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Old 2010-05-19, 15:05   #1
science_man_88
 
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Default kinetic energy

I was doing math around e=mc^2 ke=.5*m*v^2 if energy gets converted to kinetic energy in these equations, it can't convert 100% without violating the universal speed limit. can someone help explain ? I calculate .70 - .71 * c as max v achievable.

Last fiddled with by science_man_88 on 2010-05-19 at 15:13
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Old 2010-05-19, 16:12   #2
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Quote:
Originally Posted by science_man_88 View Post
I was doing math around e=mc^2 ke=.5*m*v^2 if energy gets converted to kinetic energy in these equations, it can't convert 100% without violating the universal speed limit. can someone help explain ? I calculate .70 - .71 * c as max v achievable.
http://en.wikipedia.org/wiki/Kinetic_energy

Read the section on relativistic kinetic energy.
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Old 2010-05-20, 19:04   #3
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see what I was thinking was e=mc^2 = 1/2mv^2

mc^2 = 1/2 mv^2

2*(mc^2) = mv^2

which worked out to sqrt(2)*c = v but anyways I'm an idiot lol
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Old 2010-05-21, 04:34   #4
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In addition to relativistic effects, quantum effects may also be considered at least with regards to the equipartition theorem. See http://en.wikipedia.org/wiki/Equipartition_theorem.
Quote:
The equipartition theorem makes quantitative predictions. Like the virial theorem, it gives the total average kinetic and potential energies for a system at a given temperature, from which the system's heat capacity can be computed. However, equipartition also gives the average values of individual components of the energy, such as the kinetic energy of a particular particle or the potential energy of a single spring.
This circles back to Einstein because reasoning about difficulties with this theory (ultraviolet catastrophe) led to his photon theory of light. Modern researchers are making strides:
http://www.physorg.com/news193581095.html
Quote:
A century after Albert Einstein said we would never be able to observe the instantaneous velocity of tiny particles as they randomly shake and shimmy, so called Brownian motion, physicist Mark Raizen and his group have done so.
"This is the first observation of the instantaneous velocity of a Brownian particle," says Raizen, the Sid W. Richardson Foundation Regents Chair and professor of physics at The University of Texas at Austin. "It's a prediction of Einstein's that has been standing untested for 100 years. He proposed a test to observe the velocity in 1907, but said that the experiment could not be done."
Quote:
The equipartition theorem states that a particles' kinetic energy—the energy it possesses due to motion—is determined only by its temperature, not its size or mass.
Raizen's study now proves that the equipartition theorem is true for Brownian particles; in this case, glass beads that were three micrometers across.
Raizen says he and his colleagues can now push the limits, moving the particles closer to a quantum state for observation.
"We've now observed the instantaneous velocity of a Brownian particle," says Raizen. "In some sense, we're closing a door on this problem in physics. But we are actually opening a much larger door for future tests of the equipartition theorem at the quantum level."
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Old 2010-05-22, 01:58   #5
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Quote:
Originally Posted by only_human View Post
This circles back to Einstein because reasoning about difficulties with this theory (ultraviolet catastrophe) led to his photon theory of light.
Hmm. This was Max Planck (1900), hence his constant.

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Old 2010-05-22, 04:01   #6
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Quote:
Originally Posted by davieddy View Post
Hmm. This was Max Planck (1900), hence his constant.

David
Of course it involves Planck's Constant and many other seminal ideas in quantum theory. I chose to mention this one thing because of Einstein's work on the photoelectric effect. The article is a bit dismissive of a thought experiment that Einstein proposed because Einstein felt that the test could never be performed and now these canny and sophisticated researchers have succeeded in performing it -- so I mentioned another aspect in the protean development of quantum theory. Actually in several other was it swings back to Einstein but I wasn't trying to boost him in any way. Obviously Heisenberg, Schrodinger, Pauli, Bohr, Gamow and others must be mentioned to even begin to touch on things. Planck's Constant is a keystone in the theory. It is one of the special numbers of universe, much like the fine lattice constant. I give Feynman special credit for his simple explanation of QED that made it accessible to my level of understanding -- his semi-autobiographical books are a fun jaunt too. Please pardon any gaffes in my post.-- I am typing without consulting anything.
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Old 2010-05-22, 04:22   #7
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Quote:
Originally Posted by only_human View Post
Of course it involves Planck's Constant and many other seminal ideas in quantum theory. I chose to mention this one thing because of Einstein's work on the photoelectric effect. The article is a bit dismissive of a thought experiment that Einstein proposed because Einstein felt that the test could never be performed and now these canny and sophisticated researchers have succeeded in performing it -- so I mentioned another aspect in the protean development of quantum theory. Actually in several other was it swings back to Einstein but I wasn't trying to boost him in any way. Obviously Heisenberg, Schrodinger, Pauli, Bohr, Gamow and others must be mentioned to even begin to touch on things. Planck's Constant is a keystone in the theory. It is one of the special numbers of universe, much like the fine lattice constant. I give Feynman special credit for his simple explanation of QED that made it accessible to my level of understanding -- his semi-autobiographical books are a fun jaunt too. Please pardon any gaffes in my post.-- I am typing without consulting anything.
In the context of your post, I would like Boltzmann and his tombstone
inscription to get an honourable mention too

David
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Old 2010-05-22, 05:12   #8
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Quote:
Originally Posted by davieddy View Post
In the context of your post, I would like Boltzmann and his tombstone
inscription to get an honourable mention too

David
Cool. I didn't know of his tombstone. I like the bust too. What a pithy and powerful way to make a beautiful spot for remembrance. It puts me in mind of Archimedes' tombstone.
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Old 2010-05-29, 04:14   #9
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Don't forget about the Lorentz factor. At relativistic velocities, the kinetic energy is:

\left(\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}-1\right)mc^2
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