Question

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.

Answer 1

Step-by-step explanation:

Each chair having mass of 250 kg , separated by 20 m

Total no of chair = 1000 / 20 = 50

Total mass of all chair = 50 x 250 = 12500 kg

Force required to move the chair = mg sinФ where Ф is inclination of lift .

SinФ = 200 / 1000 = .2

Ф = 11.536⁰

Force required to move the chair = mg sin11.53

= 12500 x 9.8 x sin11.53

F = 24485.42 N

velocity of lift = 10 x 1000 / (60 x 60 ) m /s

v = 2.78 m /s

Power required = F v where v is velocity of movement of lift

= 24485.42 x 2.78 W

= 68069.46 W.