How Much More Does a Compressed Spring Weigh?

It doesn't weigh any more.

How muck more does a bucket of water weigh when you lift it up and place it on a table? It has more potential energy now it's higher?

E may well equal MC² but it also equals a lot of otherthings which have nothing to do with mass, but everything to do with stress and strain...
A longbow at full draw has it's back in tension and it's belly in compression...our coiled spring has stress/strain in the form of torsion.

Del

"How much more does a bucket of water weigh when you lift it up and place it on a table?"

It actually weighs less (being further from the center of mass of Earth). However, it has the same mass.

How much less, I leave as an exercise for the reader (& anyone else with too much time on their hands).

Hi Del, you wrote: "How muck more does a bucket of water weigh when you lift it up and place it on a table? It has more potential energy now it's higher?"

You are right, but the lifting of the bucket did not impart any energy on the bucket or the water; hence no change in it's rest energy or mass. The stressed longbow does however weigh more...

Jorrie

Ah, that would explain why my arm aches...

There's Noooooo way I'm going to argue with you Jorrie....
Del _{<tippy toes off monitor left>}

Hello Jorrie:

Just to say some energy must have "been imparted" to the bucket, for at least the second or so it took to lift it, or it would not have moved?

Sorry, just getting you all going, and being my usual 'pedantic' self!

I know I am picking words from your post to make my silly point, and yes, I did read the full post, every word. Interesting one though.

I would have imagined the spring weighed the same in space and on earth. Would not like to try and chang a spring in space though...............OOOOoooh.......boing-boing.................As it bounces noiselessly out of control.

Jorrie, like Del, I am generally not inclined to dispute your superior knowledge on this point, but I'll be danged if I understand why you think a drawn longbow masses more than one that is not. Half the bow got denser (from compression) and half got less dense (from tension) but the overall mass does not change by my way of thinking. What am I missing?

I will add that I probably will regret asking this too....

Hi Rorschach.

A stretched spring will become more massive, just like a compressed spring, because it absorbs energy in both cases. Hence, both front and back sides of the longbow absorbs energy from the archer. More energy then translates to more inertial mass through E=mc².

Jorrie

Jorrie, can we at least agree that for the examples given, the difference between the Newtonian physics answer and the Quantum physics answer is really academic? The difference in mass is so miniscule as to be virtually non-existent for all practical purposes? Must we resort to Quantum mechanics for something that Newtonian mechanics has worked well enough for for hundreds of years?

Hi Rorschach, yes I agree that it is academic (or rather negligible) in most practical situations, but not all - think about nuclear fission (or fusion), where mass is converted into pure energy! The opposite can also happen in extreme cases, where pure energy is converted into mass.

Jorrie

Hello Jorrie

Your comment about nuclear fission (or fusion), converting mass into pure energy - this is true but might be confusing. You could equally well say a coal fired power station or any chemical reaction converts mass into energy. The difference is that with nuclear the energy change is high enough for the change in mass to be measurable, I believe ~ 0.7 % for 2 deuterons fusing to form a helium nucleus. In a chemical reaction the mass change is ~ 10⁷ times smaller, but it's still there. Also not everybody agrees that the energy from a nuclear power station is all that pure!

Conservation of baryons says the number of protons + neutrons is unchanged in both cases (it might be hadrons not baryons, I can't remember the difference offhand but I'm fairly sure protons and neutrons are both, perhaps you can enlighten me).

On bucket lifting, TVP45 in #47 raises an interesting point about where the energy (and mass change) is located. You could think of the bucket being raised by an expanding column of gas which would have lower energy than before, hence smaller mass, so presumably the bucket + Earth have mass raised by same amount. But is the mass change in the bucket, or shared between bucket and Earth in proportion to their masses, or what?

Cheers........Codey

Hi Codey, yes you are right about the coal fired station, which converts one molecular structure into onother and in the process releases heat energy (and hence effectively releases mass), while baryons are conserved (just the binding energy decreases).

I disagree about the conservation of baryons in nuclear fusion/fission, which converts one element into another. In order to release energy, the resulting element(s) must have less rest mass (i.e., less protons or neutrons, or both) than the original, not so?

Jorrie

Hello again Jorrie, Codey here, not logged in

I agree that in nuclear fusion/fission the resulting element(s) must have less rest mass than the original, but I don't think there are less protons plus neutrons. I'm fairly sure conservation of baryons holds for nuclear as well as chemical reactions (counting antiparticles negative of course). For chemical reactions it seems too obvious to call it a law! as nuclei are not involved.

