I have this half correct, but the other half is still wrong. Please help! You ar

Question

I have this half correct, but the other half is still wrong. Please help!

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 15.5 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's safety regulations state that the riders' centripetal acceleration should be no more than n 1.73 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? htootus you can use for the vertical loop? Number Number R, 131.5 Inn RIND = 11 17.66 ITm im hump 37.5 m Rloop ere is a hint available! the hint by clicking on the m divider bar. Click on the er bar again to hide the hint Rrump figure not to sca

Explanation / Answer

given,

initial speed of the roller coaster = 15.5 m/s

height of the incline = 37.5 m

maximum centripetal acceleration at the top of the hump = 1.73g

maximum centripetal acceleration at the bottom the the loop = 5.53g

centripetal acceleration = v^2 / r

so,

v^2 = centripetal acceleration * r

by conservation of energy

initial energy = final energy

m * g * 37.5 + 0.5 * m * 15.5^2 = m * g * Rhump + 0.5 * m ^ v^2

m * g * 37.5 + 0.5 * m * 15.5^2 = m * g * Rhump + 0.5 * m ^ centripetal acceleration * r

g * 37.5 + 0.5 * 15.5^2 = g * Rhump + 0.5 * 1.73 * g * Rhump

Rhump = 26.6797 m

again,

by conservation of energy

m * g * 37.5 + 0.5 * m * 15.5^2 = 0.5 * m ^ v^2

g * 37.5 + 0.5 * 15.5^2 = 0.5 * m ^ centripetal acceleration * Rloop

g * 37.5 + 0.5 * 15.5^2 = 0.5 * 5.53 * g * Rloop

Rloop = 17.99 m

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