An electric elevator with a motor at the top has a cable weighing 4.5 pounds per foot. When the car is at the first floor, 180 feet of cable are out, and effectively 0 feet are out when the car is at the top floor. The elevator car itself weighs 2000 pounds when empty   a) Find the work done by the motor lifting just the empty elevator car from the first floor to the top floor, ignoring the cable. b) Find the work done by the motor lifting just the cable from the first floor to the top floor. Keep in mind, that the cable gets shorter and must therefore get lighter as the elevator goes up.

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