Rocket Fuel Problem: Calculating Minimum Fuel Fraction for Rocket Broom Flight

In summary, the warlock testing a rocket broom wants to reach a velocity of 0.6u by using a rocket that fires with exhaust speed u, losing mass at a constant rate R. The minimum fraction of the initial mass that must be devoted to fuel can be found using the conservation of momentum equation. This means that the difference in speed between the rocket and the fuel that is expelled is u. By setting up a formula for the mass of fuel expelled in time dt, the minimum fraction of initial mass needed for fuel can be calculated.
  • #1
Bugeye
4
0

Homework Statement


A warlock testing a rocket broom takes off from a standing start and flies at fixed elevation. The warlock and fueled rocket system start out with mass Mi. The rocket fires with exhaust speed u, losing mass at a constant rate R, and we’ll assume air drag is negligible. If the rocket broom is to reach a velocity equal to 0.6u, what minimum fraction of the initial mass must be devoted to fuel?

Homework Equations


Conservation of momentum

The Attempt at a Solution


I really don't even know how to start. I looked at this topic but I do not understand how the fuel has initial momentum, or how to apply any of that in another situation
 
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  • #2
Welcome to PF!

Hi Bugeye :bugeye:! Welcome to PF! :smile:
Bugeye said:
The rocket fires with exhaust speed u…
…
… I do not understand how the fuel has initial momentum

The question means that the difference in speed between the rocket and the fuel that's just gone is u.

So call the mass "m" (as a function of t), and write a formula for what happens when a mass dm of fuel is expelled in time dt …

what do you get? :smile:​

(all the other smilies say "hi!" too :yuck: :cry: :cool: :confused: :zzz: :redface: :frown: :eek: :uhh: :shy: :grumpy: :!) :mad: :wink: o:) :tongue2: :devil: :biggrin: :blushing: :tongue: :rolleyes: :rofl: :approve:)
 

1. What is the "Rocket Fuel Problem"?

The "Rocket Fuel Problem" refers to the challenge of finding a suitable and efficient fuel source for rockets that can provide enough thrust to launch and propel them into space.

2. Why is finding a suitable rocket fuel so important?

Finding a suitable rocket fuel is crucial because it directly affects the cost, safety, and performance of space missions. The right fuel can determine the success or failure of a launch and impact the payload capacity and overall capabilities of a rocket.

3. What types of rocket fuels are currently being used?

The most commonly used rocket fuels are liquid hydrogen and liquid oxygen, also known as cryogenic fuels. Solid rocket fuels, such as ammonium perchlorate composite propellant, are also used for certain types of rockets. Other experimental fuels, such as methane, are being researched for future use.

4. What are the main challenges in developing rocket fuels?

The main challenges in developing rocket fuels include finding a balance between high energy output and stability, as well as ensuring safe handling and storage. Additionally, the cost and availability of materials for fuel production are also important factors to consider.

5. How are scientists working to overcome the "Rocket Fuel Problem"?

Scientists are continuously researching and experimenting with new fuel combinations and technologies to improve the efficiency and performance of rocket fuels. This includes developing more advanced propulsion systems, such as ion and plasma engines, as well as exploring alternative fuel sources, such as nuclear and solar power.

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