George Washington Gale Ferris, Jr., a civil engineering graduate from Rensselaer

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 77 kg.

Explanation / Answer

here,

diameter , d = 76 m

radius , r = 38 m

moment of inertia of the machinary , I = total mass * Radius^2

I = (36 cars* 60passangers * 77kg) * (38 )^2

I = 2.4 * 10^8 kg.m^2

time taken for one rotation(time period), T = 2 min = 120 s

angular speed , w = 2 * pi /T

w = 0.0523 rad/s

the work done required , W = change in kinetic energy

W = 0.5 * I * w^2

W = 0.5 * 2.4 * 10^8 * 0.0523^2

W = 3.29 * 10^5 J

the work done required is 3.29 * 10^5 J

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