Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: marcelo on 11/07/2011 23:07:02

Hi,
I am no physicist, but this question came to mind the other day.
The famous Einstein's equation E=mc^{2} states the equivalence between mass and energy. However nothing seems to inform the equation about the composition of this matter...so it looks like as if in principle you would get the same energy out of accelerating a gram of feathers or a gram of uranium up to light speed. Is this the case?!
puzzled

You don't get the energy by accelerating the mass to the speed of light (which is impossible anyway). The equation is mass multiplied by the speed of light squared, not just the speed of light. It's a statement of the relationship of their magnitude, not velocity per se.
And yes, one gram of feathers contains just as much energy as one gram of uranium, but one gram of feathers is much larger in volume than one gram of uranium.

SuperC is completely right  but just one more thing. Marcelo you seem to be conflating E=mc^{2} which is the energy equivalence with matter and KE=1/2mv^{2}. It is kinetic energy that you gain through
accelerating a gram of feathers or a gram of uranium
Kinetic Energy = 1/2 mass times velocity squared = 1/2mv^{2}
From this you can see the KE of a gram of feathers will be the same as the KE of a gram of uranium provided they are travelling the same speed

It is also important to remember that when exothermic chemical reactions occur there is a tiny mass loss between the total mass of the reactants and the total mass of the product associated with the liberation of energy during the reaction this is too tiny to be measurable. The mass difference is only measurable in much higher energy nuclear reactions.

Hey guys, thanks for the answers,a few replies since I got more puzzled now...
A basic aspect to clarify is the realworld situation that is described by the eq. E=mc^{2}? Supecryptid, yes it is a statement about the relationship of E,m and c, but this certainly must summarize a statement about a physic phenomenon...which one? what's then the underlying phenomenon where the relationship E=mc^{2 }can be verified?
Imatfaal I agree the phenomenon/situation is not just motion since the eq for KE describes the energy developed/required for that situation.
I just thought that E=mc^{2} described a special phenomenon (not only the motion) where the transformation of mass into energy can actually occur. This is why I thought that the nature of the matter could have something to do with the final energy obtained. If all comes down to motion and (kinetic) energy then feathers and uranium are all the same. However both grams and feather definitely DO NOT contain the same energy when it comes to CHEMICAL energy (otherwise we may fill the tank of the car with the same mass of oil, feathers , water,etc)

You must remember that ALL chemical energy is purely a superficial process with matter in which a few electrons on the outer surface of atoms are rearranged to create and destroy structured groups of atoms. These energy levels are extremely tiny when compared with the mass energy of the whole atoms or the energy levels involved in nuclear changes.

E=mc^{2} is always a bit confusing. What it's telling you is that if you have a block of mass m at rest (on your lab bench, for example) and you were to somehow turn it all into energysay photons of light, for example, you would get mc^{2} units of energy out. c is a huge number, so a tiny bit of mass can create a huge amount of energy.
It works the other way, too. If you concentrate enough energy into a small enough space, you can create particles that have mass. This is what's going on in particle accelerators: they give particles a lot of energy and collide them together. All this energy allows the creation of many kinds of new massive particles.
Finally, it can also describe how "trapped" energy can something have mass. The actual masses of all the tiny particles making up an atom are very smallnot nearly enough to give you the total mass of the atom. But when they're bound up together, the energy of those bonds gives the atom extra mass from m=E/c^{2}. Like Soul Surfer said, the chemical energy is just a tiny tiny fraction of thismost of this energy comes from bonds holding the nucleus together.

I understand that the nuclear bomb that exploded over Hiroshima actually converted about 2 grams of the U235 out of hundred Kg or so it contained into energy which must have been a disappointment to its designers if not to the inhabitants of Hiroshima.

I understand that the nuclear bomb that exploded over Hiroshima actually converted about 2 grams of the U235 out of hundred Kg or so it contained into energy which must have been a disappointment to its designers if not to the inhabitants of Hiroshima.
No. They got what they predicted.

I understand that the nuclear bomb that exploded over Hiroshima actually converted about 2 grams of the U235 out of hundred Kg or so it contained into energy which must have been a disappointment to its designers if not to the inhabitants of Hiroshima.
It wasn't an antimatter bomb so I don't think anywhere near 100% conversion of mass to energy was expected.

I understand that the nuclear bomb that exploded over Hiroshima actually converted about 2 grams of the U235 out of hundred Kg or so it contained into energy which must have been a disappointment to its designers if not to the inhabitants of Hiroshima.
Fission, the nuclear reaction that this bomb relied on, only converts a small percentage of the U235 into energy. This energy comes from the difference in rest mass between the U235 isotope and the daughter products of the fission. Fusion, the basis of the Hbomb, converts a greater percentage of mass to energy, but still only a small fraction.