Question

in 2.11 minutes, a ski lift raises four skiers at constant speed to a height of 124 m. the average mass of each skier is 63.2 kg. what is the average power provided by the tension in the cable pulling the lift?

Explanation:

Step1: Calculate the total mass of the skiers

The total mass \(m\) of the four skiers is \(m = 4\times63.2\space kg=252.8\space kg\)

Step2: Calculate the work done

The work done \(W\) in lifting the skiers is equal to the change in gravitational potential energy. Using the formula \(W = mgh\), where \(g = 9.8\space m/s^{2}\) and \(h=124\space m\).
\(W=252.8\times9.8\times124\)
\(W = 252.8\times1215.2\)
\(W=307302.56\space J\)

Step3: Convert the time to seconds

The time \(t = 2.11\) minutes. Since \(1\) minute \(= 60\) seconds, \(t=2.11\times60 = 126.6\space s\)

Step4: Calculate the average power

The average power \(P\) is given by the formula \(P=\frac{W}{t}\)
\(P=\frac{307302.56}{126.6}\)
\(P\approx2427.35\space W\)

Answer:

\(2427\space W\)