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 14.9 m/s at the top of the incline, which is 35.5 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 1.85 g at the top of the hump and no more than N 5.37 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. eend ar hcmthe loop.For this ia phase of yöur design. you decide to 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 Rhump Im im loop 35.5 m Rloop figure not to scale

Explanation / Answer

By Conservation of energy

mgh +(1/2)mVi2=mgRhump +(1/2)mVf2

9.81*35.5 +(1/2)*14.92 =9.81*Rhump +(1/2)(1.85*9.81*Rhump)

SInce a=V2/r =>V2=ar =1.85*9.81*r

Rhump=24.32 m

b)

By Conservation of energy

mgh +(1/2)mVi2=mgRloop +(1/2)mVf2

9.81*35.5 +(1/2)*14.92 =0 +(1/2)(5.37*9.81*RLoop)

SInce a=V2/r =>V2=ar =1.85*9.81*r

Rloop=17.44 m

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