(6%) Problem 15: Modern roller coasters have vertical loops like the one shown i

Question

(6%) Problem 15: Modern roller coasters have vertical loops like the one shown in the figure. The radius of curvature is smaller at the top than on the sides so that the downward centripetal acceleration at the top will be greater than the acceleration due to gravity, keeping the passengers pressed firmly into their seats Otheexpertta.com 33% Part (a) what is the speed of the roller coaster in m/s at the top of the loop if the radius of curvature there is 12 m and the downward acceleration of the car is 1.8 g? Grade Summary Deductions Potential V- 0% 100% sin() Submissions Attempts remaining: Z coso tan( ) acoso ? cotanoasi %per attempt) detailed view atan acotan sinhO cosh cotanho END Degrees Radians DEL CLEAR Submit Hint I give up! Hints: 2% deduction per hint. Hints r Feedback: 2% deduction per feedback. -? 33% Part (b) The beginning of this roller coaster is at the top of a high hill. If it started from rest at the top of this hill how high in meters, above the top of the loop is this initial starting point? You may assume there is no friction anywhere on the track. 33% Part (c) If it actually starts 4.5 m higher than your answer to the previous part yet still reaches the top of the loop with the same velocity, how much energy, in joules, did it lose to friction? Its mass is 1200 kg

Explanation / Answer

a) Fc = N + m g = 1.8 m g

m v2 / R = 1.8 m g

v2 = 1.8 g R = 1.8 * 9.81 * 12.0

v = 14.55 m/s

b) KE of roller coaster = 1/2 m v2 = 0.5 * 14.552 * m = 105.85 m

GPE of roller coaster = m g h = m * 9.81 * 12.0 = 117.7 m

ME of roller coaster = (105.85 + 117.7) m = 223.6 m

m g H = 223.6 m

H = 223.6 / 9.81

= 22.8 m

c) roller coaster loses friction

energy = m g * 4.5 = 1200 * 9.81 * 4.5

= 5.29 * 104 J

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