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

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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 36.7 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 = 5.53 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.

A- What is the minimum radius you can use for the semi-circular hump?

B- What is the minimum radius you can use for the vertical loop?

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 36.7 m above the ground. As any good ineer 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- 5.53 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 loop 36.7 m Roop Riu mp figure not to scale Previous Check Answer Next Next 91 Ext nswer

Explanation / Answer

Using conservation of energy between the top most point and the hump, we have

mgh1+0.5mv1^2=mgh2+0.5mv2^2

gh1+0.5v1^2=gh2+0.5v2^2

Taking g=9.8m/s^2, we have

9.8*36.7+0.5*13.1*13.1=9.8*R+0.5v2^2

445.46=9.8R+0.5v2^2---------------------------(i)

Maximum acceleration v2^2/R =1.77g

v2^2=1.77Rg--------------(ii)

Substituting in (i), we have

455.46=27.14R

Rhump=R=16.17m

Similarly for loop we have

455.46=0.5v2^2

and v2^2=5.53gr

rloop=r=16.8m

445.46=

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