Explain Energy (is it physical)?

[OmCheeto]

Indeed. With a spring scale, the energy explanation is obvious. With a balance scale, it is a bit trickier, but it is trickier because a force-based explanation would also be trickier.

I don't see how a force based explanation would be tricky at all.

If I put a penny on each tray of the scale, the force exerted by each penny will be the same, and given my scale has equal length arms, the torque about the fulcrum will be zero, and the scale will be in balance.

And the arms of my scale don't appear to be deforming all that much.

The balance scale actually reminds me of the normal force. N=mg. I suppose I could manipulate that equation and get energy somehow.

hmmm...

I'm just not getting this energy based scale, and I'm late for work again.

ps. 8 old pennies weigh more than 9 new pennies, but less than 10. The fulcrum on my homemade penny scale is a piece of thread, and makes it very sensitive.

 

[Naty1]

I suppose I could manipulate that equation and get energy somehow.

why not E = mc²

 

[voko]

I don't see how a force based explanation would be tricky at all.

If I put a penny on each tray of the scale, the force exerted by each penny will be the same, and given my scale has equal length arms, the torque about the fulcrum will be zero, and the scale will be in balance.

And the arms of my scale don't appear to be deforming all that much.

It gets tricky when the masses are unequal. Explain then why the scale finds some tilted equilibrium rather than rotating all the way till the arms are vertical (or blocked by something).

The simple case of equal masses is just as simple from the energy standpoint: they have equal potential gravitational energies.

 

[Dale]

It gets tricky when the masses are unequal. Explain then why the scale finds some tilted equilibrium rather than rotating all the way till the arms are vertical (or blocked by something).

The simple case of equal masses is just as simple from the energy standpoint: they have equal potential gravitational energies.

This doesn't work as an explanation. An equilibrium position is a position of minimum energy for the whole system, not a position of equal energy for two parts of a system. The minimum energy configuration is with the heavy mass at the bottom, just like with forces.

 

[voko]

This doesn't work as an explanation. An equilibrium position is a position of minimum energy for the whole system, not a position of equal energy for two parts of a system.

The equality of masses, the "untilted" equilibrium, and the equality of the potential energies of the masses are all equivalent. If potential energies are not equal, then the equilibrium is tilted, or the system is not in equilibrium at all.

 

[Dale]

The equality of masses, the "untilted" equilibrium, and the equality of the potential energies of the masses are all equivalent. If potential energies are not equal, then the equilibrium is tilted, or the system is not in equilibrium at all.

You are using energy concepts completely wrong here. To find the equilibrium position never has anything to do with the equality of GPE of the two masses separately. You look at the system as a whole and find the minimum total energy. That is the equilibrium position. The separate GPE of each side has nothing to do with it.

 

[voko]

You are using energy concepts completely wrong here.

If you think that my statements in #40 are incorrect, I would like to see some justification, not just something which I find highly subjective. I you so wish, I could provide formal proofs of the statements.

To find the equilibrium position never has anything to do with the equality of GPE of the two masses separately. You look at the system as a whole and find the minimum total energy. That is the equilibrium position. The separate GPE of each side has nothing to do with it.

I believe I said quite precisely what the equality of potential energies of the masses on a balance scale has to do with the untilted equilibrium. If you believe that is incorrect, I would like to know why.

 

[AlephZero]

I don't see how a force based explanation would be tricky at all.

It gets tricky when the masses are unequal. Explain then why the scale finds some tilted equilibrium rather than rotating all the way till the arms are vertical (or blocked by something).

It's not tricky, if you consider the geometry of the scale.

The central pivot is higher than the points where the pans hang from the beam.

When the beam tilts, one pan moves further away from the pivot (horizontally) and the other moves closer to the pivot.

The tilted equilibrium position is when the moments of the two weights about the pivot are equal (smaller weight x larger distance = larger weight x smaller distance).

 

[voko]

It's not tricky, if you consider the geometry of the scale.

The central pivot is higher than the points where the pans hang from the beam.

This is not the only possible design of the balance scale.

 

[Dale]

If you think that my statements in #40 are incorrect, I would like to see some justification

Consider a balance with raised fulcrum, equal arms, equal chains, and equal pans holding equal masses. The equilibrium position is the one with the minimum total energy, and coincidentally the GPE of the masses on each side is the same.

Now consider a balance with raised fulcrum, equal arms, unequal length (but equal mass) chains, and equal pans holding equal masses. The equilibrium position is again the one with the minimum total energy, and the GPE of each side is unequal since the one on the longer chain is at a lower potential.

Now consider a balance with raised fulcrum, one arm longer than the other, equal chains, and equal pans holding unequal masses that balance. The equilibrium position is once again the one with the minimum total energy, and the GPE of each side is unequal since the larger mass has more GPE.

