# Homework Help: Relativistic Energy Question

1. Feb 5, 2010

### tommyball

Hi-

I have a question regarding relativistic kinetic energy. If a spaceship is moving at a velocity relative to the earth and then accelerates, to compute the work done by the engine/KE, should I use the given final velocity(the problem isn't entirely clear what this speed is in reference to) to compute $$\gamma$$ or the difference in velocity? The problem is as follows:

1.A space vehicle with a mass of 50,000 kg is moving directly away from the earth at a speed of v0, relative to the earth. It sends a radio signal back to the earth, notifying ground control that it is about to begin a rocket burn to accelerate to vf. The radio frequency for the transmission is 300MHz, measured on the craft. The signal is received on earth at 260 MHz.

A) What was v0, before the burn?
B) If the speed of the vehicle after the burn is 0.4c, and no other forces act on the craft, how much work did the rocket engine do on the vehicle?

2. Relevant equations

To determine v0 I used the Doppler Shift equation:

f=f0 * sqrt[(1-(v/c)) / (1 + (v/c))]

To determine the work, I used the relativistic work/KE equation:

W = $$\Delta$$KE = mc^2($$\gamma$$ - 1)

3. The attempt at a solution

I computed v0 = 0.142c

My question is, when computing $$\gamma$$ for the W/KE equation, do I use the given vf of 0.4c or since I am trying to determine the work done by the engine, do I use a v of 0.4c-0.142c = 0.258c since the v0 is relative to the earth and in the craft's reference frame the engine is accelerating it from 0?

Thank you,
Todd
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution