Help on thrust question (1 Viewer)

[EViL.GENiUS]

Hi

could someone help me on this question.

 

[mrsajmon23]

lol i opened this up expecting it wasn't science-related.

my bad.

 

[k02033]

Minimal thrust need is just the rocket's initial weight.
ie
where is the rocket' initial weight.

The time for which the 1st stage last, is how long that 2*10^6 kg of fuel is goin to last.
the fule is burnt at 1.4*10^4kg/s

so time interval of 1st stage is just 2*10^6/1.48*10^4 , =142 sec

now generally, the acceration of rocket is given by

where m is mass of rocket at some time t, its not just m'

so
now this gives mass of rocket at time t

sub this gives


for

this equation gives rocket's acceration at any time within stage one.

Now mass of the gases at time t is just

The total force acting on the gas is

so where p is momentum of gases.







now i dont know how to get that C the fast way, (the long way is way too long for me to type here..)<-- this involves equating momentum of gas and rocket at time =146
we cant just set t=0 to find initial gas speed, since there are no gases existing yet...(this is the normal way to get C)

 

[k02033]

doesn't the question ask for instaneous quantities? what you got are averages.

 

[k02033]

can you show your full working?

v(t) = [-m'g/(1.4*10^4)]*ln[3.4*10^6 - (1.4*10^4)*t] - gt + C

how did you arrive at that?

it seems like you are using the mass of the rocket ....

i used newtons on the gas expelled, so there shouldnt be anything to do with the rocket's mass.

 

[k02033]

what plotting program do you use, looks nice

 

[k02033]

v(t) = [-m'g/(1.4*10^4)]*ln[3.4*10^6 - (1.4*10^4)*t] - gt + C

for the condition, v(0) = 0:

v(t) = [-m'g/(1.4*10^4)]*ln[3.4*10^6 - (1.4*10^4)*t] - gt + 35793.5

ah i see what you did..
my v(t) is for the propellant, not the rocket, you misread my post. Your v(t) is the rocket's velocity. Your working out was the thing that i said was too long to type out ahah, to get my C

 

[k02033]

wait.. but we have two functions for one thing here..
and i believe yours is off by a -ve sign, if you have chosen g=9.8

 

[k02033]

theres still something wrong with your working. if you graph your function, no matter what C you use its different to my graph

really? all i used was F=ma.. what shape is my function?

 

[k02033]

wait i know whats different between our workings!

yours assumes that there are no external forces acting on the system of rocket and gases and you conserved momentum.

but i take into accout of the earth's gravity as an external force, so my momentum isnt conserved

 

[k02033]

actually if you consider the simple case,

T=3.332*10^7 N
a=T/m
this force acting on say 2*10^6 kg of gas
produces 3.332*10^7/2*10^6 = 2380m/s^2 of acceleration, so thats huge!

 

[k02033]

maybe something is wrong with saying T acts on the gas?

 

[k02033]

oh man that is hideous. must be something wrong with saying T acts on gas, but the way rockets work is that the pressure in the rocket produced T on the gas and then by newton's 3rd law the gas produces T on the rocket? isnt it?

 

[k02033]

the problem with your graph is probably because of the assumed thrust to be constant throughout flight.

oh very good pt! of course T isnt constant, since the gases are falling out of the rocket, so pressure varies, yes! sense is made, thanks.