1. Its me again. The question I am about to ask, in my viewpoint, I have the answer for. But, I just wanna double check that my thinking is correct. Here goes...

I have a grandfather clock wind-up spring. It's completely unwound. So its mass is 'x' . Now, I wind it up. Would it's mass still be 'x' , or would it be 'x + energy'? I believe it to be 'x + energy' simply because of the fact that energy has mass. Any takers on this topic?  2.

3. E=mc2

If you know the energy you put in, you can calculate change in mass
compare that mass to the mass of the clock

*I wonder why is there so many E=mc2 questions lately...  4. I was thinking of E=mc^2 as well. But surely there could be a simpler way to describe it?  5.  6. Originally Posted by WaterWalker I was thinking of E=mc^2 as well. But surely there could be a simpler way to describe it?
You can't get much simpler!
c is fixed, e is the energy you've put in so m is the only thing you need to find.
Although the conversion factor of c2 ensures that any change in mass is going to be negligible - an increase of a mere 1 gramme in weight would require the energy of 568,000 (US) gallons of gasoline = ~21 kilotonnes of TNT - not many springs can take that, nor do many people have hands that strong.  7. Originally Posted by Dywyddyr an increase of a mere 1 gramme in weight would require the energy of [...] ~21 kilotonnes of TNT
I'm confused (yeah, it happens a lot) ...

How and when and why does the E=mc² or the m=E/c² conversion occur? I mean, in the example above, if I ignite 21 kt of TNT, and all the products of the explosion weigh 21 kt  1 gram, it sounds like an atomic reaction, and not a chemical reaction.

What about potential energy? Two objects A and B of the same weight are at the same altitude above the Earth and have the same potential energy, but increasing B's altitude (and potential energy) would not make it heavier than A, would it? An object would have potential energy or added mass, but not both, right? The potential energy is "stored" in its altitude, not its mass.  8. Originally Posted by Dywyddyr  Originally Posted by WaterWalker I was thinking of E=mc^2 as well. But surely there could be a simpler way to describe it?
You can't get much simpler!
c is fixed, e is the energy you've put in so m is the only thing you need to find.
Although the conversion factor of c2 ensures that any change in mass is going to be negligible - an increase of a mere 1 gramme in weight would require the energy of 568,000 (US) gallons of gasoline = ~21 kilotonnes of TNT - not many springs can take that, nor do many people have hands that strong.
Oops. Sorry. I think what I meant was a better way of explaining it. Because in this equation, if c is the speed of light, ergo, constant, then the only thing that will affect the energy outcome is a mass change. Which is what I want, but (as far as I can think) that would be from an outside source. I feel that I'm missing something. What am I missing?  9. Originally Posted by jrmonroe How and when and why does the E=mc² or the m=E/c² conversion occur?
The energy imparted to the spring by winding becomes bound up in the metal (actually the electron bonds of the metal) of the spring itself.

I mean, in the example above, if I ignite 21 kt of TNT, and all the products of the explosion weigh 21 kt – 1 gram, it sounds like an atomic reaction, and not a chemical reaction.
Yes, e=mc2 is the equation for nuclear bombs. But the equation also describes how mass and energy are related.

What about potential energy? Two objects A and B of the same weight are at the same altitude above the Earth and have the same potential energy, but increasing B's altitude (and potential energy) would not make it heavier than A, would it? An object would have potential energy or added mass, but not both, right? The potential energy is "stored" in its altitude, not its mass.
Mass is energy, energy is mass.
But "altitude" is relative - it could be on top a high table - PE with reference to the table top is zero, with reference to the floor it's a positive value.
The "extra mass" is actually the energy which is part of the system of "brick and Earth". If you lift the brick then that's equivalent to moving the Earth away from the brick. In which case would you say that the Earth has increased in mass? It's probably easier to think of the energy being "stored" in the altitude.
Unless someone else can explain this better...

When we talk about the spring the spring itself is the "system" and undergoes an increase in mass.  10. Originally Posted by WaterWalker Oops. Sorry. I think what I meant was a better way of explaining it. Because in this equation, if c is the speed of light, ergo, constant, then the only thing that will affect the energy outcome is a mass change. Which is what I want, but (as far as I can think) that would be from an outside source. I feel that I'm missing something. What am I missing?
I don't think you're missing anything.
The outside source is you winding the clock. You're imparting energy to the spring by winding it - that energy adds to the mass because of e=mc2.
A hot object is heavier (by some very small amount) than the same object cold because of the energy that the heat has given it.  11. I'm gonna try to sum it all up in a school-type fashion. Correct where I am wrong.The object, in this case the wind-up spring, would have more mass because of the energy that have been put into it by an outside source, the hand of the person, causing the particles inside the object to vibrate at an accelerated speed which, in turn, have in increased pressure on the walls of the wind-up spring. Am I correct in saying it that way?  12. Originally Posted by WaterWalker I'm gonna try to sum it all up in a school-type fashion. Correct where I am wrong.The object, in this case the wind-up spring, would have more mass because of the energy that have been put into it by an outside source, the hand of the person, causing the particles inside the object to vibrate at an accelerated speed which, in turn, have in increased pressure on the walls of the wind-up spring. Am I correct in saying it that way?
As I understand it it's more that the electron bonds of the metal are under tension (i.e. the energy is stored there) than "accelerated vibration", but yes you've got the idea.  13. On the matter of bonds between particles, it is the case that the mass of an atom differs from the sum of the masses of its constituent particles (neutrons, protons and electrons) due to the mass equivalence of the bonding energy. Most of this difference arises from forces within the nucleus and it can be measured by mass spectrometry for most elements - not just radioactive ones. However, there is also a smaller mass difference due to electron binding.

