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DYNAMICS - CASE STUDY

    Introduction


Toy Car with 360° Loop
 

It is the night before your child's birthday and you are building a toy car-loop track for your child. You have noticed that if the track is attached to the coffee table, the car will need an initial velocity to keep from falling off the track as it goes through a 360° loop.

What is known:

  • The loop height hL is 1.6 ft.
  • The start height hs is 1.8 ft.
  • The slope is 2/3.
  • Friction between the toy car and the track may be ignored.
     
    Question

   

At what initial speed should the car be launched to make the loop?


Program Diagram
   
  Approach

 
  • All forces are conservative since there is no friction.
  • Use the Conservation of Energy energy since all energy terms are conservative (no friction energy loss),

    V1 + T1 = V2 + T2