A roller coaster travels in a circular path. (a) Identify the forces on a passen

Question

A roller coaster travels in a circular path.     (a) Identify the forces on a passenger at the top of the circular loop that cause centripetal acceleration.  Show the direction of all forces in a sketch. (Do this on paper.  Your instructor may ask you to turn in this work.)
    
    (b) Identify the forces on the passenger at the bottom of the loop that produce centripetal acceleration.  Show these in a sketch. (Do this on paper.  Your instructor may ask you to turn in this work.)
    
    (c) Based on your answers to (a) and (b), at what point, top or bottom, should the seat exert the greatest force on the passenger?
    

    (d) Assume the speed of the roller coaster is 3.80 m/s at the top of the loop of radius 8.00 m.  Find the force exerted by the seat on a 57.0-kg passenger at the top of the loop.
          N
    
    Then, assume the speed remains the same at the bottom of the loop, and find the force exerted by the seat on the passenger at this point.
          N
    
    Are your answers consistent with your choice of answers for (a) and (b)?

Explanation / Answer

(a) At Top the net force = mv^2/r - mg

(b) At the Bottom the net force = mv^2 + mg

(c) The seat exert the greatest force on the passenger at bottom.(Reaction force = net force)

(d) At Top = 57[(3.8 x 3.8/8) - 9.8] = - 455.7 N

Since this is -ve =>the force is directed down words i.e. the person is actually hanging in the harness of the roller coaster so the seat is free.
At bottom = 57[(3.8 x 3.8/8) + 9.8] = 661.5 N

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