Suppose you are a roller coaster ride designer and you begin a new design with safety in mind. Safety regulations state that the riders' centripetal acceleration should be no more than n = 1.65g at the top of the hump and no more than N = 5.50g at the bottom of the hoop. Previous sections of the ride give the train a speed of 11.3 m/s at the top of the incline, which is h = 37.5 m above the ground (see figure). Ignoring the effects of friction and air resistance: (a) What is the minimum radius Rhump you can use for the semi-circular hump? (b) What is the minimum radius Rloop you can use for the vertical loop? h R hump R loop
Suppose you are a roller coaster ride designer and you begin a new design with safety in mind. Safety regulations state that the riders' centripetal acceleration should be no more than n = 1.65g at the top of the hump and no more than N = 5.50g at the bottom of the hoop. Previous sections of the ride give the train a speed of 11.3 m/s at the top of the incline, which is h = 37.5 m above the ground (see figure). Ignoring the effects of friction and air resistance: (a) What is the minimum radius Rhump you can use for the semi-circular hump? (b) What is the minimum radius Rloop you can use for the vertical loop? h R hump R loop
Principles of Physics: A Calculus-Based Text
5th Edition
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Raymond A. Serway, John W. Jewett
Chapter5: More Applications Of Newton’s Laws
Section: Chapter Questions
Problem 22P: A roller coaster at the Six Flags Great America amusement park in Gurnee, Illinois, incorporates...
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![Suppose you are a roller coaster ride designer and you begin a new design with safety in mind. Safety regulations
state that the riders' centripetal acceleration should be no more than n = 1.65g at the top of the hump and no
more than N = 5.50g at the bottom of the hoop. Previous sections of the ride give the train a speed of 11.3 m/s
at the top of the incline, which is h = 37.5 m above the ground (see figure). Ignoring the effects of friction and air
resistance:
(a) What is the minimum radius Rhump you can use for the semi-circular hump?
(b) What is the minimum radius Rloop you can use for the vertical loop?
h
R
hump
R loop](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1a523bf4-566d-44e8-913a-10e631b66e94%2Ff433ebee-87db-4fea-aba4-2c7eada69279%2F6ypnjh_processed.png&w=3840&q=75)
Transcribed Image Text:Suppose you are a roller coaster ride designer and you begin a new design with safety in mind. Safety regulations
state that the riders' centripetal acceleration should be no more than n = 1.65g at the top of the hump and no
more than N = 5.50g at the bottom of the hoop. Previous sections of the ride give the train a speed of 11.3 m/s
at the top of the incline, which is h = 37.5 m above the ground (see figure). Ignoring the effects of friction and air
resistance:
(a) What is the minimum radius Rhump you can use for the semi-circular hump?
(b) What is the minimum radius Rloop you can use for the vertical loop?
h
R
hump
R loop
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