Sapling Learning You are designing the section of a roller coaster ride shown in

Question

Sapling 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 11.3 m/satthet of the incline, whichs36.3m above the gr und. As any good engineer would, you begin your desigri with safety in mind. Your local that the riders nt's safety regulations state petal acceleration should be no more than n = 1.57 g at the top of the hump and no etfects oficon ang ai thes botom of the loop. For this initial phase of yõur design. you decide to ignore the What is the minimum radius you can use for the semi-circular hump? at is the minimum radius you can se for the vertical loop?m Number Number R oop 36.3 m Rloop figure not to scale Hint

Explanation / Answer

given
v = 11.3 m/s
h = 36.3 m
n = 1.75 g ( centripital acceleration) at top of hump
n = 5.21g at the bottom of the hoop

minimum radius of hump Rh
minimum radius of hoop = R

hence
speed at bottom of track = u
0.5mu^2 = 0.5mv^2 + mgh
u = 28.980959 m/s

hence
centripitalacceleration
u^2/Rh < 1.75g
Rh > 48.92360 m

and for the hoop
u^2/R > 5.21g
R > 16.4319850 m

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