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AbigailM
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Still preparing for a classical prelim. Not sure if my solution is correct. Any help is more than appreciated.
According to specifications, the five Saturn V booster engines collectively supplied a liftoff thrust of [itex]34 \times10^{6}N[/itex]. The specific impulse was 2580 N-s/kg. The initial mass of the rocket was [itex]3.0\times 10^{6}kg[/itex]. Given these specifications, what was the exhaust velocity, and what was the total acceleration including the acceleration of gravity, felt by the astronauts on liftoff (in g's)?
*The specific impulse is the ratio of the thrust to the rate of consumption of propellant. It is nearly constant.
[itex]v_{ex}=I_{sp}g \hspace{5 mm}\dot{m}=\frac{F_{th}}{I_{sp}}[/itex]
[itex]a(t)=\frac{\dot{m}v_{ex}}{m_{0}-\dot{m}t}-g=\frac{F_{th}g}{m_{0}-\dot{m}t}-g[/itex]
where [itex]m(t)=m_{0}-\dot{m}t \hspace{5 mm}m(t)a(t)=\dot{m}v_{ex}[/itex]
[itex]\dot{m}=\frac{3400\times 10^{4}N}{2580\frac{N.s}{kg}}=1.3\times 10^{4}\frac{kg}{s}[/itex]
[itex]a(t)=\frac{3400\times 10^{4}N}{3.0\times 10^{6}-1.3\times10^{4}\frac{kg}{s}t}g -g[/itex]
Note: Something that confused me was that that the [itex]I_{sp}[/itex] given is in m/s.
Thanks for the help.
Homework Statement
According to specifications, the five Saturn V booster engines collectively supplied a liftoff thrust of [itex]34 \times10^{6}N[/itex]. The specific impulse was 2580 N-s/kg. The initial mass of the rocket was [itex]3.0\times 10^{6}kg[/itex]. Given these specifications, what was the exhaust velocity, and what was the total acceleration including the acceleration of gravity, felt by the astronauts on liftoff (in g's)?
*The specific impulse is the ratio of the thrust to the rate of consumption of propellant. It is nearly constant.
Homework Equations
[itex]v_{ex}=I_{sp}g \hspace{5 mm}\dot{m}=\frac{F_{th}}{I_{sp}}[/itex]
[itex]a(t)=\frac{\dot{m}v_{ex}}{m_{0}-\dot{m}t}-g=\frac{F_{th}g}{m_{0}-\dot{m}t}-g[/itex]
where [itex]m(t)=m_{0}-\dot{m}t \hspace{5 mm}m(t)a(t)=\dot{m}v_{ex}[/itex]
The Attempt at a Solution
[itex]\dot{m}=\frac{3400\times 10^{4}N}{2580\frac{N.s}{kg}}=1.3\times 10^{4}\frac{kg}{s}[/itex]
[itex]a(t)=\frac{3400\times 10^{4}N}{3.0\times 10^{6}-1.3\times10^{4}\frac{kg}{s}t}g -g[/itex]
Note: Something that confused me was that that the [itex]I_{sp}[/itex] given is in m/s.
Thanks for the help.