What is the relativistic equation for finding kinetic energy?by Ralphonsicus Tags: energy, general, kinetic, relativity, special 

#1
Feb912, 02:12 PM

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. 



#2
Feb912, 02:16 PM

PF Gold
P: 7,125

The energy of a photon with frequency [itex]f[/itex] is [itex]E_{photon} = hf[/itex] where h is Planck's constant. 



#3
Feb912, 02:17 PM

Sci Advisor
PF Gold
P: 4,862

mc^2(γ  1)
where γ = 1/(√(1 v^2/c^) 



#4
Feb912, 02:19 PM

Mentor
P: 5,341

What is the relativistic equation for finding kinetic energy? 



#5
Feb912, 02:25 PM

Sci Advisor
PF Gold
P: 4,862

I missed the question about photons. What Pengwino says is correct, but (and we simulposted, 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. 



#6
Feb912, 02:26 PM

Mentor
P: 5,341





#7
Feb912, 03:33 PM

Sci Advisor
P: 5,307

The relativistic energymomentum 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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