A classic roller coaster question A classic roller coaster is designed as shown

Question

A classic roller coaster question

A classic roller coaster is designed as shown below. The coaster cars are lifted up the initial lull, which has a height of 85 feet, and released at the top of the hill with a speed of 5 ft/s. The track has a running length of 4200 feet. A fully loaded car has a weight of 4500 lb and friction/wind resistance impose an average force of 62 lb on the coaster car throughout the ride, (a) Determine the speed of the coaster car as it completes the ran (back at ground level after traveling the entire track length), (b) A magnetic brake system is used to slow the car to a speed of 2.5 ft/s at the end of the ride. If this brake applies a force of 14001bs, what length of track is required for the braking system to accomplish this task?

Explanation / Answer

(a)

Initial Energy = 0.5 * 4500 * 5 ^2 + 4500 * 32.2 * 85 = 12.372 * 10^6 lb ft ^2 / sec^2

Final Energy = 0.5 * 4500 * v^2

Initial Enerfy - Final = work done by friction and wind

so , 12.372 * 10^6 - 0.5 * 4500 * v^2 = 62 * 32.2 * 4200

so, v = 42.1 ft / sec

b) Initial speed (u) = 42.1 ft / sec

Final speed (v) = 2.5 ft/sec

retardation (a) = 1400 * 32.2 / 4500 = 10.01778 ft/sec2

v^2 = u^2 - 2*a*x

so, x = 88.1513 ft

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