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Conservation of Energy and Momentum

  1. Nov 2, 2007 #1
    1. The problem statement, all variables and given/known data
    I have a 1g object on a frictionless surface being hit with light of a frequency 632nm (directly parrallel to the surface and the object absorbs all the light). How many photons did the object absorb by the time it's moving at 1mm/s?

    2. Relevant equations

    3. The attempt at a solution
    Well I worked it out two different ways and I got two different answers:

    My first attempt is via conservation of energy:
    n*h*c/lambda + m*c^2 = gamma*m*c^2
    n is the number of photons
    h is planck's constant
    c is the speed of light
    lambda is the wavelength
    m is the mass of the object
    gamma is the 1/sqrt(1-v^2/c^2)
    Then I solved for n.

    My second attempt is via conservation of momentum:
    n*h/lambda = gamma*m*v
    Then I solved for n.

    In both cases I got different answers. So I'm not sure what's wrong.
  2. jcsd
  3. Nov 2, 2007 #2


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    Trust conservation of momentum before you trust a naive conservation of energy calc. The collision is inelastic.
  4. Nov 2, 2007 #3
    Ok thanks. But what happened to the energy? Did it radiate as heat or something?
  5. Nov 2, 2007 #4


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    Some of it could have been converted into electrical energy if the surface is connected to a power grid. Conservation can't tell you where it went. But yes, most likely answer is heat.
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