Rocket Special Relativity

1. Feb 22, 2015

SHawking01

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

A rocket, initially at rest, propels itself in a straight line by giving portions of its mass a constant (backward) speed vout relative to its instantaneous rest frame. (a) Is rest mass conserved in this process? (b) Show that m0du′ = −dm0 vout, where m0 is the rocket’s rest mass and du′ is the change in the rocket’s speed (in its instantaneous rest frame) when its rest mass changes by dm0. (c) Show that m0 du/dm0 = −(1 − u 2/c2) vout, where u is the speed of the rocket in its initial rest frame. (d) Suppose the rocket reaches speed uf relative to its initial rest frame. Show that the ratio of its initial to final rest mass is given by (m0,i/ m0,f)= (c + uf)/( c − uf)c/2vout
2. Relevant equations

3. The attempt at a solution
a)Rest mass is not conserved due to loss of kinetic energy.
b) m0c2=γ(vout)d\tilde{\m}c2+ γ(du')(m0+dm0)c2
0=γ(du')(m0+dm0)du'-γ(vout)d\tilde{\m}vout
γ(du')=1/√1-(du')2/c2 by the binomial approximation is ≈1.
m0du'=γ(vout)d\tilde{\m}vout
m0du'=-dm0vout
m0/dm0=-vout/du'
c) vout=m0du'/-dm0
I know I have to use the velocity addition formula. How do I find u and u'?

2. Feb 23, 2015

Staff: Mentor

Where is kinetic energy lost?
How do you define (total?) rest mass in the first place?

For (c), I don't think you need velocity addition, the transformation between u' and u (but I don't understand how exactly they are defined) could give the gamma factor without it.