saplinglearning.com ys 220 vy Tech Community College, Central Indiana - PHYS 220

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saplinglearning.com ys 220 vy Tech Community College, Central Indiana - PHYS 220 0BH -Fall17- Jump to College, Central Indiana-PHYS 220 08H -Falli7-RODRIGUEZ> Activities and Due Dates Ch7HW:Energy Ca 10/13/2017 11:55 PM 1.8/6 Print iCaluletor Gradeb Periodic Table estion 6 ol 10 Sapling Learming 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 16.1 m/s at the top of the indline, which is 37.1 m above the ground. As any good engineer would, you begin your design with safety in mind. Your local that the riders' centripetal acceleration should be no more than n 1.57 g at the top of the hump and no more than N 5.45 g at the bottom of the loop. For this initial phase of your design, you decide to ignore the effects of friction and air resistance. ent's safety regulations state 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 rn In gure not to scale Check Answer Next aExit

Explanation / Answer

Initially, E = PE + KE = (M x 9.8 x 37.1) + (0.5 x M x (16.1)2) = M x 493.19 m2/s2

1. At r = Rhump, a = 1.57 x 9.8 = v2 / r

v2 = 15.39 x r

and E = M x 493.19 = Mgr + 0.5 x Mv2

493.19 = 9.8 x r + 0.5 x 15.39 x r = 17.49 r

rhump = 28.19 m

2. At r = Rloop, a = 5.45 x 9.8 = 53.41 m/s2 = v2 / r

v2 = 53.41 x r

E = 493.19 x M = 0.5 x M x 53.41 x r

r = Rloop = 18.47 m

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