Question

George Washington Gale Ferris, Jr., a civil engineering graduate from Rensselaer Polytechnic Institute, built the original Ferris wheel for the 1893 World's Columbian Exposition in Chicago. The wheel, an astounding engineering construction at the time, carried 36 wooden cars, each holding up to 60 passengers, around a circle 76 m 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 of work that was required of the machinery to rotate the passengers alone. Assume each passenger had a mass of 89 kg.

Answer 1

Answer:

$KE = 4217 J$

Explanation:

As we know that the wheel is rotated at constant angular speed

so here we can say that the angular speed is given as

$\omega = \frac{2\pi}{T}$

$\omega = \frac{2\pi}{2 \times 60}$

$\omega = 0.052 rad/s$

now the moment of inertia of all passengers is given as

$I = 36(60)(\frac{76}{2})^2$

$I = 3119040 kg m^2$

now work done by machine must be equal to kinetic energy of the system

so we will have

$KE = \frac{1}{2}I\omega^2$

$KE = \frac{1}{2}(3119040)(0.052)^2$

$KE = 4217 J$