Concept explainers
A ski lift has a one-way length of 1 km and a vertical rise of 200 m. The chairs are spaced 20 m apart, and each chair can seat three people. The lift is operating at a steady speed of 10 km/h. Neglecting friction and air drag and assuming that the average mass of each loaded chair is 250 kg, determine the power required to operate this ski lift. Also estimate the power required to accelerate this ski lift in 5 s to its operating speed when it is first turned on.
The power required to operate the ski lift.
The power required to accelerate the ski lift in 5 s to its operating speed.
Answer to Problem 32P
The power required to operate the ski lift is
The power required to accelerate the ski lift in 5 s to its operating speed is
Explanation of Solution
Calculate the load of the lift at any given time.
Here, number of chairs at any given time is N and weight of each chair is w.
Calculate the work required to raise the mass by 200 m.
Here, acceleration due to gravity is g and difference between the elevation of ski lift is
Write the equation of change in time.
Here, distance is D and velocity is V.
Calculate the power needed.
Calculate the acceleration of the ski lift.
Here, change in velocity is
During the acceleration, calculate the power needed.
Here, the initial and final velocity of a ski lift are
Calculate the vertical distance travelled during the acceleration.
Here, time to accelerate the ski lift to its operating speed is t and angle to raise the ski lift is
Calculate the power needed to acceleate the ski lift in 5 s.
Calculate the total power required to accelerate the ski lift.
Conclusion:
Since the lift is 1 km long and chairs are spaced 20 m apart, calculate the number of chairs at any given time.
Substitute 50 chairs for N and 250 kg/chair for w in Equation (I).
Substitute 12,500 kg for m,
Substitute 1 km for D and 10 km/h for V in Equation (III).
Substitute 360 s for
Thus, the power required to operate the ski lift is
Convert the unit of velocity from km/h to m/s.
Substitute 0 for
Substitute 0 for
Calculate the value of
Substitute
Substitute 1.39 m for h, 5 s for
Substitute 34.1 kW for
Thus, the power required to accelerate the ski lift in 5 s to its operating speed is
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