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?

  2. jcsd
  3. Pengwuino

    Pengwuino 6,942
    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 5,890
    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 5,890
    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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