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Answer :
Final answer:
The work done by the person would be approximately 92.18 ft-lb. This was calculated using the formulas for work and force, applying the given person's weight and the total distance climbed on the spiral staircase.
Explanation:
The work that the person does in climbing the stairs can be calculated using the formula for work which is Work = Force x Distance. In this case, the force is the person's weight and the distance is the height the person climbed on the stairs.
Given the person's weight is 198 lb, and rises 10 feet after one complete revolution, the total height after one and a half revolutions would be 15 feet (10 ft for one revolution and an additional half of the 10 ft for the half revolution). Therefore, the work done can be calculated as follows:
- Convert the person's weight to force. We use the formula: Force = Weight/Gravity, where gravity = 32.2 ft/s^2. So, Force = 198 lb/32.2 ft/s^2 = 6.145 lb.ft/s^2
- Calculate the work done. Work = Force x Distance, therefore, Work = 6.145 lb.ft/s^2 x 15 ft = 92.175 lb.ft^2/s^2, which is approximately 92.18 ft-lb (rounded to two decimal places).
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