It is a simple fact which is true of many systems of many different kinds: equilibrium is determined by extremizing the total energy. A stable equilibrium is a minimum, and an unstable equilibrium is a maximum. The equality of the GPE of different parts of a system is a red herring, it is an irrelevant and occasional coincidence rather than the feature which defines equilibrium.

 

[voko]

Consider a balance with raised fulcrum, equal arms, equal chains, and equal pans holding equal masses.

Equal arms, equal chains and equal pans were implicit requirements. Sorry if that was not clear.

It is a simple fact which is true of many systems of many different kinds: equilibrium is determined by extremizing the total energy. A stable equilibrium is a minimum, and an unstable equilibrium is a maximum.

I never debated this.

The equality of the GPE of different parts of a system is a red herring, it is an irrelevant and occasional coincidence rather than the feature which defines equilibrium.

"The equality of the masses of different parts of a system is a red herring, it is an irrelevant and occasional coincidence rather than the feature which defines equilibrium."

True, but how useful in the particular case we are talking about?

 

[Dale]

Equal arms, equal chains and equal pans were implicit requirements. Sorry if that was not clear.

This is not the only possible design of the balance scale.

Interesting.

True, but how useful in the particular case we are talking about?

An irrelevant conincidence is never useful, just coincidental. Particularly on a forum where we are trying to provide correct and factual information so that people can learn about physics. Physics is about a small set of underlying principles which you can apply to understand many systems, not a long laundry list of random coincidences that can only be applied to one specific system each.

 

[voko]

Interesting.

It is entirely possible to build scales that violate this:

"The central pivot is higher than the points where the pans hang from the beam."

yet meet the requirements I listed above.

An irrelevant conincidence is never useful, just coincidental.

The purpose of a scale is to measure the equality of mass. Being able to establish the equality of masses, however irrelevant and co-incidental it may be in the grand scheme of things, is all important in this particular domain. I do not understand why you are trying to say it is irrelevant. The equality of associated GPEs is very obviously equivalent.

A few messages ago I stated very explicitly that the minimum of potential energy is what defines the equilibrium. So I am not debating this, and I am not trying to invent some other principle. I am merely stating that as easily as someone can say a scale measures force, one can say it measures energy. Which was, if you look a few further messages back, in the context of my statement that it is possible to do physics without force as a concept.

 

[Dale]

The purpose of a scale is to measure the equality of mass. Being able to establish the equality of masses, however irrelevant and co-incidental it may be in the grand scheme of things, is all important in this particular domain. I do not understand why you are trying to say it is irrelevant. The equality of associated GPEs is very obviously equivalent.

Yes, the purpose of any balance scale is to measure the mass (not necessarily equality of mass). The equality of GPE of each side is irrelevant and coincidental for only for a specific design, as I showed. The important thing for all balance scales of all designs is that the total energy be minimum at the equilibrium position when the unknown mass is correctly measured.

A few messages ago I stated very explicitly that the minimum of potential energy is what defines the equilibrium. So I am not debating this, and I am not trying to invent some other principle.

Then you should have stopped at that point, before you started inventing some other principle. And once it was pointed out that you were inventing some other principle you should have just said "oops" and moved on. This needn't have turned out as the big production that it has.

I am merely stating that as easily as someone can say a scale measures force, one can say it measures energy. Which was, if you look a few further messages back, in the context of my statement that it is possible to do physics without force as a concept.

I agree with that. It is possible to do physics without forces and it is possible to analyze a balance scale in terms of energy. I didn't object to your overall point, only to your description of the equilibrium condition as being due to equality of GPE, which you should have recognized as being a valid objection given your previous comments.

 

[AlephZero]

It is entirely possible to build scales that violate this:

"The central pivot is higher than the points where the pans hang from the beam."

Of course it's possible to build something that way.

Do you have a reference (preferably with a picture or drawing) of a pracitcal balance scale built that way? Unless it has some other clever design features, I think it would be useless because the equilibrium position would be unstable.

 

[Baluncore]

Energy in Physics is like money in an economy, but ideal, without forgery and inflation.
Indeed the exchange rate between different currencies can be linked back to the fundamental economic currency that we call energy.

 

[Drakkith]

Energy in Physics is like money in an economy, but ideal, without forgery and inflation.
Indeed the exchange rate between different currencies can be linked back to the fundamental economic currency that we call energy.

Kind of like the quote in my signature!

 

[Baluncore]

Yes, kind of, but without the magic.
I can find no peer reviewed references to OmCheeto. What is it ? Did you invent it ?

 

[Drakkith]

Yes, kind of, but without the magic.
I can find no peer reviewed references to OmCheeto. What is it ? Did you invent it ?

You'll have to ask him.

 

[voko]

The important thing for all balance scales of all designs is that the total energy be minimum at the equilibrium position when the unknown mass is correctly measured.

As I said a few messages ago, this principle is far too broad. Many scales will have an equilibrium position when masses are not equal, and many (even though I am tempted to say 'all' here) scales will have an equilibrium position when one mass is too big to be measured, not to mention the infinitely many mechanical systems with some equilibrium which are useless for any practical purpose. You need some additional idea to measure masses.