One can think of an atom or compound as analogous to the wound up grandfather clock.  14. Ok. So where can I get further info on that electron bonds under pressure thing. I've checked on wiki, but can't find the proper thing dealing with it. And, if at all possible, any formulas pertaining to it. I want to physically go and work it out. (I tend to understand topics better that way. Just call me weird). Thanks.  15. Originally Posted by jrmonroe How and when and why does the E=mc² or the m=E/c² conversion occur? I mean, in the example above, if I ignite 21 kt of TNT, and all the products of the explosion weigh 21 kt – 1 gram, it sounds like an atomic reaction, and not a chemical reaction.
The thing is, in a nuclear reaction, you could get that same gram-equivalent amount of energy released from a few kg of material rather than the tons of TNT. If you built a matter-antimatter bomb, you could get that gram-equivalent amount of energy from a gram!

The difference comes about because chemistry is about bonds between electrons. These are pretty weak (little energy) compared to the bonds holding the nucleus together (mucho energy).  16. Originally Posted by WaterWalker Ok. So where can I get further info on that electron bonds under pressure thing. I've checked on wiki, but can't find the proper thing dealing with it. And, if at all possible, any formulas pertaining to it. I want to physically go and work it out. (I tend to understand topics better that way. Just call me weird). Thanks.
And it's at this point you exhaust my knowledge... If all you want to do is simply "work out" the added mass then e=mc2 should suffice.
Just check the spring characteristics, obtain a figure for maximum energy stored when wound and feed that value into the Einstein equation.  17. I guess I've been out of school for too long ...

If I pump thermal energy (heat) into an object, it gets heavier?

A spinning flywheel is heavier than an identical stationary one?

In what form of mass does any of this increased energy (spring tension, chemical energy, heat, spinning flywheel, etc) become?  18. Originally Posted by jrmonroe If I pump thermal energy (heat) into an object, it gets heavier?
Yep.

A spinning flywheel is heavier than an identical stationary one?
Yep.

In what form of mass does any of this increased energy (spring tension, chemical energy, heat, spinning flywheel, etc) become?
Just energy. As that nice Mr Einstein showed, mass and energy are equivalent. Including in their gravitational effects.  19. jrmonroe, for simplicity's sake, we have left out the 'time' variable in this post. Over a period of time, the system will tend to go back to equilibrium. We have taken an instant in time. To explain - As you wind up the spring, your putting energy into it. This heats up the spring (by an extremely small amount). Over a minute or so, the spring will 'release' this energy into the atmosphere as heat. As the spring unwind, it releases energy and gets colder at the same time. To compensate for this, it takes up heat(energy) from the environment around it. It tries to go back to its original form, its original energy state. If it didn't, it would reach critical mass, and things would be a bit different here on earth then.   20. Originally Posted by WaterWalker As the spring unwind, it releases energy and gets colder at the same time. To compensate for this, it takes up heat(energy) from the environment around it. It tries to go back to its original form, its original energy state.
It would only get colder until it reached equilibrium with its surroundings - i.e. it's releasing the stored energy - the "extra" heat that it has.
And its "original form" (ground state) is unwound, so it'll be "at rest" when in such a state and won't "try" to take in any more energy.  21. Originally Posted by jrmonroe What about potential energy? Two objects A and B of the same weight are at the same altitude above the Earth and have the same potential energy, but increasing B's altitude (and potential energy) would not make it heavier than A, would it?
Yes it would. Check out binding energy on wikipedia and pay special attention to mass deficit:

As an illustration, consider two objects attracting each other in space through their gravitational field. The attraction force accelerates the objects and they gain some speed toward each other converting the potential (gravity) energy into kinetic (movement) energy. When either the particles 1) pass through each other without interaction or 2) elastically repel during the collision, the gained kinetic energy (related to speed), starts to revert into potential form driving the collided particles apart. The decelerating particles will return to the initial distance and beyond into infinity or stop and repeat the collision (oscillation takes place). This shows that the system, which loses no energy, does not combine (bind) into a solid object, parts of which oscillate at short distances. Therefore, in order to bind the particles, the kinetic energy gained due to the attraction must be dissipated (by resistive force). Complex objects in collision ordinarily undergo inelastic collision, transforming some kinetic energy into internal energy (heat content, which is atomic movement), which is further radiated in the form of photons—the light and heat. Once the energy to escape the gravity is dissipated in the collision, the parts will oscillate at closer, possibly atomic, distance, thus looking like one solid object. This lost energy, necessary to overcome the potential barrier in order to separate the objects, is the binding energy. If this binding energy were retained in the system as heat, its mass would not decrease. However, binding energy lost from the system (as heat radiation) would itself have mass, and directly represents the "mass deficit" of the cold, bound system.

When you separate two gravitationally bound objects, you add energy, and as a result mass increases. Originally Posted by jrmonroe An object would have potential energy or added mass, but not both, right? The potential energy is "stored" in its altitude, not its mass.
It's stored in the object or objects, not some place else.  22. Originally Posted by Farsight It's stored in the object or objects, not some place else.
If a brick is sat on a table top it has PE with regard to the floor = extra energy = extra mass.
But zero PE with regard to the table top = no extra energy = no extra mass.
How much does the brick weigh?  23. Originally Posted by Farsight  Originally Posted by jrmonroe An object would have potential energy or added mass, but not both, right? The potential energy is "stored" in its altitude, not its mass.
It's stored in the object or objects, not some place else.
I'm not so sure of that. If I pulled the two plates of a charged capacitor apart by some amount, the extra energy would be in the energy of the electric field. It would seem simplest to assign the mass to the field as well. This may be picking nits, or there may be something in general relativity that would change the argument in the case of gravity, but it does seem more likely that the force-field itself has a mass as well as an amount of energy.

I hope someone knows for sure whether this is true.  Bookmarks
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