Question

6. Kingda Ka Roller Coaster (30 points) 

a) (6 pts) Ignoring friction, sketch a diagram showing the centripetal, gravitational, and normal forces acting of the passenger train of the Kingda Ka roller coaster as it rounds the bottom of the “Big Dip.” Draw each force with its correct direction. Draw the largest force as the longest vector, and the smallest force as the shortest vector.

d) (6 pts) Ignoring friction, sketch a diagram showing the centripetal, gravitational, and normal forces acting of the passenger train of the Kingda Ka roller coaster as it rounds the top of the “Big Hill.” Draw each force with its correct direction. Draw the largest force as the longest vector, and the smallest force as the shortest vector. 

e) (3 pts) Use the following data to show that the magnitude of the centripetal force acting on the passenger train at the top of the “Big Hill” is 1.47 x 105 N. Data: Track radius of curvature 100 m Mass of passenger train = 16.6 x 103 kg Speed of passenger train = 29.8 m/s 

f) (6 pts) Use both the centripetal force and the force of gravity to calculate the force that the track exerts on the passenger train at the top of the “Big Hill."

Answer 1

* Answer: R AN R Img Here N → indicates + Normal Reaction my? R → centri petal Force mg → Gravitational force # At Bottom my2 mg R N = mg+ my² R Y mv R R ung

* At Top : my² R N4 mg N = mul R mg Given data: R = 100m 6.6*108kg m= 16.6 X 1 V = 29.8 m/s 16.6710 (29.8) * mua R 100 = 147.01 XION uixos = 1.47 8105N .: Therefore, magnitude of cantoi petal forove = 1.47 X10 N. © using of both contoipetal force and force of gravity N = my? -mg R N = (1.47X105)-162 x105 N - 16,000 - - 0.66 105N So, less than zero (o) weight less