John Taylor Classical Mechanics Chapter 3, Problem 7

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SUMMARY

The discussion focuses on solving Problem 7 from John Taylor's "Classical Mechanics," which involves calculating the speed of a space shuttle after two minutes of launch in a vacuum. The initial mass of the shuttle is 2x10^6 kg, and the final mass is 1x10^6 kg, with an average exhaust speed of 3000 m/s. The calculated shuttle speed at the end of this stage is 2079.4 m/s. Additionally, the thrust is determined using the equation mdv/dt = (-dm/dt)v_ex, where thrust is defined as the reactionary force during the launch phase.

PREREQUISITES
  • Understanding of rocket propulsion principles
  • Familiarity with the conservation of momentum
  • Knowledge of differential equations in physics
  • Proficiency in applying the thrust equation in mechanics
NEXT STEPS
  • Study the derivation of the thrust equation in rocket dynamics
  • Learn about the conservation of mass and momentum in space travel
  • Explore advanced topics in fluid dynamics related to exhaust velocity
  • Investigate the implications of thrust-to-weight ratio in rocket launches
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Students of classical mechanics, aerospace engineers, and anyone interested in the physics of rocket launches and propulsion systems.

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John Taylor "Classical Mechanics" Chapter 3, Problem 7

1. Homework Statement [/b]
The first couple of minutes of the launch of a space shuttle can be described very roughly as follows: The initial mass is 2x10^6kg, the final mass (after 2 min) is about 1x10^6 kg, the average exhaust speed is about 3000 m/s and the initial velocity is 0. If all this were taking place in outer space, with negligible gravity, what would be the shuttle speed at the end of this stage? What is the thrust during the same period and how does it compare with the initial total weight of the shuttle (on earth)?
I already answered the first question, and got 2079.4 m/s


Homework Equations


mdv/dt=(-dm/dt)v>ex


The Attempt at a Solution


Am not able to get dv/dt.
 
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you know ##\frac{dm}{dt}##, ##v_{ex}##. Thrust is the reactionary force. Solve R.H.S.
 

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