How Does Rocket Fuel Consumption Impact Acceleration?

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The discussion revolves around calculating the acceleration of a rocket car designed to break a land speed record while ensuring the driver’s safety by limiting acceleration to 5g. The car has a total mass of 6000 kilograms, with 2000 kilograms of that being fuel, which is expelled at a constant speed of 900 meters per second over 15 seconds. Initial calculations mistakenly used the mass of the fuel instead of the total mass, leading to confusion about the acceleration value. The correct approach requires using the total mass of 6000 kilograms to determine the thrust and resulting acceleration. Ultimately, the correct acceleration calculation should yield a value that adheres to the safety limit established for the test.
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Homework Statement



A rocket car is developed to break the land speed record along a salt flat in Utah. However, the safety of the driver must be considered, so the acceleration of the car must not exceed 5g (or five times the acceleration of gravity) during the test. Using the latest materials and technology, the total mass of the car (including the fuel) is 6000 kilograms, and the mass of the fuel is one-third of the total mass of the car (i.e., 2000 killograms). The car is moved to the starting line (and left at rest), at which time the rocket is ignited. The rocket fuel is expelled at a constant speed of 900 meters per second relative to the car, and is burned at a constant rate until used up, which takes only 15 seconds. Ignore all effects of friction in this problem.

Find the acceleration a_0 of the car just after the rocket is ignited.
Express your answer to two significant figures.


Homework Equations



F=ma, Rate of fuel consumption = 400/3

The Attempt at a Solution



In 15s, 2000Kg of fuel is burnt so in one second, it is 400/3.
Velocity is 900m/s so change in momentum will be 120,000.
This divided by mass will give you 60Kg. Am I right or not? I just do not know!
Thanks a lot for your time and effort.
 
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mit_hacker said:
In 15s, 2000Kg of fuel is burnt so in one second, it is 400/3.
OK, that's dm/dt.
Velocity is 900m/s so change in momentum will be 120,000.
OK, that's the thrust, in Newtons.
This divided by mass will give you 60Kg.
What mass did you use? (Acceleration has units of m/s^2.)
 
It says initial so I used a mass of 2000 which now I realize is a mistake. It should be 6000 and the answer comes to 20m/s^2. Is that right?
 
No. Use the total mass.
 
The total mass is 6000 isn't it?
 
mit_hacker said:
The total mass is 6000 isn't it?
My bad... you're right. That includes the fuel.
 

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