At what minimum speed must a roller coaster be traveling when upside down at the top of a circle (Fig. 5–34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m.

Figure 5–34

Solution 13P:

Step 1 of 2:-

Here we have to find the minimum speed required for the roller coaster, so that the passengers will not fall out at the top of the circle.

At the top, the normal force will act downwards.

There is already one force downwards by the weight of the passenger.

So, the force equation can be written as,

------------------(1)

But the passengers will feel a centrifugal force which is radially outwards and equal in nagnitude with the centripetal force.

So, equation (1) can be written as,

.

---------------------(2)