In the example I mentioned 2 deuterons have between them 2 protons plus 2 neutrons, as does the helium nucleus. Also there are reactions where protons change to neutrons or vice versa, as when a nitrogen nucleus ¹⁴N⁷ in the atmosphere absorbs an electron and becomes carbon-14 ¹⁴C⁶. Starts with 7 protons plus 7 neutrons and ends with 6 protons plus 8 neutrons, 14 baryons before and after.

Of course these specific cases don't prove a general point, but I believe it holds.

Cheers.........Codey

I agree. The mass defect is not due to a difference in the number of nucleons, but to a change in the total nuclear binding energy. This is true for both nucleosynthesis and fission. Mirror nuclei may result (is in ¹⁴N⁷ → ¹⁴C⁶ ), but the baryon number is conserved.

So if you impart energy to the bucket of water, say by heating it, does it then become more massive? Heating water causes greater motion of the molecules, so there would be acceleration of each one compared to its previous state. Is this increased acceleration at the micro level what we are calling increased mass at the macro level? If not, I'm not following your argument here...

Hi EnviroMan.

Yep, a heated bucket/water with the same number of water molecules would weigh more than a cold one. It has to do with the velocity of the molecules (kinetic energy), not the acceleration, I think. After all, acceleration does not directly translate to energy, but velocity does, not so?

Jorrie

It's even less intuitively obvious than most things to do with relativistic phenomena, that's for sure, but I suppose I can swallow it. Not the hot water, unless you steep some tea or coffee grinds in it, though. Kinetically enhanced water molecules are more massive than cooler ones, eh? Must be something practical in that...

E=MC^2 possibly used for calculating the energy requirements to compress the spring, and holding energy, but once its compressed its the same mass.

Essentially, you have a piece of wire wrapped in a helicoil shape, with lots of air in between the windings, compressing the spring just removes that air-gap between the windings, but you still retain the winding.

A Spring is just a helical wound "torsion bar" would you say that a torsion bar that is "Wound up" have more mass than 1 sitting idly by? maybe the greater mass would be the clamping mechanism that is holding each bar/spring in its compressed state?

Springs shouldn't be stroked more than about 30% of their free length (or some place around here) as they will fatigue and break if compressed too far (problem found with some chinese made products)

Hi ODD Parts, your idea is correct - a compressed spring weighs more than an uncompressed spring if it's center of mass is held at the same height and place. All forms of energy are equivalent to mass.

How much more? If you know the amount of energy that went into the spring's compression (less any heat loss), you can indeed use E = mc² to calculate how much more the spring weighs.

Jorrie

Hi Jorrie. However this mass increment is sth that you cannot measure with any conventional way. If you weigh the compressed spring you'll find that its weight is the same as it is when it's uncompressed. So you have (in a way) a mass increment but not in a "conventional way": It just represents the energy that it's stored in the spring structure as it is compressed... or it's just equivalent to this energy...

It's the similar situation as in the case of a battery: The charged battery weighs the same as an uncharged battery. Or in the case of putting an object at a higher place: it weighs the same as if it stands at a lower place (assuming not a big difference in height). In these both cases this "mass increment" (considered by SR) shows just the stored energy... nothing more, nothing less...

Hi George, I'm afraid I'm in disagreement.

Any form of energy absorbed specifically by an object, be it heat, stress, electro-chemical (like in a battery), contributes marginally to its inertial mass. With gravitational mass equal to inertial mass, it means that the weight of the object goes up for a given position in a gravitational field.

I think you are only thinking of "mechanical energy" (kinetic and potential) in a gravitational field. In the case of an object being lifted to higher ground, the object itself does not absorb any energy and in fact becomes marginally lighter due to the larger distance from Earth. In the case of an object being accelerated, its so-called "relativistic mass" increases, but its rest mass remains the same.

Jorrie

Yes, Jorrie. After a second thought you are right. I was sure that the potential or the kinetic energy of an object does not infuence its mass. But the "battery example" was bad.

[Yes, afterall, there is an equivalence between energy and mass. When an object absorbs energy of any form, this can be perceived as an increment of its mass. Or, in other words, any quantity of mass or energy affected by a gravitational field... and, of course, this (stored) energy is affected too...]

Thanks for the correction.

Hi Jorrie,

Good to read your wisdom again.

