What is the danger level of riders flying off a Ferris wheel with a radius of 8 m and a velocity of 8 m/s?

To determine the danger level of riders flying off a Ferris wheel, we need to consider the concepts of centripetal force and gravitational force. In particular, we can analyze whether the gravitational force acting on the riders is sufficient to keep them safely in their seats while the Ferris wheel is in motion.

The first step is to calculate the centripetal acceleration required to keep the riders moving in a circular path. This acceleration can be obtained from the formula:

[ a_c = \frac{v^2}{r} ]

where ( v ) is the velocity and ( r ) is the radius of the Ferris wheel.

Given that the radius ( r ) is 8 m and the velocity ( v ) is 8 m/s, we calculate:

[ a_c = \frac{(8 , \text{m/s})^2}{8 , \text{m}} = \frac{64 , \text{m}^2/\text{s}^2}{8 , \text{m}} = 8 , \text{m/s}^2 ]

Next, we compare this centripetal acceleration to the acceleration due to gravity, which is approximately (