x
Solved

# Einstein's formula and springs

Posted on 2004-04-28
Medium Priority
1,413 Views
Einstein's famous formula says that E = mc^2, meaning that there is a conversion relationship between mass and energy.

Let's say we have combination spring and latch, and we can determine the mass of the spring+latch to an arbitrary degree of precision.  Then we compress the spring and latch it in the compressed state, thereby storing energy in the compressed spring.  Since there is a relationship between mass and energy, does this mean that the compressed spring+latch will mass more than the uncompressed spring+latch?

Similarly, does a spinning gyroscope mass more than a stationary gyroscope?

How about a charged battery vs. a discharged battery?
0
• 5
• 5
• 5
• +3

LVL 5

Expert Comment

ID: 10943808
3 x yes.
0

LVL 2

Expert Comment

ID: 10944752
Einstein's E = mc^2 conversion relationship, is just that, a conversion relationship.  If you want to calculate the total mass in the system as if you converted all the energy to mass and added that to the mass of the object, then there would be more mass than just the object mass itself.  But there is not more mass, there is the mass of the object plus the energy of the object (which does not have mass, unless you convert it to mass or it's a type of energy that does have mass (some say light has mass)), the system cannot be both more massive and still have the potential or kinetic energy at the same time.  Let's say we converted all the mass in the spring and latch combination to energy, then the mass would be zero.  If you could contain all that energy, then you could calculate the mass of that energy to be the same as original using E = mc^2, but the actual energy does not have that mass, it would only have that mass if you converted the energy back to mass.  You are getting mixed up between the actual mass of the energy and the energy to mass conversion factor.  I don't know what the actual mass of the energy would be if any, it might depend on what type of energy you are converting to.  You can tell that a system with both mass and energy does not have more actual mass (without converting the energy to mass) than a system with the same amount of mass but no energy, because mass and energy have different units of measure.  If I take 1 gram and I add 1 watt to that gram, do I now have more than a gram, not unless I convert that 1 watt of energy to mass first.
0

LVL 6

Expert Comment

ID: 10944759
It would weigh dE / c^2 kg more. Should be too insignificat for anyone to notice.
0

LVL 2

Expert Comment

ID: 10944773
I meant to say 1 watt-hour.
0

LVL 2

Expert Comment

ID: 10944789
ysfx

> It would weigh dE / c^2 kg more. Should be too insignificat for anyone to notice.

huh?

Shouldn't it be m = E / c^2 more massive ?  (If you were to convert it.)
0

LVL 6

Expert Comment

ID: 10944904
m0 = original mass
dm = change in mass
dE = change in Energy (extra PE with compressed spring, rotational momentum of gyroscope, PE of charged capacitor/battery)
dm = dE / c^2
m0 + dm = m (the new mass, but dm is extremely small)
m0 ~ m

I think by special relativity, in some sense, mass is energy. This is still in much controversy/discussion, but has not been disproven.
0

LVL 6

Expert Comment

ID: 10944915
From my understanding of E=mc^2... a thrown ball is "technically" heavier than a ball at rest.
0

LVL 6

Expert Comment

ID: 10945361
The compressed spring has more mass.
If you have 1 gram and add 1 watt you have more mass.

Consider, that one gram.  When you add the 1 watt what happens? I would guess it gets hotter? And as it cools how might the energy dissipate? Some might come out via radiation, infra-red photons. So since those photons have mass (no rest mass, but mass all the same), and that mass came from that watt, the gram plus one watt must have had more mass then the gram all alone.

0

LVL 6

Expert Comment

ID: 10945385
uh, watt-hour....
0

LVL 6

Expert Comment

ID: 10945657
Let the battery discharge through a light bulb - photons again.  Where did the mass that made them come from?

Let the gyroscope spin down or the spring un-spring by driving a electrical generator -  and let the electricity flow through that light bulb...
0

LVL 2

Expert Comment

ID: 10945712
If I have a system with 1 gram + 1 watt-hour = (1 gram + 1/c^2)  of mass (supposedly I can calculate the total mass of the system by calculating the mass of the energy using E=mc^2 then add that to the rest of the mass), then I physically convert that 1 watt-hour to mass and add it to the 1 gram, I will have (1 gram + 1/c^2) of mass + 0 watt-hours of energy, so where did the 1 watt-hour go?  By your logic I have the same mass, but now I'm missing 1 watt-hour of energy?
0

LVL 85

Expert Comment

ID: 10945745
Your question is confusing.
When you say "calculating the mass of the energy using E=mc^2 then add that to the rest of the mass" what do you mean by "rest of the mass"?  All of the mass is energy.
I also don't understand what you mean by "physically convert that 1 watt-hour to mass"
A watt hour is mass.
0

LVL 2

Expert Comment

ID: 10945770
I'm talking about 1 gram of matter for 'the rest of the mass'.  And physically converting 1 watt-hour of energy into mass, like a nuclear reaction only in reverse.
0

LVL 6

Accepted Solution

robertjbarker earned 100 total points
ID: 10945956
Energy is mass. E=Mc^2.  The equals sign in there means "is".  If you have a gram of stuff and you add 1 watt-hour you have something that is more massive by 1 watt-hour.