I would raise the argument that, when we lift a bucket, there is an increase in potential energy but we don't know where the heck it's being kept! It doesn't seem to be in the bucket, so we should not expect to measure any mass change. We can say we've strained a field, but we have no easy way to talk about changing the mass of that field. I'm hopeful we'll see a Higgs particle or three from the LHC so that we can start to understand mass. Perhaps...

Thank you, Jorrie- and all who have contributed to this question.

I have learned thru all contributions to consider many aspects of relativity, and, that clear definitions of terms are necessary to answer this question. Apparently, even though the original question is simple, its answer may be cosmic, in that the answer could actually be either sub-atomic in its relativity on an order of 10 x -7 power (or more), or must be extrapolated to the size of the universe to make a significantly measurable quantity.

On the other hand, the answer may border on whether or not the Higgs Boson has mass, which we are on the thread of discovering now, as we accelerate the most tiny particles known of to speeds that approach (or exceed?) that of light.

Practically speaking, on Earth, in our perceivable 4 dimensional space, apparently, there is no appreciable measurable gain in weight of a compressed spring. In the universe, if the springs mass were compressed by a black hole, there may be some inversion of reality that we are striving to understand- yet I only propose these ideas so that we may entertain thoughtful discussion, and perhaps stumble upon a previously under utilized reality that may be of practical use in our lifetime here on earth. I have other questions that I will propose that may be more down-to-earth soon. Thank you all for participating. I learned a great deal.

Spurred on by Jorrie's assertion that the mass of a compressed spring is actually greater, here's my stab at estimating the original question:

Assume a vertical coil spring is compressed by placing a 1 gram mass on top, and it's length is reduced by 1cm.

Energy stored in spring = potential energy lost by the mass moving down.

E = m * g * h ≈ 10^-3 * 9.8 * 10^-2 (in SI units),

= 9.8 * 10^-5 J, call it 10-4 J.

So,

mass gained by spring = E / c² ≈ 10^-4 / (3 * 10⁸)² ≈ 10^-20 kg.

[_{Haven't really got too much time on my hands - just couldn't resist having a go} ]

Any comments?

Assuming the spring is standing on a table ..the table top is also slightly compressed and is presumably storing a tiny amount of energy and is also a bit heavier....Now each of the tables legs rests on the floor, now.... can you see where I'm going with this?

Del

Well, yes...you're drifting toward madness. Which is one of the two possible wavefunctions for a cat, the other being utter hedonism.

But, you're right. It's nonsense to think about added energy increasing the weight of something like a bucket. It is not the mass of the bucket that increases, it is the mass+energy that increases when you lift it. And that energy is reference-frame dependent. From the bucket's point-of-view, some fool Atlas lifted the earth.

And, just to run this into the ground (being a good hillbilly, I only know three facts so I repeat them over and over), the equation is

E ≈ mc² and holds only in the low energy limit.

Yes, and I remind you, it is turtles all the way down...

What weights more? A pound of Lead or a pound of feathers?

This sounds like a loaded question. As in one I saw in a cartoon back in the '60's. If you have a sailboat and on that sailboat a large fan aimed at the sail, will the fan propel the sailboat through the water?

Does and electric bulb weigh more when it is lit? Does an electric fan weigh more when it is running? Does electricity have weight? Is that why the electric lines sag from pole to pole? Why do I have a harder time getting up in the morning, when I have no energy? How come I can't stop talking in questions?

Welcome aboard!

"How come I can't stop talking in questions?"

It's OK, you're just making up for a few folks who can only talk in answers. This evens out the questions and answers so CR4 doesn't tilt to the side too much.

One more answer from me concerning the change of mass. If the mass has changed, then so has the density. If mass goes up, density goes down. And vice versa. If not, you have just created new mass from nothing.

Sounds like the theory of cosmic evolution, doesn't it?

Actually if the mass goes up and the volume is unchanged then the density went up too. But I suspect we are talking about masses in the range of fractions of an electron.

"I suspect we are talking about masses in the range of fractions of an electron ..."

I don't think so - if my sums are anywhere near, the mass change is of the order of 10⁷ atomic mass units (for my example).

which efunda's nice little unit converter converts to 1.66054×10^-16 g

Sorry, don't understand. eFunda converts 1 amu to 1.66054×10^-27 kg.

My answer was 10^-20 kg.

10^-20 / 1.66054×10^-27 ≈ 6.02 x 10⁶

Hi John, I think your calc is correct. The eFunda result must be a units issue, but I haven't checked...

