Force and acceleration of a rocket

In summary, a rocket with a total mass of 1.00 × 10^4 kg, where eighty percent of the mass is fuel, is launched vertically with a thrust equal to its weight at ignition. The ejected exhaust gases have a constant speed of 9.00 × 10^2 ms ^–1 and the rate of fuel consumption and acceleration due to gravity are also constant. By using Newton's Second Law and the given information, the mass of gases ejected per second and the acceleration of the rocket when the fuel is almost exhausted at time te can be calculated. The thrust remains constant throughout the duration of the flight due to the constant rate of fuel ejection and exhaust gas speed.
  • #1
Sarah0001
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Homework Statement



A rocket, total mass 1.00 × 10^4 kg, is launched vertically; eighty per cent of the mass being fuel. At ignition, time t = 0, the thrust equals the weight of the rocket. The ejected exhaust gases have a speed of 9.00 × 10^2 ms ^–1. Assuming the rate of fuel consumption and the acceleration due to gravity are constant,

calculate: (i) the mass, m, of gases ejected per second (ii) the acceleration, ae , of the rocket when the fuel is almost exhausted at time te

The part I am stuck on is part ii - I am confused on how the thrust is equal to 1.00 × 10^4 * g as seen on the uploaded work solutions below.
F net = Thrust - Weight of rocket
Total Mass of rocket * net acceleration = Thrust - 0.2* total mass rocket *acceleration due to gravity
I am confused on how the Thrust is equal to the weight of the total mass of the rocket. Is there a physical explanation for this

Homework Equations


F=ma
W = Mg

3. My attempt at a solution
Am I correct in my logic that since the exhaust gases cause the thrust of the rocket, then

the net acceleration of the rocket would be the mass of the exhaust gases at time te multiplied by acceleration due to gravity and this product divided by the mass of the rocket, as this is what the thrust force is acting on.

Although this gets to the same numerical answer, I am not convinced I used Newton's Second Law in terms of the worked solutions as I am currently unable to understand how thrust at that time where fuel is nearly exhausted, equals 1.00*10^4 *g. I just thought that thrust equals the exhaust gases * g , and acting on the rocket. I feel there is something wrong in my understanding.
 

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  • #2
Sarah0001 said:
am confused on how the thrust is equal to 1.00 × 10^4 * g
You are given this:
Sarah0001 said:
At ignition, time t = 0, the thrust equals the weight of the rocket.
That is, at ignition there is no acceleration. But as fuel burns the weight goes down and the thrust exceeds the weight.
Sarah0001 said:
the net acceleration of the rocket would be the mass of the exhaust gases at time
The thrust comes from the expulsion of the exhaust. This depends on the rate of ejection of fuel mass and the speed at which it is ejected.
Sarah0001 said:
multiplied by acceleration due to gravity
How can gravity contribute to thrust?!
 
Last edited:
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  • #3
[/QUOTE]That is, at ignition there is no acceleration. But as fuel burns the weight goes down and the thrust exceeds the weight.

The thrust comes from the expulsion of the exhaust. This depends on the rate of ejection of fuel mass and the speed at which it is ejected.
haruspex said:
You are given this:
Thank you

Since both the speed at which it is ejected is constant (9.00*10^2 ms^-1), and as the rate of ejection of fuel is constant too (which is in Kg s^1 ?) does this mean we can assume the thrust to be constant from t=0 throughout the duration of the flight?
 
  • #4
Sarah0001 said:
Since both the speed at which it is ejected is constant (9.00*10^2 ms^-1), and as the rate of ejection of fuel is constant too (which is in Kg s^1 ?) does this mean we can assume the thrust to be constant from t=0 throughout the duration of the flight?
Yes.
 
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Related to Force and acceleration of a rocket

1. What is the relationship between force and acceleration in a rocket?

The force acting on a rocket is directly proportional to its acceleration. This means that as the force increases, the acceleration of the rocket also increases.

2. How does the mass of a rocket affect its acceleration?

The mass of a rocket is inversely proportional to its acceleration. This means that as the mass of the rocket increases, its acceleration decreases.

3. What other factors besides force and mass can affect the acceleration of a rocket?

Apart from force and mass, the design and shape of the rocket, as well as the amount and type of fuel used, can also affect its acceleration. Air resistance and external forces such as gravity can also impact the acceleration of a rocket.

4. How is the force of a rocket calculated?

The force of a rocket is calculated using Newton's second law of motion, which states that force is equal to mass multiplied by acceleration (F=ma). In the case of a rocket, the force is equal to the mass of the rocket multiplied by its acceleration due to the expulsion of fuel.

5. What is the role of Newton's third law of motion in the acceleration of a rocket?

Newton's third law of motion states that for every action, there is an equal and opposite reaction. This law plays a crucial role in the acceleration of a rocket, as the force pushing the rocket upwards (action) is equal to the force pushing the expelled fuel downwards (reaction). This results in a net force acting on the rocket, causing it to accelerate in the opposite direction of the expelled fuel.

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