If you have oxygen and hydrogen and you combine it together to get water you get molecules of water and heat and photons.  If you wait for things to cool down - you wait for all that energy to leave the immediate area - the molecules of water have less mass than the oxygen and hydrogen you started with.  The energy that left the area was mass.

More extreme.  If you have deuteronium (heavy hydrogen) and you combine to get helium and wait for things to cool down, the helium you have has less mass than the heavy hydrogen you started with - even though you have the same number of protons, neutrons, and electrons before and after the bang.
0

LVL 6

Expert Comment

ID: 10946649
"By your logic I have the same mass, but now I'm missing 1 watt-hour of energy?"

No, because the 1 watt-hour of energy was always mass.
0

LVL 5

Expert Comment

ID: 10946717
This distinction between watt-hours and grams is immaterial.  They are just conveninet units for meausuring vastly different densities of matter-energy.
0

LVL 22

Author Comment

ID: 10948725
I was pretty sure it would mass more, I just wanted some second opinions.

I was very sure that the spinning gyroscope would mass more because fast-moving objects appear to get heavier as they approach the speed of light.  So that got me thinking,   What if you had a battery hooked up to a motorized gyroscope with a timer, all sealed inside a box?  You could measure the mass of the box precisely.  Then when the timer expired, and the battery began to spin up the gyroscope, the box would get heavier.  This contradicted my understanding of conservation of mass, namely that if nothing goes into the box and nothing comes out of it, then the mass of the box should not change.  So my question became "why would the mass of the box not change?"  and the only conclusion I could come up with was that the charged battery massed more than a discharged battery.

So, wouldn't all potential energy have mass then?  What if you had a highly compressed spring mechanically attached to a gyroscope.  Then the compressed spring must be more massive than the released spring, by the same reasoning.

What if you had two reservoirs of fluid, a full one at a height and an empty one down lower.  You could harness the energy of the falling fluid to spin up the gyroscope.  So the fluid at altitude with potential energy is more massive than the same fluid at ground level?  Hmmm, that seems weird.
0

LVL 5

Expert Comment

ID: 10948767

Not to be polemic, but my "3 x yes" answer was perfectly correct and came before any other answer.  ysfx also answered correctly before robertjbarker.  Shouldn't you split points and give the correct answer to me and the two assists to the other?   :-)
0

LVL 22

Author Comment

ID: 10948963
PointyEars:  Yours was a correct answer, but it was not a good answer.  I wasn't looking for a quiz-show answer; I was looking for an explanation.  robertjbarker's posts had the best answer.  He saw what I was driving at and made a good effort to justify his reasoning.  He answered my question in the same sense it was asked.

ysfx's main addition was to algebraically convert E=mc^2 to dM=dE/c^2.  I wasn't asking about the precise quantity of the increase in mass, and besides I brought up Einstein's equation in my question and I thought its basic implications were obvious.

0

LVL 6

Expert Comment

ID: 10965543
Not for points... but I wanted to explain my post.

I brought up the equations to bring to your notice why you would not notice the mass difference of a charged battery as opposed to a discharged battery, theoretically.

To explain your latter post... it examplifies the relativity part of Einstein's theory. Since you look at a larger scenario, you will have to take into account all the other energy. It would be similar to your black box with a battery and gyroscope.

Just thought you may have misunderstood my post, but if you already knew... extra kudos for you.
0

LVL 6

Expert Comment

ID: 10965545
NovaDenizen << This pouridge is too cold, this pouridge is too hot, this pouridge is just right. But that's why experts-exchange is such a great forum, there's always an expert than understands what the questioner wants.
0

LVL 22

Author Comment

ID: 10986966
Sorry if I sounded rude or finicky.
0

## Featured Post

Question has a verified solution.

Are you are experiencing a similar issue? Get a personalized answer when you ask a related question.

Have a better answer? Share it in a comment.

## Join & Write a Comment Already a member? Login.

How to Win a Jar of Candy Corn: A Scientific Approach! I love mathematics. If you love mathematics also, you may enjoy this tip on how to use math to win your own jar of candy corn and to impress your friends. As I said, I love math, but I gu…
Foreword (May 2015) This web page has appeared at Google.  It's definitely worth considering! https://www.google.com/about/careers/students/guide-to-technical-development.html How to Know You are Making a Difference at EE In August, 2013, one …
This is a video describing the growing solar energy use in Utah. This is a topic that greatly interests me and so I decided to produce a video about it.
Although Jacob Bernoulli (1654-1705) has been credited as the creator of "Binomial Distribution Table", Gottfried Leibniz (1646-1716) did his dissertation on the subject in 1666; Leibniz you may recall is the co-inventor of "Calculus" and beat Isaac…
###### Suggested Courses
Course of the Month10 days, 17 hours left to enroll

#### 608 members asked questions and received personalized solutions in the past 7 days.

Join the community of 500,000 technology professionals and ask your questions.