In 2.0 minutes, a ski lift raises 5 skiers at constant speed to a height of 190 m. The average mass of each skier is 65 kg. What is the average power provided by the tension in the cable pulling the lift?
power=work/time=mg*h/time=5*65*g*190/120
To calculate the average power provided by the tension in the cable pulling the ski lift, we need to use the formula for power:
Power = Work / Time
First, let's calculate the work done by the tension in the cable. The work done is equal to the force exerted by the tension multiplied by the displacement. In this case, the displacement is the height the skiers are lifted, which is 190 m. The force exerted by the tension is equal to the total weight of the skiers being lifted.
The weight of each skier can be calculated using the formula:
Weight = mass * gravitational acceleration
Since the mass of each skier is given as 65 kg and the acceleration due to gravity is approximately 9.8 m/s², we can calculate the weight of each skier:
Weight = 65 kg * 9.8 m/s² = 637 N
The total weight of the 5 skiers being lifted is:
Total Weight = Weight * Number of Skiers = 637 N * 5 = 3185 N
Now we can calculate the work done by the tension:
Work = Force * Displacement = Total Weight * Displacement = 3185 N * 190 m = 604,150 J
Finally, we can calculate the average power provided by the tension using the time given:
Average Power = Work / Time = 604,150 J / (2.0 min * 60 s/min) = 10,069 W (or 10.07 kW)
Therefore, the average power provided by the tension in the cable pulling the ski lift is approximately 10.07 kW.