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Energy Needed To Go A Given Speed

  1. Jun 18, 2011 #1
    Hey, I don't have much of a physics background.

    I have been searching for an equation that shows how much energy is needed to make a given mass go a given speed.

    For example, lets say I want to send 1 gram at half light speed. How much energy is required?

  2. jcsd
  3. Jun 18, 2011 #2

    Doc Al

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    Sounds like you want to calculate the kinetic energy of the mass.

    For low speeds (compared to the speed of light) the kinetic energy is KE = ½mv². But for fast speeds, it's a bit more complicated:

    (I can't seem to get Latex to work.)
  4. Jun 18, 2011 #3


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    Welcome to PF!

    Hi Sothh! Welcome to PF! :smile:

    For a speed of v metres per second, the energy of a mass of m kilograms is mc2/√(1 - v2/c2) joules.

    If v = 0 (the mass is at rest), that energy is obviously just mc2, which is therefore called the rest-mass.

    So the extra energy needed to get it to speed v (the kinetic energy) is mc2(1/√(1 - v2/c2) - 1) joules. :wink:

    If v/c is very small, then that extra (kinetic) energy is approximately mc2(v2/2c2), ie mv2/2.
  5. Jun 18, 2011 #4

    Just to confirm I am using this correctly, it should take 20 kilograms around 9e+12 kilojoules to go .1c, correct?
  6. Jun 18, 2011 #5

    Doc Al

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    Sounds about right.
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