1. The problem statement, all variables and given/known data
The space shuttle, with an initial mass M = 2.41 x 106kg, is launched from the surface of the earth with an initial net acceleration a = 26.1 m/s^2 . The rate of fuel consumption is R = 6.90 x 103kg/s. The shuttle reaches outer space with a velocity v0= 4632m/s, and a mass of M0= 1.45x106kg. How much fuel must be burned after this time to reach a velocity vf = 5343 m/s
2. Relevant equations
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3. The attempt at a solution
I've tried first setting up the exhaust velocity of the gases. As we are given the net acceleration, we can say that the net force F is: F = Ft - W (where Ft is thrust force, and it is given by Ft = Rvex where vex is the exhaust velocity). By clearing this equation, I found that the exhaust velocity was vex = 1.254 x 104m/s.
For the other part, we will have that momentum is conserved in the following way:
m0v0 = mgvex + (m0 - mg)vf
Where mg and vex is the mass of the gas expelled and exhaust velocity. By clearing this equation, I found out that we had the following equation:
(m0v0 - m0vf)/(vex - vf) = mg
Keep in mind that vex is negative. I found that the final mass of the gases was 5.74 x 104kg, however, it's wrong. Can someone help me in finding what i did wrong in my procedure? Thank you.
The space shuttle, with an initial mass M = 2.41 x 106kg, is launched from the surface of the earth with an initial net acceleration a = 26.1 m/s^2 . The rate of fuel consumption is R = 6.90 x 103kg/s. The shuttle reaches outer space with a velocity v0= 4632m/s, and a mass of M0= 1.45x106kg. How much fuel must be burned after this time to reach a velocity vf = 5343 m/s
2. Relevant equations
-
3. The attempt at a solution
I've tried first setting up the exhaust velocity of the gases. As we are given the net acceleration, we can say that the net force F is: F = Ft - W (where Ft is thrust force, and it is given by Ft = Rvex where vex is the exhaust velocity). By clearing this equation, I found that the exhaust velocity was vex = 1.254 x 104m/s.
For the other part, we will have that momentum is conserved in the following way:
m0v0 = mgvex + (m0 - mg)vf
Where mg and vex is the mass of the gas expelled and exhaust velocity. By clearing this equation, I found out that we had the following equation:
(m0v0 - m0vf)/(vex - vf) = mg
Keep in mind that vex is negative. I found that the final mass of the gases was 5.74 x 104kg, however, it's wrong. Can someone help me in finding what i did wrong in my procedure? Thank you.
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