What is the relativistic equation for finding kinetic energy?

  1. 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. jcsd
  3. Pengwuino

    Pengwuino 7,119
    Gold Member

    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.
     
  4. PAllen

    PAllen 5,376
    Science Advisor
    Gold Member

    mc^2(γ - 1)

    where γ = 1/(√(1- v^2/c^)
     
  5. Ryan_m_b

    Staff: Mentor

    Here you go :wink: http://bit.ly/xZN1YS
    I don't think so because they are massless.
     
  6. PAllen

    PAllen 5,376
    Science Advisor
    Gold Member

    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.
     
  7. Ryan_m_b

    Staff: Mentor

    I tried to make it clear I wasn't sure :smile: good to learn though, cheers.
     
  8. tom.stoer

    tom.stoer 5,489
    Science Advisor

    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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