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

Section5.3: Nonuniform Circular Motion

Problem 5.5QQ: Which of the following is impossible for a car moving in a circular path? Assume that the car is...

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You are designing the section of a roller coaster ride shown in the figure. Previous sections of the ride give the train a speed of 10.7 m/s at the top of the incline, which is h=37.5 m above the ground. As any good engineer would, you begin your design with safety in mind. Your local government's safety regulations state that the riders' centripetal acceleration should be no more than n=1.73 g at the top of the hump and no more than N=5.45 gat the bottom of the loop. For this initial phase of your design, you decide to ignore the effects of friction and air resistance. (Figure not to scale)What is the minimum radius Rhump you can use for the semi-circular hump?What is the minimum radius Rloop you can use for the vertical loop?
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