And once it was pointed out that you were inventing some other principle you should have just said "oops" and moved on.

I do not see any "oops" in what I have said so far and I do not see any other principle. I have merely stated that in a particular scale design, in the context that scales may be interpreted as a contraption for measuring energies rather than forces - which you have agreed with - the equality of masses is equivalent to the equality of their potential energies. I am not claiming any generality of this, yet I find this observation important in the context "balance scales and the force vs energy dilemma".

 

[voko]

Of course it's possible to build something that way.

Do you have a reference (preferably with a picture or drawing) of a pracitcal balance scale built that way? Unless it has some other clever design features, I think it would be useless because the equilibrium position would be unstable.

Your statement was: "The central pivot is higher than the points where the pans hang from the beam."

A scale can have the pivot at the same level or even lower than the points where the pans are attached, and it can have a rigidly attached counter-weight below the pivot, so the entire rotating assembly is T-shaped. This will have stable equilibria within a range of mass deltas.

 

[jbriggs444]

Your statement was: "The central pivot is higher than the points where the pans hang from the beam."

A scale can have the pivot at the same level or even lower than the points where the pans are attached, and it can have a rigidly attached counter-weight below the pivot, so the entire rotating assembly is T-shaped. This will have stable equilibria within a range of mass deltas.

Let h be the height by which the pan attachment points are elevated above the pivot point. Let H be the distance that the counterweight hangs below the pivot point. Let m be the total mass in the two pans combined. Let M be the mass of the counterweight.

If mh > MH then such an arrangement will not be stable, even when the test masses in the two pans are identical.

 

[voko]

Let h be the height by which the pan attachment points are elevated above the pivot point. Let H be the distance that the counterweight hangs below the pivot point. Let m be the total mass in the two pans combined. Let M be the mass of the counterweight.

If mh > MH then such an arrangement will not be stable, even when the test masses in the two pans are identical.

Well, technically it will still have a stable equilibrium, but upside down :)

Practically, of course, the counter-weight and the masses will have to be within certain limits for the device to work as intended. That is true for any scale.

 

[OmCheeto]

You'll have to ask him.

I do believe I spend too much time on PF. I had a dream about this thread this morning. Odd thing is, I remember it clearly.

Voko and I were in physics lab, and the instructor placed a rock on the table. He asked us to describe the kinetic and potential energy of the rock, in relation to the table top.

My answers were zero, and, um, zero.

Voko's answer looked like the following: Click to see

 

[Enigman]

Yes, kind of, but without the magic.
I can find no peer reviewed references to OmCheeto. What is it ? Did you invent it ?

I was tempted to reply--"Its a meditating cheetah"--but as I have an extreme sense of propriety and a huge amount of self control I won't.
:p

 

[voko]

Voko's answer looked like the following: Click to see

Nah, you dreamed incorrectly :)

The kinetic and potential energies are not deduced from a Hamiltonian or a Lagrangian. They are required to formulate those things to begin with, so they are "given" pretty much like forces are "given" in the Newtonian formalism.

And writing equations with energies is not really more complex than with forces, to put it mildly. The success of the Lagrangian mechanics is a solid confirmation.

 

[AlephZero]

A scale can have the pivot at the same level or even lower than the points where the pans are attached, and it can have a rigidly attached counter-weight below the pivot, so the entire rotating assembly is T-shaped. This will have stable equilibria within a range of mass deltas.

Fair enough, I hadn't thought about using a counterweight to provide a moment to counteract the instability.

But with my mindset of working in aerospace, a counterweight is just an extra part in the device and extra mass, and those are two good reasons for not having one if you can make a design that works without it.

(Of course a torsion spring would be lighter than a counterweight, and provide the same functionality)

 

[voko]

But with my mindset of working in aerospace, a counterweight is just an extra part in the device and extra mass, and those are two good reasons for not having one if you can make a design that works without it.

A have seen a few "chemist" style scales, and they had a tall stand, a dial at the bottom, and the pointing needle (more like a spear) all the way from the fulcrum to the dial. I think it doubled as a counterweight. I cannot say with certainty, however, that the fulcrum was "low" in them, so they could have been a combination design.

 

[AlephZero]

But interesting as this digression on scales may be, it doesn't change the point I was trying to make in my first post, which is that all these designs are just as easy to understand using "forces and moments" as using energy. Either way, you need to understand the kinematics of the machine to make a mathematical model of it.

 

[voko]

But interesting as this digression on scales may be, it doesn't change the point I was trying to make in my first post, which is that all these designs are just as easy to understand using "forces and moments" as using energy. Either way, you need to understand the kinematics of the machine to make a mathematical model of it.

I do not disagree. My idea that balance scales can be tricky was a result of quite a few discussions with somebody having a hard time with some particular variety of balance scales.

 

[Dale]

Closed pending moderation