Jum Print Calculator uestion 8 of 17 Map do Sapling Learning macmilan laarning Y

Question

Jum Print Calculator uestion 8 of 17 Map do Sapling Learning macmilan laarning 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 13.1 m/s at the top of the incline, which is 39.1 m above the ground. As any good neer would, you begin your design with safety in mind. Your local ent's safety regulations state that the riders' centripetal acceleration should be no more than n 1.89 g at the top of the hump and no efiects af fiction anq ar the bathom of the loop. For this initial phase of your design. you decide to ignore the What is the minimum radius you can use for the semi-circular hump? What is the minimum radius you can use for the vertical loop? Number Number hump loop in 39.1 m Rloap figure not to scale O Previous Gve Up & View Solulion 0 Check Answer 0 Next Exit about us |careers privacy policy terms of use contact us Hint

Explanation / Answer

At the top, the train has energy E = PE + KE = mgh + ½mv²
E = M * 9.8m/s² * 39.1m + ½ * M * (13.1m/s)² = M * 469m²/s²
(I'm going to drop units for ease of typing -- all units are "standard".)

At the top of the hump, the radius is r and the energy is
E = 469*M = M * 9.8 * r + ½Mv²
469 = 9.8r + v²/2
v² = 938 - 19.6r
The constraint is a = 1.89 * 9.8 = 18.5,
and recall a = v² / r = (938 - 19.6r) / r = 18.5
38r = 938
r = 24.6 m

At the bottom of the loop, E = 469M = ½Mv²
v² = 938
a = 5.61 * 9.8 = 55 = v² / r = 938 / r
r = 17.1 m

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