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

Answer:

80000 lb-ft

Explanation:

$mg$ = Weight

h = Height

The work done by the car is

$W_{car}=mgh\\\Rightarrow W_{car}=500\times 100\\\Rightarrow W_{car}=50000\ lb-ft$

Weight of the cable is 6 pounds per feet

Total weight of cable

$6\times 100=600\ lb$

Work done to lift the cable

$W_{cable}=mgh$

$\\\Rightarrow W_{cable}=600\times 50$

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