Solving the Ferris Wheel Problem: Estimating Work Requirement

[jonlevi68]

I've been thinking about this problem for the last half hour, but can't seem to come up with a way of finding a solution. Maybe some of you can help.

"George Washington Gale Ferris. Jr., a civil engineering graduate from RPI, built the original Ferris wheel. The wheel carried 36 wooden cars, each holding up to 60 passengers, around a circle 76m in diameter. The cars were loaded 6 at a time, and once all 36 cars were full, the wheel made a complete rotation at constant angular speed in about 2 min. Estimate the amount fo work that was required of the machinery to rotate the passengers alone."

I approached this problems through two methods:

1) W = (1/2)(I)(wf^2 - wi^2), where I is the inertia, wf is the final angular velocity and wi is the initial angular velocity, and

2) W = t(thetaf - thetai), where t is the torque, thetaf is the final angle and thetai is the initial angle.

But both attempts give me zero (which, for some reason, doesn't seem liek the right answer). If the ferris wheel is traveling at a constant angular speed, then shouldn't wi = wf, and therefore W = 0? And, if it completes a revolution, shouldn't thetaf = thetai and, also, W = 0?

Thanks for any help.

 

[OlderDan]

I think you need to focus on the loading process. Once the wheel is loaded it should be finished working. The 2 min ride is work free.

 

[kyle8921]

I can understand your confusion and frustration in trying to solve this problem. However, it's important to remember that in order to accurately estimate the work requirement for the Ferris wheel, we need to consider the forces and energy involved in the rotation of the wheel.

First, let's consider the work-energy theorem, which states that the work done by a force is equal to the change in kinetic energy of an object. In this case, the force is being applied to rotate the Ferris wheel and the object is the wheel itself. So, we can calculate the work done by the machinery by looking at the change in kinetic energy of the wheel.

Next, let's consider the forces acting on the wheel. We have the weight of the passengers and the weight of the wheel itself, which creates a torque that must be overcome by the machinery. This torque is what causes the wheel to rotate.

We also need to consider the frictional forces acting on the wheel, which may decrease the efficiency of the machinery and require more work to be done.

Taking all of these factors into account, we can estimate the work requirement by considering the forces, energy, and efficiency involved in rotating the Ferris wheel. It may also be helpful to break the problem down into smaller components, such as calculating the work required for each rotation of the wheel or for each car as it is loaded and unloaded.

In summary, solving this problem requires a thorough understanding of the forces and energy involved in rotating the Ferris wheel, and breaking it down into smaller components may help in finding a solution. I hope this helps and good luck in finding the solution!