Rocket Propulsion - Varying mass

In summary, a rocket with a mass of 2.55 * 105 kg and 1.81 * 105 kg of fuel is fired for 250 seconds with an exhaust speed of 3.27 m/s and a fuel consumption rate of 480 kg/s. The thrust of the rocket engine can be found using the equation F = dp/dt. The mass of the rocket after the engine burn is 1.35 * 105 kg and the final speed attained is 2.08 m/s.
  • #1
P-Illiterate
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Homework Statement


A rocket at rest in space, where there is virtually no gravitational force, has a mass of 2.55 * 105 kg, of which 1.81*105 kg is fuel.The engine consumes fuel at the rate of 480 kg/s and the xhaust speed is 3.27 m/s. The engine is fired for 250 s.
  1. Find the thrust of the rocket engine?


    [*]What is the mass of the rocket after the engine burn?
    [*]What is the final speed attained?

Homework Equations


Eq 1: Vf = Vi + Uexln |Mi/Mf|

The Attempt at a Solution


I think I know the first ine
Thrust = RUex
(480*3.27E3)

2 and 3 confuses me

Are they asking about Mass final? Shouldnt I find Vf first?
Mass Initial - 2.55E5
Mass Final after the fuel burns = 7.4E4

The answer for 2 is 1.35 E5 kg, 3 is 2.08E3 m/s

Thank you so much! :D
 
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  • #2
:blushing: I got the answer! o:)
 
  • #3
you have got the rate of fuel consumption and removal. just use f = dp/dt (Newton's original law)
 

Related to Rocket Propulsion - Varying mass

1. How does varying mass affect rocket propulsion?

Varying mass can have a significant impact on rocket propulsion. As a rocket burns fuel, its mass decreases, which means it becomes easier to accelerate. This is because the same amount of thrust is now acting on a smaller mass, resulting in a greater acceleration. On the other hand, as a rocket carries more payload or fuel, its mass increases, making it more difficult to accelerate and reducing its overall speed.

2. How does a rocket's mass change during a space mission?

A rocket's mass changes constantly during a space mission. At liftoff, the rocket is at its heaviest due to the amount of fuel and payload it is carrying. As it burns fuel and releases its payload, the rocket's mass decreases, making it easier to accelerate. However, as it approaches its destination and needs to decelerate, it may need to carry additional fuel, increasing its mass once again.

3. How does varying mass affect a rocket's fuel efficiency?

Varying mass can have a significant impact on a rocket's fuel efficiency. As the rocket's mass decreases, it becomes more efficient in terms of fuel consumption since it requires less fuel to achieve the same acceleration. However, as the rocket's mass increases due to carrying more payload or fuel, its fuel efficiency decreases as it needs more fuel to accelerate.

4. How is mass variation accounted for in rocket design?

In rocket design, mass variation is a crucial consideration. Engineers must carefully calculate the amount of fuel and payload a rocket can carry while still achieving its desired speed and trajectory. They also take into account the changing mass during a space mission and design the rocket's systems to be able to handle these variations without compromising its performance.

5. Can varying mass affect a rocket's stability?

Yes, varying mass can affect a rocket's stability. As the rocket's mass changes, its center of mass also shifts, potentially altering its stability. This is why engineers carefully design rockets with a specific center of mass and consider how it may change during a mission. They also implement control systems to adjust the rocket's stability if needed.

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