An electric elevator with a motor at the top has a multistrand cable weighing $6$ lb divided by ft$.$ When the car is at the first$$ floor, $120$ ft of cable are paid$$ 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 to the$$ top?

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Part $1$

The amount of work required is

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enter your response here $$ft$-$lb$.$

$($Simplify your$$ answer.$)$