The roller coaster car having a mass m is released from rest

The roller coaster car having a mass m is released from rest at point A. If the track is to be designed so that the car does not leave it at B, determine the required height h using the work-energy method or the conservation of energy method. Also, find the speed of the car when it reaches point C. Neglect friction.

Solution

Here ,

at the point B ,

let the speed of the car at B is v

Now ,as

m * v^2/r = m * g

v^2/7.5 = 9.8

v = 8.57 m/s

Now , for the height h

Using conservation of energy

m * g * (h - 20) = 0.5 * m * v^2

9.8 * (h - 20) = 0.5 * 8.57^2

h = 23.75 m

the height h is 23.75 m

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let the speed of car is vc

using conservation of energy

0.5 * m * v^2 = m * g * h

0.5 * v^2 = 9.8 * 23.75

v = 21.6 m/s

the speed of car at the point C is 21.6 m/s