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

In summary, the conversation discusses the necessary fuel consumption for a space shuttle to reach a desired velocity after reaching outer space. The initial mass, acceleration, and rate of fuel consumption are given, along with the final velocity and mass. The conversation also mentions attempts at solving the problem and the ultimate solution.
  • #1
car202
13
0

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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  • #2
At least take a guess at what you need to know !
 
  • #3
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?
 
  • #4
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?
 
  • #5
Oops, I solved the problem! FYI answer is 5.96×10^4 kg.
 

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

1. What is rocket propulsion fuel burn?

Rocket propulsion fuel burn is the process of burning fuel in a rocket engine to produce thrust, which propels the rocket forward. It is the main mechanism by which rockets are able to overcome the force of gravity and reach space.

2. What types of fuel are used in rocket propulsion?

There are various types of fuel used in rocket propulsion, including liquid propellants such as liquid hydrogen and liquid oxygen, and solid propellants such as ammonium perchlorate and aluminum. Each type has its own advantages and is used in different types of rockets.

3. How is rocket propulsion fuel burned?

Rocket propulsion fuel is burned by mixing it with an oxidizer, such as liquid oxygen, and igniting it in a controlled manner in the combustion chamber of the rocket engine. The resulting hot gases are then expelled through the nozzle, creating thrust.

4. What factors affect the efficiency of rocket propulsion fuel burn?

The efficiency of rocket propulsion fuel burn is affected by several factors, including the type of fuel used, the design of the rocket engine and combustion chamber, and the ambient conditions such as air pressure and temperature. It is also affected by the ratio of fuel to oxidizer, known as the mixture ratio.

5. How is the amount of fuel required for a rocket determined?

The amount of fuel required for a rocket is determined by various factors, including the mass of the rocket, the desired velocity, and the specific impulse of the fuel. Specific impulse is a measure of how efficiently the fuel is used to produce thrust, and it is a key factor in determining the amount of fuel needed for a given mission.

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