What is the relativistic equation for finding kinetic energy?


by Ralphonsicus
Tags: energy, general, kinetic, relativity, special
Ralphonsicus
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Feb9-12, 02:12 PM
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Let's say, I wanted to find the kinetic energy of a ball travelling at 99% the speed of light, what is the equation used for that calculation?

And also, do photons have kinetic energy?

Thanks.
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Pengwuino
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Feb9-12, 02:16 PM
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Quote Quote by Ralphonsicus View Post
Let's say, I wanted to find the kinetic energy of a ball travelling at 99% the speed of light, what is the equation used for that calculation?

And also, do photons have kinetic energy?

Thanks.
The formula for a particle of mass m has a kinetic energy is given by [itex](\gamma - 1)mc^2[/itex] where [itex]\gamma = {{1}\over{\sqrt{1-{{v^2}\over{c^2}}}}}[/itex] where c is the speed of light.

The energy of a photon with frequency [itex]f[/itex] is [itex]E_{photon} = hf[/itex] where h is Planck's constant.
PAllen
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Feb9-12, 02:17 PM
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mc^2(γ - 1)

where γ = 1/(√(1- v^2/c^)

Ryan_m_b
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Feb9-12, 02:19 PM
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What is the relativistic equation for finding kinetic energy?


Quote Quote by Ralphonsicus View Post
Let's say, I wanted to find the kinetic energy of a ball travelling at 99% the speed of light, what is the equation used for that calculation?
Here you go http://bit.ly/xZN1YS
Quote Quote by Ralphonsicus View Post
And also, do photons have kinetic energy?
I don't think so because they are massless.
PAllen
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Feb9-12, 02:25 PM
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I missed the question about photons. What Pengwino says is correct, but (and we simul-posted, else I wouldn't have bothered) adding a little more, and disagreeing with Ryan_m_b:

Since a photon is massless it has no rest energy. Therefore all of its energy is kinetic. For a massive particle, you can say the frame dependent energy has a minimum - the rest energy; the frame dependent additional energy is kinetic. For a photon, there is no minimum - you can redshift to arbitrarily close to zero energy by choice of frame, consistent with its having no rest energy and all kinetic energy.
Ryan_m_b
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Feb9-12, 02:26 PM
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Quote Quote by PAllen View Post
disagreeing with Ryan_m_b...Since a photon is massless it has no rest energy. Therefore all of its energy is kinetic
I tried to make it clear I wasn't sure good to learn though, cheers.
tom.stoer
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Feb9-12, 03:33 PM
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The relativistic energy-momentum relation reads

[tex]E^2 = (mc^2)^2 + p^2c^2[/tex]

From this equation the kinetic energy can be determined directly

[tex]E_\text{kin} = E - mc^2 = \sqrt{(mc^2)^2 + p^2c^2} - mc^2[/tex]

For photons we have m=0 and therefore

[tex]E_\text{kin} = E = pc[/tex]

For m>0 one gets the equations with v<c mentioned above, of course


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