Answer :
A person who weighs 151 lb is walking exactly half a revolution up a circular spiral staircase of a radius of 5ft. The work that has been done by the person is 1203.4 ft-lbf.
The energy that the person is putting into the staircase is the work done by the person.
The staircase has a total length of L = 2πrh = 2π(5)(0.5) = 15.71 ft and a height of h = 0.5(2πr) = 15.71/2 = 7.86ft.
The angle subtended by a half-revolution is 2π.
Therefore, the angular displacement of the staircase is 2π/2 = π rad.
Hence, the work done by the person is:
W = mgh where m is the mass of the person, g is the acceleration due to gravity and h is the height of the staircase. First, the mass of the person is obtained by dividing the weight by the acceleration due to gravity.
m = 151/32.2 = 4.69 slug.
Then, the work done by the person is
W = (4.69)(32.2)(7.86) = 1203.4 ft-lbf.
The work done by the person is 1203.4 ft-lbf.
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