0/100 Calculator 17 11:00 PM Periodic Table Print 5 of 16 pling Learning You are

Question

0/100 Calculator 17 11:00 PM Periodic Table Print 5 of 16 pling Learning 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 incline, which is 38.7 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 1.77 g at the top of the hump and no more than N 5.29 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. 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 laap 38.7 m Rloop figure not to scale O Previous Give Up & View Solution Hint Check Answer 0 Next Ert

Explanation / Answer

here,

initial speed , u = 16.1 m/s

initial height , h0 = 38.7 m

a)

for hump

let the radius be r

using conservation of energy

0.5 * m * v^2 + m * g * R = 0.5 * m * u^2 + m * g * h

0.5 * v^2 + 9.81 * R = 0.5 * 16.1^2 + 9.81 * 38.7 ....(1)

and

centripital accelration , a = v^2 /R

1.77 * 9.81 = v^2 /R ...(2)

from (1) and (2)

R = 27.5 m

b)

for loop

let the radius be r

using conservation of energy

0.5 * m * v^2 + m * g * R = 0.5 * m * u^2 + m * g * h

0.5 * v^2 + 9.81 * R = 0.5 * 16.1^2 + 9.81 * 38.7 ....(1)

and

centripital accelration , a = v^2 /R

5.29 * 9.81 = v^2 /R ...(2)

from (1) and (2)

R = 14.2 m

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