QuestionMay 29, 2025

In 1.91 minutes a ski lift raises four skiers at constant speed to a height of 124 m. The average mass of each skier is 70.3 kg. What is the average power provided by the tension in the cable pulling the lift?

In 1.91 minutes a ski lift raises four skiers at constant speed to a height of 124 m. The average mass of each skier is 70.3 kg. What is the average power provided by the tension in the cable pulling the lift?
In 1.91 minutes a ski lift raises four skiers at constant speed to a height of 124 m. The average mass of each skier is 70.3 kg. What is the
average power provided by the tension in the cable pulling the lift?

Solution
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Answer

The average power is approximately 2997.5 W (watts). Explanation 1. Calculate Total Mass Total mass m = 4 \times 70.3 \, \text{kg} = 281.2 \, \text{kg}. 2. Calculate Work Done Work done W = m \cdot g \cdot h = 281.2 \, \text{kg} \times 9.8 \, \text{m/s}^2 \times 124 \, \text{m}. 3. Calculate Time in Seconds Time t = 1.91 \, \text{minutes} \times 60 \, \text{s/min} = 114.6 \, \text{s}. 4. Calculate Average Power **Power** P = \frac{W}{t}.

Explanation

1. Calculate Total Mass<br /> Total mass $m = 4 \times 70.3 \, \text{kg} = 281.2 \, \text{kg}$.<br /><br />2. Calculate Work Done<br /> Work done $W = m \cdot g \cdot h = 281.2 \, \text{kg} \times 9.8 \, \text{m/s}^2 \times 124 \, \text{m}$.<br /><br />3. Calculate Time in Seconds<br /> Time $t = 1.91 \, \text{minutes} \times 60 \, \text{s/min} = 114.6 \, \text{s}$.<br /><br />4. Calculate Average Power<br /> **Power** $P = \frac{W}{t}$.
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