How much Force does it take to Break?

In order to answer this question, the #16 Ferris Wheel from Eli Bridge Company will be used as the example.

Preliminary math:
The Ferris Wheel spins at 4.75 rounds per minute. That is 0.0792 Rounds per second or 12.63 seconds per round.
The Ferris Wheel has a diameter of 20.4 m. That is 10.2m in its radius and about 64.09m in its circumference.
The velocity, then is 5.08m/s
The maximum load mass is 3,701kg between 16 seats, or 231.3kg per seat.
The Ferris Wheel without any passenger is 22,000 lbs, which is 9,979 kg.

The Physics:
Since the Ferris Wheel goes around at constant speed, it is an example of Uniform Circular Motion. In uniform circular motion, the acceleration is velocity (v) squared over radius. It is important to note the difference between speed and velocity. The Ferris Wheel is moving at the same speed in a circle, but since the direction the velocity is always changing, it does not have a constant velocity. And at every point, the acceleration, as well as its net force, is towards the center of the wheel.

Let's look at the forces being applied to the cart at the top of the wheel.
Forces on top
Notice that the Normal force (N) is pushing down on the cart, as well as the Force of Gravity. Let's say the positive direction is down towards the center of the circle. And according to the Newton's Second Law, the net force equals the mass multiplied by its acceleration. In this case, the acceleration is the centripetal acceleration pointed to the center.

The Net Force Equation can be written as
Normal force
Notice that the centripetal acceleration is written as the velocity squared over the radius, and what the Normal Force equals to. As the velocity increases, it will go past the gravitational force and start to push against the cart itself. By putting in the recommended specifications for the example Ferris Wheel, with 231.3kg for mass, 5.08m/s as velocity, 10.2m as radius and 9.8m/s^2 as the gravity:

Normal force = -1682.57N,

which explains why someone may feel lighter at the top.

This means that the Ferris Wheel will start to be under strain if more velocity is added. As velocity increases, the Normal force will start to become less negative, and eventually the normal force will be high enough to be working against the steel support. Stress exerted on the steel support can be calculated as Force/Area. And considering the massive size of the support, it can take quiet a while for the steel supports to break, and become deadly.

But does this mean that if the material is strong enough to  withhold moving at amazing speed, you can ride it without worrying about dying? Not exactly...