Originally posted by wolfgang59
That is what I thought. But when I did the calculations it didnt stack up!
Assume engines are OFF. assume Ship mass of 1,000,000 kg
Determine new velocity and calculate ship's loss in KE .
Sorry - I prefer my calculations without so many numbers in them 🙂
OK, the one thing we know is that momentum is conserved.
v = Initial spaceship velocity = 1,000,000 m/s
V = Final spaceship velocity
u = Final astronaut velocity wrt ship = 1m/s
m = astronaut mass = 100 kg
M = spaceship mass (without astronaut) = 1,000,000 kg
OK, we know is that momentum is conserved.
(M + m)v = MV + m(V + u)
=> V = v - mu/(M + m)
=> V = 1000000 - 1/10001 (~ 999999.9999)
Increase in KE of astronaut
= 0.5m(V + u)^2 - 0.5mv^2
= 0.5m[v + Mu/(M + m)]^2 - 0.5mv^2
= 0.5mMu[2v + Mu/(M + m)]/(M + m)
"Increase" in KE of ship (going to be -ve)
= 0.5MV^2 - 0.5Mv^2
= 0.5M[v - mu/(M + m)^2] - 0.5Mv^2
= 0.5Mmu[mu/(M + m) - 2v]/(M + m)
And the increase in total KE:
= 0.5Mmu^2/(M + m)
This is independent of v - which it has to be, because the increase in energy must be frame-independent. The energy comes from the work done by the astronaut in walking.