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Rockets

Rockets. Momentum and Impulse. Rocket Propulsion. In rockets fuel is burning at all times so we must include this decrease in mass. Exhaust. A rocket fired in outer space. Velocity of the Rocket. Momentum.

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Rockets

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  1. Rockets Momentum and Impulse

  2. Rocket Propulsion • In rockets fuel is burning at all times so we must include this decrease in mass. Exhaust A rocket fired in outer space

  3. Velocity of the Rocket Momentum

  4. At the end of time, t, the velocity has increased to (v + dv) and the mass has decreased to (m + dm) [dm is negative]. • The rocket’s momentum at this time (m + dm)(v + dv) • The x-component of momentum of the rocket and exhaust is as follows:

  5. Momentum for the Rocket

  6. Continued

  7. Rockets • Effective rockets burn fuel at a large rate • That means dm/dt is large and it is a negative number so the acceleration is positive • If the velocity of the exhaust is constant then we integrate to find the relationship between v at any time and the mass.

  8. Integrate In rockets mo/m is very large.

  9. Problem 1 • A rocket is in outer space, far from any planet, when the rocket engine is turned on. In the first second of firing, the rocket ejects 1/120 of its mass with a relative speed of 2400 m/s. What is the rocket’s initial acceleration?

  10. Answer

  11. Problem 2 • Suppose that ¾ of the initial mass mo of the rocket above is fuel, so the final mass is m=mo/4 and that the fuel is completely consumed at a constant rate in a total time t = 90 sec. If the rocket starts from rest, find its speed at the end of this time.

  12. Answer

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