A ski-lift has a one-way length of 987 m and a vertical rise of 275 m. The chairs are spaced 21 m apart, and each chair can seat three people. The lift is operating at a steady speed of 14 km/hr. Neglecting friction and air drag and assuming the average mass of each loaded chair is 242 kg, determine the power required to operate this ski lift (a). Also estimate the power required to accelerate this ski lift in 6.4 s to its operating speed when it is first turned on (b).
This is my most recent stab at the solution for part (b), is this the right idea? Can you poke a hole in it or two? I am not even sure that this makes sense. Please note part (a) is correct, but I am having a hard time arriving at a solution for part (b).
The Attempt at a Solution
(a) 987m / 21m =47 chairs * 242 kg= 11,374 kg total
11,374 kg * 9.81 m/s2 * 14 km/hr ((1 m/s) / (3.6 km/hr)) ((1 kJ/kg) / (1000 m2/s2))= 119,237 W / 1000 W/kW= 119.237 kW which is correct per my homework solution.
(b) This is the part I am struggling with, and I know there are a couple of ways to approach it.
1/2 m (V22-V12)*sin(θ) ; Where m=11374 kg, sin(θ)= 275/987, V = 3.8888 m/s
= 23963.5 J / 1000 J/kJ = 23.96 kJ
P= above answer/ the given time to accelerate, so P= 23.96 kJ/6.4 s = 3.74 kW