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DYNAMICS - CASE STUDY

    Introduction


Coordinate System

 

Just prior to the Winter Olympics, the Olympic committee must erect a 15-meter ski jump. If the jump is not sturdy enough, the force of the skier could cause the jump to collapse.

What is known:

  • The shape of the ski jump is described by the equation

    y = f(x) = x2/40   (m)

  • The largest contestant has a total mass of 90 kg, including equipment.
  • The skier starts from rest at a height of 15 m.
  • Friction and the size of the skier and skis may be ignored.
     

Problem Animation
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  Question

 

At the end of the jump, what is the normal force exerted on the skier by the jump?

What is the total acceleration of the skier at the end of the jump?

   
  Approach

 
  • Use the principle of conservation of energy (covered in more detail in the following chapter) to find the skier's velocity at the end of the jump.
  • Apply Newton's Second Law, using the equations for normal and tangential coordinates developed in the Curvilinear Motion: Normal/Tangential Coordinates section of previous chapter.