How Does Rocket Fuel Consumption Impact Acceleration?

[mit_hacker]

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.

 

[Doc Al]

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.)

 

[mit_hacker]

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?

 

[Doc Al]

No. Use the total mass.

 

[mit_hacker]

The total mass is 6000 isn't it?

 

[Doc Al]

The total mass is 6000 isn't it?

My bad... you're right. That includes the fuel.