Question

An elevator is constructed using an electric motor at the top which is used to lift the elevator's car via a cable. The cable weighs 6 pounds per foot. The cable is 100 feet long when the elevator car is at the first floor, and it is effectively 0 feet long when the car is at the top floor. The elevator's car weighs 500 pounds How much work W does the motor do just lifting the cable and car when it takes the car from the first floor to the top floor

Answer 1

80000 lb-ft

Step-by-step explanation:

`mg` = Weight

h = Height

The work done by the car is

`W_(car)=mgh\\\Rightarrow W_(car)=500* 100\\\Rightarrow W_(car)=50000\ lb-ft`

Weight of the cable is 6 pounds per feet

Total weight of cable

`6* 100=600\ lb`

Work done to lift the cable

`W_(cable)=mgh`

`\\\Rightarrow W_(cable)=600* 50`

h = 50 as the CG will be center of the length of the cable

`W_(cable)=30000\ lb-ft`

Total work done by the motor will be the sum of the work done

`W=W_(car)+W_(cable)\\\Rightarrow W=50000+30000\\\Rightarrow W=80000\ lb-ft`

The work done to lift the car and motor is 80000 lb-ft