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Relativity and energy conservation

  1. Mar 24, 2008 #1
    1. The problem statement, all variables and given/known data

    A rocket uses a photon radiation engine. Knowing that from a reference R the initial and final rest masses of the rocket are Mi and Mf show that

    Mi / Mf = sqrt [ ( c + v ) / ( c - v ) ]

    and that the rocket was initially resting on R

    2. Relevant equations

    Total Energy = Mo.c^2 + T (kinetic)

    T= Mo.(c^2).{ [1 - (v^2 / c^2)]^(-1) -1 }

    3. The attempt at a solution
    I calculated the total energy on the instants i and f, like this

    Ei = Mi.c^2

    Ef = Mf.c^2 + Tf

    and since there's conservation of the total energy Ei = Ef

    in the end i got

    Mi / Mf = sqrt [ ( c^2 ) / (c^2 - v^2) ]

    so... i must have assumed something wrong ;/
    any tips?
  2. jcsd
  3. Mar 25, 2008 #2
    any help? /cry
  4. Mar 25, 2008 #3

    Shooting Star

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    Homework Helper

    Let E and p be the magnitudes of the total energy and momentum of the photons respectively. If the velocity v of the rocket is directed to the right, say, then the direction of p is to the left. Let 'g' denote gamma(v).

    E = pc --(1) (for photons)

    By conservation of momentum,

    p = Mf*g*v --(2)

    Initial total energy = final total energy =>

    Mi*c^2 = E + Mf*g*c^2 --(3)

    Now, put E = pc = Mf*g*v and do the algebra. It's not very hard.
  5. Mar 25, 2008 #4
    hi, thx a lot for the help with the equations :)

    got the math right, thx again for the help
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