You are designing the section of a roller coaster ride shown in the figure. Prev

Question

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 15.5 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 government's safety regulations state that the riders' centripetal acceleration should be no more than n 1.61 g at the top of the hump and no effects ffcion a7d at the botom of the loop. For this initial phase of your design, you decide to ignore the What is the minimum radius you can What is the minimum radius you can use for the vertical loop? use for the semi-circular hump? Number Number in leop 39.1 m Rloop Rhmp figure not to scale O Previous Check Answer 0 NextExit- Hint

Explanation / Answer

here,

initial speed , u0 = 15.5 m/s

h0 = 39.1 m

for hump

let the speed at the top of hump be v

using conservation of energy

0.5 * m * v^2 = 0.5 * m * u^2 + m * g * (h0 - r)

v = sqrt(15.5^2 + 2 * 9.81 * (39.1 - r) ....(1)

and

centripital accelrationa = v^2 /r = 1.61 g

(15.5^2 + 2 * 9.81 * (39.1 - r) = r * 1.61 * 9.81  

soloving for r

r = 28.4 m

for loop

let the speed at the bottom of loop be v

using conservation of energy

0.5 * m * v^2 = 0.5 * m * u^2 + m * g * (h0 )

v = sqrt(15.5^2 + 2 * 9.81 * (39.1)

v = 31.7 m/s

and

centripital accelrationa = v^2 /r = 5.37 g

31.7^2 /r = 5.37 * 9.81

soloving for r

r = 19 m

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