Rocket Calculation Question (1 Viewer)

[Nimue]

It would be much appreciated if someone could help me with this:

"An Apollo launch vehicle has a total mass of 3.4x10^6 kg at lift-off. The first stage contains 2.0x10^6 kg of propellants (fuel and oxygen) which is consumed at a rate of 1.4x10^4 kg/s

a) Find the minimum thrust of the engines at lift-off
b) If that thrust is sustained, find the time over which the first stage operates and acceleration of the vehicle at that time. (You can neglect air friction, but assume the whole flight is verticle)
c) Find the speed of the exhaust gases"

Thanks.

 

[karnbmx]

Alright.

a) "minimum thrust" means that the rocket's acceleration MUST be at least 9.8ms^-2, so that it can overcome the downward acceleration due to gravity.

So as, a = T - mg/m,
rearrange for T (this would be T = ma + mg)
but as a = g (ignoring the negative),
T= 2mg. Use that to calculate Thrust.

b) you know the rate of consumption of fuel and the amount of fuel in the first stage, so you can simply find the time by dividing that amount by the rate given.

for the acceleration, use the same a = T - mg/ma BUT now subtract the mass of the first stage from the initial mass of rocket (remember, use the T you found in the first question, it will ALWAYS be constant).

c) Remember how the momentum of gases = momentum of the rocket? Use that principle to calculate the speed of exhaust gas.

Firstly, you need the velocity of the rocket AFTER exhausting the first stage:

use v = u + at, (where u = 0, a = value found in part B, t = value found in part B)

THEN, using momentum of gases = momentum of rocket, calculate the speed of exhaust gases.

Sorry I don't have exact numbers, but that's how I think this question should be approached. Just out of curiosity, where did you get this one from?

Hope this helps!