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DYNAMICS - CASE STUDY

    Introduction


Problem Diagram

 

After a particularly long lunch, an employee, in a hurry to return to work, slams his car (Car 1) into his boss's new Mercedes (Car 2), resulting in immediate termination of his employment.

What is known:

  • Car 1 weight w1 = 2,500 lb
  • Car 2 weight w2 = 3,500 lb
  • Car 1 moment of inertia about the CG
       I1-cg = 1,164.6 slug-ft2
  • Car 2 moment of inertia
       I2-cg = 2,101.5 slug-ft2
  • Car 1 velocity v1 = 52 mph
  • Car 2 velocity v2 = 0 mph
  • impact angle α = 45°
  • position vectors for Cars' CGs
    r1/P = (3sinα - 6cosα)i + (6sinα + 3cosα)j ft
    r2/P = -5i - 3j ft
  • coefficient of restitution e = 0.2
     

Problem Graphic
  Question

 

What are the translational and rotational velocities of the two vehicles immediately after the impact? Assume the bodies are perfectly rigid and the impact is elastic.

   
  Approach

 
  • Use the Conservation of Angular and Linear Momentum as well as the coefficient of restitution to determine the velocities of each car.
  • Ignore the friction between the car and the ground.
     
   
 
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