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

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SUMMARY

The discussion focuses on calculating the minimum fuel fraction required for a rocket broom to achieve a velocity of 0.6 times the exhaust speed (u). The initial mass of the rocket system is denoted as Mi, and the mass loss rate is represented by R. Key concepts include the conservation of momentum and the relationship between the expelled fuel and the rocket's velocity. Participants emphasize the importance of understanding how the expelled fuel contributes to the rocket's momentum during flight.

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  • Knowledge of mass flow rates in rocket systems
  • Basic algebra for formulating equations
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  • Learn how to apply conservation of momentum in dynamic systems
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Aerospace engineers, physics students, and anyone interested in rocket propulsion and performance analysis will benefit from this discussion.

Bugeye
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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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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 :cry: :cool: :confused: :zzz: :redface: :frown: :eek: :rolleyes: :shy: :!) :mad: :wink: o:) :-p :devil: :biggrin: :blushing: :-p :rolleyes: :smile: :approve:)
 

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