11. Calculate the minimum amount of energy necessary for a 1250 kg rollercoaster?

Question

11. Calculate the minimum amount of energy necessary for a 1250 kg rollercoaster to complete a vertical loop, radius of 30 meters, safely for the riders.

12. How tall must the hill leading in to the loop be if the roller coaster has a velocity of 12 m/s at the top of the hill?

Answer 1

11.

F = mg = mv^2/r

(1250)(9.80) = (1250)(v^2)/(30)

v^2 = 294 (I won't take the square root because we need v^2 as it is)

KE = (1/2)mv^2

KE = (1/2)(1250)(294)

KE = 1.83 x 10^5 J


12.

KE = (1/2)(1250)(144) = 9.00 x 10^4 J

9.00 x 10^4 = mgh = (1250)(9.81)h

h = 7.34 m