Final answer:
The work done by a person weighing 109 lb rising 17 ft after one revolution on a spiral staircase is calculated using potential energy and is approximately 2513.66 Joules.
Step-by-step explanation:
To find the work done by a person weighing 109 lb (which is approximately 49.44 kg) walking up a spiral staircase, we use the concept of gravitational potential energy (PEg). The formula for potential energy is PEg = mgh, where m is the mass in kilograms, g is the acceleration due to gravity, and h is the height in meters. Since the weight is given in pounds, we first convert it to kilograms by dividing by 2.205 (1 kg = 2.205 lb).
In this scenario, the height (h) the person rises is 17 ft, which we convert to meters by multiplying by 0.3048 (1 ft = 0.3048 m).
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- Convert the weight to mass: 109 lb / 2.205 ≈ 49.44 kg.
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- Convert the rise in height to meters: 17 ft * 0.3048 ≈ 5.18 m.
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- Use the value of g = 9.8 m/s2.
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- Calculate the work: Work = mass * g * height = 49.44 kg * 9.8 m/s2 * 5.18 m ≈ 2513.66 Joules.
Thus, the work done by the person is approximately 2513.66 Joules.