# Relativity and energy conservation

1. Homework Statement

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. Homework 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?

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any help? /cry

Shooting Star
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.

hi, thx a lot for the help with the equations :)

got the math right, thx again for the help