How Does Rocket Fuel Consumption Impact Acceleration?

In summary, a rocket car is being developed to break the land speed record on a salt flat in Utah while ensuring the safety of the driver. The car's acceleration must not exceed 5g and it has a total mass of 6000 kilograms with one-third of that being fuel. The rocket fuel is expelled at a constant speed of 900 meters per second and is burned at a constant rate until used up in 15 seconds. The acceleration of the car just after the rocket is ignited can be calculated using the equations F=ma and rate of fuel consumption = 400/3. The answer is 20m/s^2.
  • #1
mit_hacker
92
0

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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  • #2
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.)
 
  • #3
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?
 
  • #4
No. Use the total mass.
 
  • #5
The total mass is 6000 isn't it?
 
  • #6
mit_hacker said:
The total mass is 6000 isn't it?
My bad... you're right. That includes the fuel.
 

Related to How Does Rocket Fuel Consumption Impact Acceleration?

What are Newton's three laws of motion?

Newton's first law states that an object will remain at rest or in uniform motion in a straight line unless acted upon by an external force. Newton's second law states that the force applied to an object is equal to the mass of the object multiplied by its acceleration. Newton's third law states that for every action, there is an equal and opposite reaction.

How do Newton's laws apply to everyday life?

Newton's laws are used in many everyday activities, such as driving a car, riding a bicycle, or playing sports. For example, when you push a shopping cart, you are applying a force to it, causing it to accelerate (Newton's second law). When you jump off a diving board, your body moves in the opposite direction due to the force of the board pushing against you (Newton's third law).

What is the difference between mass and weight?

Mass is a measure of the amount of matter in an object, while weight is a measure of the force of gravity acting on an object. Mass is constant, while weight can vary depending on the strength of the gravitational pull. For example, an object may have the same mass on Earth and the moon, but its weight will be different due to the difference in gravitational pull.

Can Newton's laws be broken?

No, Newton's laws are fundamental principles of physics and have been extensively tested and proven to be true. However, they may not always seem to apply in certain situations, such as in outer space or at extremely high speeds, due to the effects of other forces.

How did Newton's laws contribute to our understanding of the universe?

Newton's laws of motion revolutionized our understanding of the universe and paved the way for modern physics. They provided a mathematical framework for explaining the motion of objects, including planets and celestial bodies, and helped us understand the forces at work in the universe.

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