Each hour, a traditional double-seat chairlift can move 1200 people, having an average mass of 60.0 kg, up a ski hill. A high-speed quad chair can move 2400 people in 30.0 minutes up the hill. The upper terminal is 100 m higher than the lower terminal.
a. How much power would the traditional double-seat chairlift need to overcome the force of gravity?
b. How much power would the high-speed quad chairlift need to overcome the force of gravity?

Question

Each hour, a traditional double-seat chairlift can move 1200 people, having an average mass of 60.0 kg, up a ski hill.  A high-speed quad chair can move 2400 people in 30.0 minutes up the hill.  The upper terminal is 100 m higher than the lower terminal.
a.	How much power would the traditional double-seat chairlift need to overcome the force of gravity?
b.	How much power would the high-speed quad chairlift need to overcome the force of gravity?

anonymous · Answer

1st chairlift:- 
The work done = gain in PE 
=>W = mgh 
=>W = 1200 x 60 x 9.8 x 100 = 70560000 J in one hour 
=>Power(P) = Work done/sec = 70560000/3600 = 19600 Watt = 19.6 kW 
2nd chairlift:- 
The work done = gain in PE 
=>W = mgh 
=>W = 2400 x 60 x 9.8 x 100 = 141120000 J in 30 minutes 
=>Power(P) = Work done/sec = 141120000/(30 x 60) = 78400 Watt = 78.4 kW 
In second case the mass is increased=>More PE to be gained=>More work, secondly the time to do the required work is reduced=>More Power is required