## Sunday, August 16, 2009

### Does a Compressed Spring Weigh More Than an Uncompressed Spring?

Does a compressed spring weigh more than an uncompressed spring? The answer is surprisingly yes!

To understand why this is the case, we only need to look at the famous equation, e=mc². Since energy is directly related to mass, adding energy to a system affects the mass the following way: m=e/c². So if we were were to add 1,000 joules of potential energy to a spring, its mass would increase by 1,000 / c² or 1.113 × 10^-14 grams.

The same principle can be applied any time we add energy to a system. For example, heating an object increases its mass, and accelerating an object increases its mass as well. In fact, the reason why it is impossible to go the speed of light is because as an object approaches the speed of light, its mass increases so much that the engines require more and more energy to increase its speed. Accelerating to the speed of light would take an infinite amount of energy.

While these concepts go against common sense, the mathematics behind them are sound.

1. Of course the weight is negligible at such a small change. I thought, physics not being a strong suit for me, that the energy in a spring is the same whether compressed or not. Or does that have to do with potential energy?

1. there are different types of potential energy. in this case we would be giving elastic potential energy by compressing it.

2. Bah, I am an idiot, I remember the answer to this now. The energy is added from the force of compressing the spring.

1. no it's not. this is completely wrong.

2. um.... He's actually right.

3. No. This is incorrect. This formula is for mass, not weight. Two different things. The weight of the spring increases (original mass of spring plus force on the spring). The mass never changes. This is an improper use of this formula

3. You aren't an idiot, it took humans a long time to learn this.

1. humans never learned this. this is wrong.

4. In equation e=mc^2, the mass is relative.so how it is possible for rest mass. Also the theory of relativity is the theory of moving objects.

1. er..no.. actually that e=mc^2 is ONLY for resting objects, moving objects are E = root ((m_0*c^2))^2+(pc)^2)
where m_0 is the resting mass and PC are the euclidian momentum vectors (0 if at rest, which results in E=mc^2).

The full energy of an object is only applicable at speed tho, an object standing still has an "energy level" that, however, does nothing if the outside parameters do not change. If you change the compression of the coil you add to that energy level by giving it eleastic energy (this energy can dissipate by plastic change of the coil to a more dense form)and add some (neglegibly small) amount of mass.

2. But you also have to equate an object at rest isn't it is just relative to your perspective

5. Thanks for sharing this useful information! Hope that you will continue with the kind of stuff you are doing.
Compression springs

6. This is nonsense. The energy is not converted into mass, hence a compressed spring doesn't weigh more at all... unless you're going to contend we can remove the spring and be left with the extra mass that materialized due to the added energy.

1. Right? Your argument makes sense to me... Because if you lifted the mass higher, adding potential energy in the form of height (mgh), would that also cause the spring to increase in mass? In that sense, it's "mass" would be relative to it's proximity to other objects?

2. I looked into it and the way I understand it, the claim is right but not in the way the article implies. Not ALL of the energy you put into a spring gets converted into mass. If that was the case, there would be no energy left to actually compress the sting. However, during compression some elementary particles of the Sping's atoms will be elevated into a higher energy state e.g. they get accelerated. As those particles approach the speed of light, they gain a slight mass increase due to the relativistic conservation of momentum. The effect is very tiny an absolutely negligible in any practical sense.
http://galileoandeinstein.physics.virginia.edu/lectures/mass_increase.html

3. Einstein would beg to disagree: http://en.wikipedia.org/wiki/Mass_energy_equivalence

also, in order to have a mass change of 1 milligram, 0.001g, you would need to add 90 Terajoules of energy, compared to the 63 TJ of the Hiroshima Atomic Bomb.
So even if the physics were right (which it is not), you would need an absurdly large amount of energy to try to see any increase at all.

