How much fuel is needed to reach a specific velocity in rocket propulsion?

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Homework Help Overview

The problem involves rocket propulsion, specifically calculating the amount of fuel required for a space shuttle to reach a certain velocity after achieving a previous speed. The context includes parameters such as mass, acceleration, fuel consumption rate, and velocities at different stages of the shuttle's flight.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the application of equations related to rocket propulsion, including the use of mass flow rate and changes in velocity. Some express confusion regarding the derivation of acceleration and the variables involved in the equations.

Discussion Status

The discussion includes attempts to apply relevant equations, with some participants questioning their understanding of the relationships between variables. One participant indicates they found a solution, but there is no consensus on the methods used or the correctness of the approaches discussed.

Contextual Notes

Participants are navigating through the complexities of the equations involved in rocket propulsion, with some expressing uncertainty about constants and variable relationships. There is a mention of previous incorrect answers, indicating a trial-and-error approach to understanding the problem.

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Homework Statement


The space shuttle, with an initial mass M = 2.41E+6 kg, is launched from the surface of the Earth with an initial net acceleration a = 26.1 m/s2. The rate of fuel consumption is R = 6.90E+3 kg/s. The shuttle reaches outer space with a velocity of vo = 4632 m/s, and a mass of Mo = 1.45E+6 kg. How much fuel must be burned after this time to reach a velocity vf = 5158 m/s?
 
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well i got some answer..but all of them were wrong. Ve(dm/dt) = M(dv/dt), Vf-Vi= Ve(ln(Mi/Mf)...As it reaches outer space, I got acceleration of 43.38 and since gravity is not acting, added 9.81 to get 53.19. I set this to dv/dt. Got Ve. And plugged into formula...but did not work. What's wrong?
 
My only question is, on equation Ve(dm/dt) = M(dv/dt), how do we get dv/dt? I really don't get it..Is it constant?
 
Oops, I solved the problem! FYI answer is 5.96×10^4 kg.
 

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