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

AI Thread Summary
The discussion revolves around calculating the fuel required for a rocket to achieve a specific velocity, focusing on the space shuttle's parameters. The shuttle has an initial mass of 2.41 million kg and reaches an initial velocity of 4632 m/s, needing to attain a final velocity of 5158 m/s. The user initially struggled with the equations related to thrust and acceleration, particularly how to derive dv/dt. After some calculations and adjustments, they found that the amount of fuel needed to reach the desired velocity is approximately 5.96×10^4 kg. The conversation highlights the complexities of rocket propulsion calculations and the importance of understanding the underlying physics.
car202
Messages
12
Reaction score
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?
 
Physics news on Phys.org
At least take a guess at what you need to know !
 
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.
 

Thread 'Struggling to understand the concept of this question (ice cube in water optics question)'

TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
View full post »
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
View full post »

Similar threads

Trouble with a Rocket Propulsion question (Variable Mass & Momentum)
Replies
2
Views
2K
Rocket acceleration problem: confused about Newton's 2nd Law
Replies
42
Views
5K
What is the Initial Mass of Fuel Needed for a Rocket to Reach 0.1c?
Replies
9
Views
3K
Rocket Propulsion Homework: Calculating Travel Time
Replies
3
Views
2K
Forces - Space Shuttle Takeoff Calculations
Replies
22
Views
2K
How Does Rocket Ejection Mass Affect Its Velocity in Space?
Replies
1
Views
2K
How Does the Relativistic Rocket Equation Describe Velocity?
Replies
2
Views
2K
Rocket Launch: Achieving Escape Velocity w/ Fuel-Mass Ratio of 300
Replies
3
Views
2K
How Fast Will the Rocket Travel After Using All Its Fuel?
Replies
7
Views
2K
Question about the upthrust of a rocket
Replies
5
Views
3K

Hot Threads

Recent Insights

Back
Top