Jump to... Print Calculator Periodic Table Question 11 of 14 MapA Sapling Learni

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Jump to... Print Calculator Periodic Table Question 11 of 14 MapA 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 11.9 m/s at the top of the incline, which is 37.5 m above the ground. As any good engineer would, you begin your design with safety in mind. Your local government' that the riders' centripetal acceleration should be no more than n 1.69 g at the top of the more s safety regulations state hump and no 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 37.5 m figure not to scale O Preveus Gwe Up & View Solution Check Answer 0 Next -el Ext Hint 0 888F Fs 44 FT 5 7 8 9 0

Explanation / Answer

let u = 11.9 m/s

h = 37.5 m
let R is the radius of the hump.
let v is the speed of the rooler coaster car at the top of the hump.

v^2 - u^2 = 2*g*(R - h)

v^2 = u^2 + 2*g*(R-h)

and
Force towards the center, F = m*v^2/R

m*a = m*v^2/R

m*1.69*g = m*v^2/R

1.69*g = v^2/R

1.69*g = (u^2 + 2*g*(h-R))/R

1.69*9.8 = (11.9^2 + 2*9.8*(37.5 - R))/R

==> R_hump = 24.2 m <<<<<<<<<---------------------------Answer

at the bottom of the loop,

F = m*g + m*v^2/R

5.53*m*g = m*g + m*v^2/R

5.53*g = g + (u^2 + 2*g*h)/R

5.53*9.8 = 9.8 + (11.9^2 + 2*9.8*37.5)/R

R_loop = 19.7 m <<<<<<<<--------------------------------Answer

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