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DYNAMICS - CASE STUDY

    Introduction


Problem Graphic
 

When designing rockets to transport a given payload into space, rocket scientists must determine the optimal mass of fuel for the rocket to carry. How can they determine the maximum velocity a rocket will attain based on the amount of fuel it carries?

What is known:

  • The total initial mass of a rocket and its fuel is mo.
  • The fuel has an initial mass mf, and burns at a constant rate of dmf/dt = c.
  • The fuel is expelled from the rocket at a constant speed vf relative to the rocket.
  • The rocket is fired vertically from rest.
  • Drag resistance of the air may be neglected.
   
  Question

 

What is the velocity of the rocket in terms of given parameters once it has burned all of its fuel?

     
    Approach

   
  • Use conservation of linear momentum to determine the force exerted on an object as a result of emitting a continuous flow of mass.
  • Use Newton's Second Law to derive an equation relating the sum of forces acting on the rocket to the rocket's acceleration.
  • Integrate to determine the rocket's velocity.
     
   
 
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