Question

At what minimum speed must a roller coaster be traveling when upside down at the top of a circle so that the passengers do not fall out? Assume a radius of curvature of 7.5

Answer 1

`v_(min) \approx 17.153\,(m)/(s)`

Step-by-step explanation:

The roller coaster begins with maximum kinetic energy and no gravitational potential energy. The gravitational potential energy reaches its maximum when roller coaster is upside down at the top of the circle. The physical model for the roller coaster is constructed by means of the Principle of Energy Conservation:

`(1)/(2)\cdot m \cdot v_(min)^(2) = m\cdot g \cdot h`

The minimum velocity is:

`v_(min) = √(2\cdot g \cdot h)`

Let assume that radio of curvature is measured in meters. Hence:

`v_(min) = \sqrt{2\cdot (9.807\,(m)/(s^(2)) )\cdot(15\,m)}`

`v_(min) \approx 17.153\,(m)/(s)`