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DYNAMICS - CASE STUDY

    Introduction


Problem Diagram

 

Billy and Susan just received toy cars from their grandparents. Billy's car was a sports-car model and Susan's was a box car model. Whose car will run fastest downhill?

What is known:

  • Each car body weighs 10 lb.
  • The wheels on both cars weigh 1 lb each.
  • The cars are rolled down a 13.7 ft hill.
  • The sports car comes with rim wheels that have nearly all of the wheel's mass at the rim.
  • The box car comes with wheels that are uniform disks, with the mass evenly distributed throughout.
  Questions

 

What is the speed of each car at the bottom of the hill? Which one is going faster?

   
  Approach

   
  • Use the Conservation of Energy Principle:

    T1 + V1 = T2 + V2
  • Note that both rotational kinetic energy and translational kinetic energy are present.
     
   
 
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