4. To be clear, @alcalde, I completely agree. The "debunker" is full of bunk.

5. no, alcalde is wrong. Energy and mass have a direct and complete correlation according to most physicists theories. That means energy IS mass and mass IS energy.
This is hard to understand I know but thinking there is "conversion" going on here is wrong, there is no converting anything to anything, they are both one and the same, it's useless to disconnect the two and see where they're needed.
And yes, the change in mass is ridiculously small, so what? The saying "does it weigh more" never mentioned a scale. We can assume that these theories are largely correct since all observations till now fit.
About the energy levels, you are thinking very, very small. These calculations also work on other planets, galaxies and so on, potential, kinetic and rest energy change masses of suns, planets, galaxies and so on. Again, the "myth" was only "changes weight", no scale.

@Aaron Wilson, yes the mass changes, however the further you get from the center of the gravitational object, the smaller your gravitational constant g becomes (g=g_0*(r/r+h)^2, where r is the mean radius, h is height above sea level and g_0 is the gravitational constant) so potential energy E=mgh would constantly become smaller the higher you go, this results in an energy flux and thus a mass flux.

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7. This "debunking" is COMPLETELY INCORRECT. Matter can only ever change into energy in an atomic reaction. And ENERGY CAN NEVER CHANGE INTO MATTER. I suggest you read your physics before you try to "debunk" any further physics related questions.
http://en.wikipedia.org/wiki/Mass_energy_equivalence

"A spring's mass increases whenever it is put into compression or tension. Its added mass arises from the added potential energy stored within it, which is bound in the stretched chemical (electron) bonds linking the atoms within the spring."

http://en.wikipedia.org/wiki/Mass_energy_equivalence#Practical_examples

2. [citation needed]

Except that "citation needed" is an understatement in this case.

Extraordinary claims require extraordinary evidence. This sounds like someone took E=MC^2 a bit too literally.

3. Citation found:

That blew my mind. But it does seem to have a nice symmetry with the mass increase that accompanies kinetic energy (e.g. as an object's speed approaches that of light, the objects mass approaches infinite).

4. Have a look at this:
http://en.wikipedia.org/wiki/Talk:Mass%E2%80%93energy_equivalence#Okay.2C_and_let.27s_point_out_early_that_mass_is_never_converted_to_energy.2C_and_vice_versa

5. Energy can never change into matter? Bullshit. Pair production is a thing - one photon of light energy turning into a particle-antiparticle pair; matter.

8. If the mass/energy of a given system is increased by mechanical tension, that increased mass/energy must come from somewhere. It cannot be created out of thin air. Therefore, the compression mechanism and/or the surrounding air would have to loose mass/energy in order to effect an increase in the spring being compressed.

As a system, the mass/energy of the spring, the compression mechanism, and the surrounding air would remain constant.

The problem with this thought experiment (and let's be clear this is only a thought experiment - no empirical data is available here) is that it is impossible to have the spring compressed and also weigh only the spring or only the compression mechanism. They can only be measured as a system or individually without the compression. Therefore, once they become a system, the weight of that system does not change if one part of the system compresses another.

1. Not quite. Suppose I do the work to compress a spring and then use a vice to keep it shut. I have lost energy, the spring has gained it. If I measure the sum of the mass of the uncompressed spring and the mass of the vice, it will differ from that of the compressed spring in the vice.

9. so, if I have a spring and a rope on a very precise scale and the weigh X. If I tie the rope around the spring to compress it and weight them again, they will weigh X+Y, where Y > 0?

1. From my gut understanding no, as the energy added in compression is taken from the atomic bonds within the rope, thus negating the change in energy ergo mass.

10. The confusion here is caused by a misunderstanding of terms. When a system composed of an uncompressed spring is compressed, it has energy/relativistic mass added to it. Relativistic mass and energy are equivalent. However "weight" refers only to gravity's relationship with REST mass, not relativistic mass. Energy cannot become rest mass, therefore the compressed spring will not weigh more.

When a spring is compressed, it DOES gain relativistic mass. However, since energy and relativistic mass are equivalent, this is the same as saying "When energy is added to a system, it has more energy."