Jorrie

[Tried to edit this in, but got there too late]

Google give mass of electron = 9.10938188 × 10^-31 kg

"If the mass has changed, then so has the density. If mass goes up, density goes down. ..."

That doesn't necessarily follow - the volume may change. In fact, I suspect that with the case of a compressed spring, the %age volume change will (initially) be many orders of magnitude greater than the %age mass change. Compressing the spring will heat it - the metal will (probably) expand.

May be I don't understand the term "mass". Let me say it this way. In any given substance, volume and weight determines density. If I compress the substance, the volume goes down and the density goes up. Weight stays the same. Correct or incorrect? I think I used the term mass when I should have used volume in my previous comment.

So, can someone tell me what the definition of "mass" really is? Or at least the one we are using here?

Mass is just the amount of 'stuff'.

Weight is what happens when gravity acts on stuff.
E.G You have the same mass whether you are on the Moon, in space or on the Earth...however your weight changes due to the differing gravities.

Another way of looking at it is the 'inertia' of an object...If you punch an anvil in outer space it will still hurt your hand, even though it has no 'weight' (but of course, no one can hear you scream)

Del

Not to put too fine a point on it, but "no weight" is a bit of a misunderstanding. Gravity knows no bounds, but it diminishes in influence over distance. Pluto is bound by the gravity of our Sun even though it is many millions of miles away, and we are bound by the gravity of our galactic center even though we are many light years out from it. So that anvil will have a miniscule weight with a constant (?) mass wherever it sits. The (?) is to indicate that imparting energy to it by punching it may increase the mass a bit, providing Jorrie can convince me hot water is more massive than cold water. I remain a touch skeptical...

I always thought that hot water was less massive because it expands, making it less dense, even if the heat energy it acquires increases it's mass-energy, the expansion more than compensates.

Hi Del, you said: "Mass is just the amount of 'stuff'."

Yes, if you include energy in your 'stuff'.

Jorrie

If I was sat on top of that there spring compressing it, and the spring weighed a bit more, would that mean that I weighed a bit less thinking in terms of conservation of energy? Ie. I am using my energy to compress it so I'm lighter! If this sounds funny, it's because I was chatting to my dear Mum who raised this point and I didn't have the answer! Can anybody explain in 'Mum' talk?

Somehow I doubt it's transferable - but then they say you use more calories chewing up a stalk of celery than you gain from consuming it, so maybe it would work...

In the frame of reference of the floor the bottom of the spring is sitting on, yes. In that frame you have a reduced potential energy and, if we only knew how to weigh your energy content, we'd find it a little lower. A GA to your mum!

I shall post it to England post haste! Thank you TVP45, my Mum will be pleased!

After reading all the discussion, let's answer this experimentally. Learning by thought has its limits. Get a spring and a c-clamp and put them on a digital scale. Now compress the spring with the c-clamp and measure them again. Anybody got a scale with enough digits?

Hi S, I guess the only way would be to find a huge spring with enough stiffness, plus a huge c-clamp! Measurement of mass could be done by applying a precise force and measuring the acceleration in some way. Since you need to go BIG, I suppose a huge chemical balance could do, since it is intended to compare inertial masses accurately.

However, even going for a spring that needs 100 kg to be compressed say 10 meters, will only yield a inertial mass difference of order 10^-10 gram! I don't think even a chemical balance would suffice...

J

Why to particularize the discussion to a spring? Let's consider a coil made out of lead (or any other malleable, permanent deformable material). What will its mass after "compression"? What will be after "expansion"?

And, pardon my ignorance, why do we need E=mc² when we are with out feet on earth (are we?) at low speed or no speed at all?

Ne strileai, tovarisch komisar! (Don't shoot, comrade commissar)

The confusion here, I think, rests in the attempt to separate mass and energy as though we can ever talk about one and not mention the other. What Einstein's equations say is that, if we have a mass, there is an energy equivalence; likewise if we have an energy, there is a mass equivalence. It is generally not useful (and actually confusing) to think about converting mass to energy or converting energy to mass.

To try to make a little more sense of this, think about a weekend question I screwed up a couple of weeks ago. I made a bad pun about frogs on a railroad track, and didn't remember that Brits call them couplings instead of frogs. So Kris and SaddleChariot and Del, etc weren't in on the bad pun. So, suppose I have 3 frogs and Kris has 3 couplings and I ship Kris one of my frogs. Now I have 2 frogs and Kris has 4 couplings, but nothing happened to the piece of steel. That is, number of frogs plus number of couplings is conserved; only the names are changed.