Rocket Mass & Velocity: Calculating Gas Ejection Rate

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In summary, the conversation discusses the problem of finding the rate at which gases must be ejected from a rocket in order to achieve a desired acceleration. The conversation also mentions the use of the equation M*dv/dt = \sum F(ext) + v(rel)*dM/dt and the need to consider external forces such as gravity, which depends on the altitude of the rocket. The conversation concludes with the acknowledgement that finding the external force may be the key to solving the problem.
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hjr
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Homework Statement


A rocket traveling 1950 m/s away from the Earth at an altitude of 6600 km fires its rockets, which eject gas at a speed of 1300 m/s (relative to the rocket).
If the mass of the rocket at this moment is 2.25×104 kg and an acceleration of 1.4 m/s^2 is desired, at what rate must the gases be ejected?

Homework Equations



M*dv/dt = [tex]\sum[/tex] F(ext) + v(rel)*dM/dt

The Attempt at a Solution



I thought i could just solve for dM/dt in the above equation and plug in the numbers to get the answer but that didnt work. I think my problem is with finding all the external forces, which i think is just mg. I just need a hint to start.
 
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*bump*
 
  • #3
The external force at altitude of 6600 km is not mg.

ehild
 
  • #4
ehild said:
The external force at altitude of 6600 km is not mg.

ehild

so when I find g is that all i have to find? ->for the external force?
 
Last edited:
  • #5
The external force is gravity that depends on the altitude.
F=GmM/r2, and r is the distance from the centre of Earth, r=radius or Earth + altitude

ehild
 
  • #6
alright thanks
 

FAQ: Rocket Mass & Velocity: Calculating Gas Ejection Rate

How do you calculate the mass of a rocket?

The mass of a rocket can be calculated by adding the mass of its components, including the propellant, payload, and structure. The mass of the propellant can be determined by measuring its weight before and after it is loaded into the rocket.

What is the equation for calculating rocket velocity?

The equation for calculating rocket velocity is v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time. This equation takes into account the initial velocity of the rocket and the acceleration due to the gas ejection rate.

How does gas ejection rate affect rocket mass and velocity?

The gas ejection rate plays a crucial role in determining the mass and velocity of a rocket. As gas is ejected from the rocket, it decreases the overall mass and increases the velocity of the rocket due to the conservation of momentum.

What factors can affect the gas ejection rate of a rocket?

The gas ejection rate of a rocket can be affected by several factors, including the type and amount of propellant used, the design and size of the rocket nozzle, and the pressure inside the rocket's combustion chamber. External factors such as air resistance can also impact the gas ejection rate.

How can rocket mass and velocity be optimized through gas ejection rate?

To optimize rocket mass and velocity, the gas ejection rate must be carefully calculated and controlled. This can be achieved by using an efficient propellant and nozzle design, as well as adjusting the pressure in the combustion chamber. Additionally, minimizing air resistance and carefully considering the mass of the rocket's components can also help optimize its performance.

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