Final answer:
Your apparent weight on a Ferris wheel varies because of the changing support force from the seat, which affects the centripetal force. At the bottom, your apparent weight is greater due to the addition of centripetal and gravitational forces. To feel weightless at the top, the Ferris wheel would need to be rotating fast enough that the centripetal force alone provides the necessary force to keep you moving in a circular path.
Step-by-step explanation:
When you ride on a Ferris wheel, your apparent weight changes due to the varying centripetal force as you move around the wheel. At the top of the wheel, there's only gravitational force acting on you downwards, and the support force from the seat is what provides the centripetal force, making you feel lighter. However, at the bottom of the wheel, both the support force from the seat and the gravitational force are acting downwards, thus the apparent weight is higher.
To calculate your apparent weight at the bottom of the Ferris wheel, we use the following: your real weight (mg), centripetal force (mv²/r), and combine them to get the apparent weight (mg + mv²/r). Given the mass (m) is 60kg, the radius (r) is 7.2m, and that the wheel completes one revolution every 28s (which gives us the velocity (v)), we can plug these into the formula.
For you to feel weightless at the top of the Ferris wheel, the normal force (apparent weight) needs to be zero, meaning the centripetal force must equal the gravitational force (mg = mv²/r). Solving for v and using the circular motion formula (v = 2πr/T), we can find the period (T) - the time it takes for one revolution.