Answer:
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
[tex]W_c = 4.54 * 750 * 8.81 = 33443.2 N[/tex]
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
[tex]W_c * s_c = 33443.2 * 114.33 = 3823534.5 J[/tex]
Similarly the work required to pull up 204.5 kg of coal up 228.66 m is
[tex]Mgs = 204.5*9.81*228.66 = 458725 J[/tex]
The total work is 3823534.5 + 458725 = 4282260 J or 4.3 MJ
