A cable that weighs 10 lb/ft is used to lift 450 lb of coal up a mine shaft 750 ft deep. Find the work done.

4.3 MJ

Explanation:

Metric unit conversion

10 lb/ft = 10 lb/ft * (1/2.2) kg/lb = 4.54 kg/ft

450 lb = 450 lb * (1/2.2) kg/lb = 204.5 kg

750 ft = 750 * (1/3.28) m/ft = 228.66 m

Let g = 9.81 m/s2

weight of the cable is its mass per length times its length times g

Assume uniform weight, then the center of mass of the cable is in the half the length, the work required to pull 33443.2N cable up 228.66/2 = 114.33 m is

Similarly the work required to pull up 204.5 kg of coal up 228.66 m is

The total work is 3823534.5  + 458725 = 4282260 J or 4.3 MJ

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