Answer:
a) 68.125 KW
b) 43.04 KW
Explanation:
Distance =d= 1 km
Height = h = 200 m
Spacing between chairs =D= 20 m
No. of people per chair = 3
Speed = V= 10 km/h= 10000m\3600 s=2.8 m/s
mass of chair = 250 kg
Work to operate sky lift
W= mgh
Number of chairs any moment operational = N= 1 km/20=1000m/20=50
So, total mass of chairs = 50 × 250 =12500kg
so, w= mgh=12500×9.8×200=2452500 j
Power is rate of work - we need time for operation time of lift
Time= t = distance/speedf= 1km/(10km/h)=1km/(10 km/3600s)=360s
So, Power P= Work/time=w/t=12500/360=68125 j/s=68.125 KW
Now calculating power for operating speed in 5 sec
We calculate accelleration=a for 5 sec
a= speed / time= V/52.8/5=0.28 m/sec2
for vertical acceleration we calculate θ angle first;
tanθ= height /distance= 200/1000= 0.2
==> θ=11.34°
Vertical acceleration = a₁=a sinθ= 0.28× sin 11.34=0.10835 m/sec2
to calculate height gained during startup use;
S=vit+1/2at2
here s=H
vi=0m/s
t=5 sec
==> H = 0+1/2a₁×t=0.5×0.10835 ×5²=0.5×0.10835×5×5=1.362 m
Total Work =mgH+0.5×m×V²=12500(9.8×1.362+0.5×2.8×2.8)=215240.56 j
Again power = work / time=215240.56/5=43048.112 W=43.04 KW
