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Lecture Sheet
Lecture Day Three

January 14, 2004

  • Circular motion in a vertical circle:
    Question: At what point is the speed of the ball the greatest? The least?



  • Net force on the ball at the top of the circle: The force on the ball at the top of the circle:


  • Net force on the ball at the bottom of the circle: The force on the ball at the bottom of the circle:


    1. Suppose an airplane is traveling at 250-m/s when it enters its dive with a radius of 900 meters. Find the force on the pilot that has a mass of 65-kg (143.65-lb) and determine the g-force. Using the Fb equation, the force on the pilot is found by,


    The g-force:  

     

    Find the same answer using the centripetal acceleration equation:  

     

     

    Page Two
     

  • Critical speed: the minimum speed necessary to keep the ball at the top. Found by setting the Ft equation equal to zero:  

     

     

    This equation can be used for several situations:

    2. If a roller coaster will have a speed of 14 m/s at the top of the second hill, what radius should the curve be such that the people will rise out of their seats?


    Question: Does it matter how heavy a person is for the last example? In other words, would a heavy person not lift off the seat at the same time a lighter person would?  

     

     

    Question: What causes the airtime on a roller coaster?  

     

     

    3. If a roller coaster has an upside down loop with a radius of 30 meters, what is the minimum speed necessary such that the people wouldn't even need a harness to stay in their seats?  

     

     

     

    Question: What happens if the speed is less than the critical speed?