1. So, if I got this right a TV thats on has more relativistic mass, then when its off?

11. I believe that is correct. ANYTHING added to a system, energy or matter, increases its relativistic mass. A tv that is on has more Rel. Mass than one that is off. Heat that tv up in an oven and you have added even more Rel. Mass. Fire it out of a cannon and you've got still more.

Now as has been correctly pointed out by other posters, the proportion of the total Rel. Mass represented by the electricity, by the heat, by the motion, by the compression, is extremely miniscule having to be expressed in scientific notation. In order to double the Rel. Mass of our TV, we would have to accelerate it to about 86% the speed of light, which would require a staggering quantity of energy.

Anyway, I am not an expert, just a hobbyist, so I welcome correction. But I think it starts making more sense when you learn to think about Matter and Energy as just different forms of the same kind of "stuff", as counterintuitive as that feels.

12. Not only is it true but the compressed spring is warmer also.

13. A spring made of iron will weigh more than one made of plastic (slinky, etc.) The same exact principle applies here.

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16. The spring does increase in mass. Suppose the spring has mass m and energy E. Then its rest energy is E = mc^2.

Now suppose the spring is compressed. It gains a small amount of potential energy ΔE > 0 and now has mass M.

Then its new energy is E + ΔE = Mc^2.
But E = mc^2, so ΔE = Mc^2 - mc^2 = c^2(M - m).

Since ΔE > 0, then M - m > 0 and so M > m. The spring has increased in mass by M - m = ΔE/c^2.

17. I read you blog and find very useful information about spring.This is really a thinkable stuff.
compression springs

18. Um i know E=MC2 but........ i hypothesize 2 points; that due to thermodynamics and quantum 'friction' that when a spring is compressed the matter of which it is comprised actually releases the added energy as heat(still within the system) and if said thermal energy escapes the system then the spring will not decompress....
Also the thermodynamic system here in question cannot only be the compressed spring but must also include the 'compressor'.

19. The link below will help explain this phenomenon. Because empty space is NOT really empty. Believe it or not, empty space is where atoms get most of their mass. knowing that quarks actually make up a proton, there is actually a very small amount of "empty" space between the quarks that make up a proton, and scientist have found that it costs energy to clear out a vacuum INSIDE a proton. and this "vacuum" is the ENERGY that gives an atom 99% of its mass. this is proven by the given the equation E=mC^2. If you rearrange it to solve for m, you get m=E/(C^2), meaning that mass is directly related to energy. the more energy of any object, the greater its mass will be. Empty Space (Meaning its not really empty) is the very foundation that the universe is supported on.

20. Since heat = energy, then this would mean that the hotter something is the more mass it will have. just like a hot cup of tea will have more mass than the same cup of tea at a cooler temperature. if compressing a spring will cause it to raise slightly in temperature, then the mass of the spring will slightly increase as the temperature rises.

22. Well, of course energy can become matter, that's what's been thought to happen moments after the big bang, forming strings, quarks, and eventually hydrogen, and has been proven in the large Hadron collider. Matter is just energy bound up really tightly into a storage form, and what gives matter mass is its energy.

23. Does this same logic mean that if you lift a spring in the air it will have a greater mass because of GPE?

24. Your explanations for show a comparison between a compression springs and uncompressed is really great.

25. The spring is one of the most important parts of the suspension. Its very informative and interesting article.all the points are very useful. Simple but very effective writing. Thanks for sharing such a nice post.
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26. This video explain very nicely why the spring has more mass:

27. E = mc^2 only applies to kinetic energy. Increasing your potential energy does not change your mass. If that was so, then all of us would be crazy heavy, because there is LOADS of gravitational potential energy pulling us towards the Earth. Also, E = mc^2 is mainly used for determining how much energy you would get if you converted the mass of something into energy.

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30. That's why we can't break the natural law.
If we can achieve speed of light,time travel would be possible.

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32. OMG!
I didn't know these facts about springs

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