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Modern roller coasters have vertical loops like the one shown in the figure. The radius of curvature is smaller at the top than on the sides so that downward centripetal acceleration at the top will be greater than the acceleration due to gravity, keeping the passenger pressed firmly on the seat. What is the speed of the roller coaster at the top of the loop if the radius of curvature there is 15.0m and the downward acceleration of the car is 1.50g?

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Sagar Yadav
Sagar YadavLv10
11 Nov 2020

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Related textbook solutions

Physics: Principles with Applications
7th Edition, 2013
Giancoli
ISBN: 9780321625922

Related questions

Modern roller coasters have vertical loops like the one shown in Figure 6.38. The radius of curvature is smaller at the top than on the sides so that the downward centripetal acceleration at the top will be greater than the acceleration due to gravity, keeping the passengers pressed firmly into their seats. What is the speed of the roller coaster at the top of the loop if the radius of curvature there is 15.0 m and the downward acceleration of the car is 1.50 g?
 
 
Figure 6.38. Teardrop-shaped loops are used in the latest roller coasters so that the radius of curvature gradually decreases to a minimum at the top. This means that the centripetal acceleration builds from zero to a maximum at the top and gradually decreases again. A circular loop would cause a jolting change in acceleration at entry, a disadvantage discovered long ago in railroad curve design.

Modern roller coasters have vertical loops like the one shown in Figure 6.38. The radius of curvature is smaller at the top than on the sides so that the downward centripetal acceleration at the top will be greater than the acceleration due to gravity, keeping the passengers pressed firmly into their seats. What is the speed of the roller coaster at the top loop if the radius of curvature there is 15.0 m and the downward acceleration of the car is 1.50 g?

Figure 6.38 Teardrop-shaped loops are used in the latest roller coasters so that the radius of curvature gradually decreases to a minimum at the top. This means that the centripetal acceleration builds from zero to a maximum at the top and gradually decreases again. A circular loop would cause a jolting change in acceleration at entry, a disadvantage discovered long ago in railroad curve design. With a small radius of curvature at the top, the centripetal acceleration can more easily be kept greater than g so that the passengers do not lose contact with their seats nor do they need seat belts to keep them in place. 

 

A roller coaster at six flags incorporates some clever designs. Each vertical loop instead of circular is teardrop shaped. The speeds are fast enough to be safe. The biggest loop is 40m high. Suppose the speed at the top of the loop is 13m/s and the corresponding centripetal acceleration of the riders is 2g. a) what is the radius of the arc of the teardrop at the top. b) if the total mass of a car plus the riders is M, what force does the rail exert on the car at the top? c) supposed the roller coaster had a circular loop of radius 20.0m. If the cars have the same speed, 13m/s at the top, what is the centripetal acceleration of the riders at the top? d) comment on the force force at the top in the situation described in part c and on the advantage of having teardrop shaped loops.

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