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## Main Question or Discussion Point

An electric elevator with a motor at the top has a cable weight 4.5 lb/ft. When the car is at the first floor, 198 ft of cable are paid out, and effectively 0 ft are out when the car is at the top floor. How much work does the motor do just lifting the cable when it takes the car from the first floor the to the top?

This is what I've done:

180=4.5k

k=40

force=40x

work = integral from 0 to 180 40x dx

then I took the anti derivative and it was (40x^2)/2 which ends up 20x^2

I then plugged in 180 for x

20(180)^2 = 648000

The correct answer is 72900. Any thoughts?

This is what I've done:

180=4.5k

k=40

force=40x

work = integral from 0 to 180 40x dx

then I took the anti derivative and it was (40x^2)/2 which ends up 20x^2

I then plugged in 180 for x

20(180)^2 = 648000

The correct answer is 72900. Any thoughts?