Rocket Exhaust Gases: Initial & After 29s Acceleration

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SUMMARY

The discussion focuses on calculating the initial and subsequent acceleration of a rocket with an initial mass of 7.30×103 kg, which expels exhaust gases at a rate of 6.00×101 kg/s and a relative velocity of 2.100×103 m/s. To determine the initial acceleration, one must first calculate the thrust using the formula Fs dt = dm·vr. The total force acting on the rocket includes both thrust and gravitational force, which must be considered as the rocket loses mass during ascent. After 29 seconds, the acceleration can be recalculated using the updated mass.

PREREQUISITES
  • Understanding of Newton's second law (F = ma)
  • Knowledge of thrust calculation in rocketry
  • Familiarity with mass flow rates in propulsion systems
  • Basic principles of gravitational force
NEXT STEPS
  • Calculate thrust for varying mass flow rates in rocket propulsion
  • Explore the impact of gravity on rocket acceleration over time
  • Learn about the Tsiolkovsky rocket equation for more complex scenarios
  • Investigate the effects of changing exhaust velocities on rocket performance
USEFUL FOR

Aerospace engineers, physics students, and anyone involved in rocket design and propulsion analysis will benefit from this discussion.

sloanmp
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A rocket with initial mass of 7.30×103 kg is fired in the vertical direction. Its exhaust gases are ejected at the rate of 6.00×101 kg/s with a relative velocity of 2.100×103 m/s. What is the initial acceleration of the rocket? What is the acceleration after 29 s have elapsed?
 
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sloanmp said:
A rocket with initial mass of 7.30×103 kg is fired in the vertical direction. Its exhaust gases are ejected at the rate of 6.00×101 kg/s with a relative velocity of 2.100×103 m/s. What is the initial acceleration of the rocket? What is the acceleration after 29 s have elapsed?

I think you will first need to find such a thing like the Thrust of the rocket, which can be obtained by:

F_s dt = dm\cdot\vector{v}_r

With the thrust, which is clearly a force, you can solve for F =ma, m being the initial one (take into account that your rocket is losing mass as it goes up).
Hint: The total force is the thrust + the gravity!
 

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