three terms on either side of the equation in this problem, but I thought I should check what the accepted equation for a balance was.

 

After googling balance equation, I found no results other than accounting references. After googling balance paradox, I was surprised to see that there were some hits that seemed to try and show a paradox without any explanations.

 

Hasn't anyone ever formalised an equation for the balance yet?

 

You could be more successful with math.

Edited July 17, 2017 by DimaMazin

[mistermack]

I haven't read all of the posts in depth, but it seems to me that it simply to do with the location of the centre of gravity of the balance beam when unloaded.

If it's below the pivot, then the beam will naturally return to the horizontal, because any tilt on the beam causes the centre of gravity to rise.

So the beam is levelled by gravity acting through the c of g.

 

If the c of g was above the pivot, the beam would be unstable, and want to flip to whatever side it's tilted to on release.