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 a a steady speed of 10 km/h. Neglecting friction and air drag and assuming 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. (steady power = 68.1 kW; start-up = 43.7 kW)
1 answer:
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Answer:
v = 0.42m/s
Explanation:
In order o calculate the linear speed of the point at the border of the wheel, you first take into account that the total acceleration of such a point is given by:
(1)
atotal: total acceleration = 1.2m/s^2
ar: radial acceleration of the wheel
at: tangential acceleration
The tangential acceleration is also given by:
(2)
r: radius of the wheel = (40cm/2 )= 20cm = 0.2m
α: angular acceleration = 4.0rad/s^2
You replace the expression (2) into the expression (1) and solve for the radial acceleration:
Next, you use the following formula for the radial acceleration and solve for the linear speed:
The linear speed of the point at the border of the wheel is 0.42m/s