Rocket Propulsion: Boosting 3.10T to 10K m/s

[Jacob87411]

A rocket for use in deep space is to have the capability of boosting a total load (payload plus the rocket frame and engine) of 3.10 metric tons to a speed of 10 000 m/s.

(a) It has an engine and fuel designed to produce an exhaust speed of 2800 m/s. How much fuel plus oxidizer is required?

(b) If a different fuel and engine design could give an exhaust speed of 4600 m/s, what amount of fuel and oxidizer would be required for the same task?

I honestly have no idea where to even start because this hasnt been gone over in class or in the book, so if anyone could just give me a basic idea of how to approach it it would be helpful

 

[tony873004]

Treat it like a momentum problem. Initial momentum is 0. Final momentum of the system must also be 0.

 

[Astronuc]

Have you covered thrust (force) as a function of rocket exhaust velocity and mass flow rate?

Try this for some ideas - http://exploration.grc.nasa.gov/education/rocket/thrsteq.html

 

[Jacob87411]

No we haven't covered it but I read it but I still don't really understand the problem. The engine can produce a speed of 2800 and you need to know how much fuel is required to get it up to 10,000?

 

[tony873004]

What is the momentum of the rocket + payload after it has been accelerated to 10,000 m/s?

 

[Jacob87411]

Momentum=Mass * Velocity...So 3.1*10,000?

 

[tony873004]

Momentum is conserved. Prior to burning the fuel, call the momentum 0. What do you need to add to (3.1*10000) to get 0?

 

[Jacob87411]

Obviously -31,000...but its not -31,000 metric tons...

Is it the momentum caused from the engine that gives a speed of 2800 m/s...so

P=mv
-31,000=2800m, m=11.07

 

[tony873004]

you got it. -31000 metric tons m/s is the momentum of the fuel. When added to the momentum of the empty rocket, they equal 0 which is what the original momentum was. So you conserved momentum.

Then you divided the momentum (-31000) by the velocity (-2800 since it is in the direction opposite the rocket) and got 11.07 metric tons.

 

[Jacob87411]

Thats what I originally thought and put it as an answer but it says its wrong

 

[tony873004]

Is this webassign?

Becareful of your units. You computed it in metric tons. Is it asking for metric tons, or kilograms?

In webassign, the teacher has the option to enforce or not enforce significant digits. 10,000 has only 1 significant digit, so your answer should have the same.

How many tries do you get?

 

[Jacob87411]

Yes its webassign..It wants it in metric tons..ive used 3/5 and 2/5 on the first and second respectively

 

[tony873004]

I don't know what to tell you, unless its a significant figure issue. But you probably know from the other problems whether or not the teacher enforces sig figs.