Question

In a roller coaster ride loop the radius of curvature is more at bottom than at top. Why?​

Answer 1

Answer:

Rollercoasters use a hill for riders to gain speed followed by an upside down loop. The loops are designed with large radius bottoms and small radius tops, and such a shape is called a clothoid. Answer the following questions in order to find out why the clothoid is used. The speed of the rollercoaster is 22 m/s at the bottom of the loop and 8 m/s at the top of the loop. a. Use quantitative force diagrams to determine the size of the force on the rider by the seat at the top and bottom of the loop. 221000(8)12,8005.012,80010,0002,800msnetnetNgNNkgmvFNrmFFFNFFNb. Now suppose the rollercoaster had been designed with the small 5 meter radius at the bottom and the large 10 meter radius at the top. Use quantitative force diagrams to determine the size of the force on the rider by the seat at the top and bottom of the loop. 221000(22)96,800596,80010,000107,000msnetnetNgNNkgmvFNrmFFFNFNFN221000(8)6,400106,40010,0003,600msnetnetNgNNkgmvFNrmFFFNFFN c. Why is the clothoid shape used in rollercoasters? As can be seen in part b. the radius of curvature at the top must be small enough that the net force is larger than the force of gravity. If not, the rollercoaster won't make it over the top. Also if the radius of curvature is too small at the bottom the upward force on the person can be more than they can tolerate. In the example, the force is almost 11 times the body weight. 221000(10)100001000(22)48400104840010,00058,000NgkgmsnetnetNgNNFmgkgNkgmvFNrmFFFNFNFNFN= 58,000N Fg= 10,000N FN= 2,800N Fg= 10,000N FN= 107,000N Fg= 10,000N FN= 3,600N Fg= 10,000N r1 r2

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