Question

At what minimum speed must a roller coaster be travelling when upside down at the top of a circle so that the passengers will not fall out? Assume a radius of curvature of 7.4m.

Answer 1

Given:

The radius of curvature r = 7.4 m.

To find the minimum speed of roller coaster to avoid the passengers' fallout.

Step-by-step explanation:

Two forces act on the roller coaster, centripetal force and force due to gravity.

The condition to avoid passengers' fallout is

`\begin{gathered} centripetal\text{ force = force due to gravity} \\ (mv^2)/(r)=mg \\ v=√(gr) \end{gathered}`

Here, the velocity is denoted by v.

The acceleration due to gravity is g = 9.8 m/s^2.

The radius is denoted by r.

On substituting the values, the velocity will be

`\begin{gathered} v=\text{ }√(9.8*7.4) \\ =8.51\text{ m/s} \end{gathered}`

The minimum speed of the roller coaster will be 8.51 m/s.