# What is the relativistic equation for finding kinetic energy?

by Ralphonsicus
Tags: energy, general, kinetic, relativity, special
 P: 47 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.
PF Gold
P: 7,120
 Quote by Ralphonsicus 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 $(\gamma - 1)mc^2$ where $\gamma = {{1}\over{\sqrt{1-{{v^2}\over{c^2}}}}}$ where c is the speed of light.

The energy of a photon with frequency $f$ is $E_{photon} = hf$ where h is Planck's constant.
 Sci Advisor PF Gold P: 5,059 mc^2(γ - 1) where γ = 1/(√(1- v^2/c^)
Mentor
P: 5,473
What is the relativistic equation for finding kinetic energy?

 Quote by Ralphonsicus 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 by Ralphonsicus And also, do photons have kinetic energy?
I don't think so because they are massless.
 Sci Advisor PF Gold P: 5,059 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.
Mentor
P: 5,473
 Quote by PAllen 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.
 Sci Advisor P: 5,451 The relativistic energy-momentum relation reads $$E^2 = (mc^2)^2 + p^2c^2$$ From this equation the kinetic energy can be determined directly $$E_\text{kin} = E - mc^2 = \sqrt{(mc^2)^2 + p^2c^2} - mc^2$$ For photons we have m=0 and therefore $$E_\text{kin} = E = pc$$ For m>0 one gets the equations with v

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