I'm doing a sample exam for my physics final on thursday, and this question confused me. There's no answer key posted, unfortunately.
'A spaceship fires a rocket with a mass of 5k at a speed 0.8c along the positive y axis in the frame of reference of the spaceship. The spaceship is moving at 0.9c along the x axis in your frame of reference.
a) What do you measure the velocity of the rocket to be?
I got 0.349c for this.
b) What do you measure the momentum of the rocket to be?
I got 1.2x10^9 kgm/s for this.
c) How much work did the spaceship do to launch the rocket?
This is the part I'm stuck on. I know the work-energy theorem says work = change in kinetic energy, and for relativity KE = (gamma - 1)mc^2, but what do I use for the v in the gamma expression? 0.349c? 0.8c? 0.9c?
It seems to me that it would probably be the speed of the rocket relative to the spaceship (0.8c), but I have no way of knowing if that's right or not.
I'd appreciate it if somebody could confirm this or correct me. :)
Answers & Comments
Verified answer
a) do you think the rocket is launched in the same direction as the spaceship, or opposite to it?
http://www.physics.adelaide.edu.au/~dkoks/Faq/Rela...
b) you didn't show your work. Did you use gamma * m * v for this number? v and gamma should be rest frame values.
c) that is where you have to read the sentence carefully, to see for whose frame you are supposed to end up with the value. "You" are in the rest frame, and it is clear that a) and b) are supposed to be rest frame values. c) seems to be asking from the frame of the ship.