Consider a circular roller coaster loop of radius 12 m. You already know that if

Question

Consider a circular roller coaster loop of radius 12 m. You already know that if the car starts from a height of 2.5 r at rest, the normal force acting on the car at the top will vanish. Now assume the car starts from a level track, a height of 12 m above the ground. The track first guides the car to ground level and then into the loop. At which initial speed must the car move on the elevated track (height 12 m) such that it still has the required speed at the top of the loop for the normal force to vanish?

Explanation / Answer

initial energy car must have to mahe normal force 0 = mas * g * 2.5 * r

initial energy car must have to mahe normal force 0 = mass * g * 2.5 * 12

if car starts from 12 m height then it also must possess same energy so,

mass * g * 2.5 * 12 = mass * g * h + 0.5 * mass * v^2

9.8 * 2.5 * 12 = 9.8 * 12 + 0.5 * v^2

v = 18.783 m/s

speed needed = 18.783 m/s

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