Estimating Work on the Ferris Wheel: George Washington Gale Ferris Jr.

[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]

Did you post this problem twice? I just replied to the same problem somewhere else.

This is probably where it belongs

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 attempts to solve this problem. However, in this case, both of your approaches are not applicable to finding the work required for the Ferris wheel to rotate the passengers. Let me explain why.

The first method you used, W = (1/2)(I)(wf^2 - wi^2), is used to calculate the rotational kinetic energy of an object. In this case, the Ferris wheel is not a single rotating object, but rather a system of many interconnected parts (such as the cars, the wheel itself, and the machinery). Therefore, this formula cannot be used to accurately estimate the work required for the wheel to rotate the passengers.

The second method you used, W = t(thetaf - thetai), is used to calculate the work done by a torque on an object. While this formula is more applicable to the Ferris wheel, it still cannot be used in this case. This is because the Ferris wheel is not being rotated by a single torque, but rather by multiple torques acting on different parts of the system. Additionally, the angle of rotation (theta) is not constant, as the wheel is constantly rotating and not stopping at a specific angle.

To accurately estimate the work required for the Ferris wheel to rotate the passengers, we would need more information about the specific design and mechanics of the wheel. This would include factors such as the weight of the cars, the friction of the wheel, and the power of the machinery. Without this information, it is not possible to provide an accurate estimation of the work required.

In conclusion, while your attempts to solve this problem are appreciated, they are not applicable in this case. As a scientist, it is important to have all the necessary information and use the appropriate formulas and methods to solve a problem. In this case, we would need more information to accurately estimate the work required for the Ferris wheel to rotate the passengers.