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Rockets

Learn about rockets, momentum, and impulse in rocket propulsion. Explore how fuel burning affects mass decrease and exhaust velocity to calculate rocket momentum. Discover the relationship between rocket acceleration and mass depletion, and solve rocket propulsion problems.

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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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