Answer:
2275000 lb.ft
Explanation:
Let work done on the cable be denoted by: W_ca
Let work done on the coal be denoted by: W_co
Now, dividing the cable into segments, let x represent the length from top of the mine shaft to the segment.
Meanwhile let δx be the length of the segment.
We are told the cable weighs 8 lb/ft. Thus;
Work done on one segment = 8 × δx × x = 8x•δx
Therefore, work done on cable is;
W_ca = ∫8x•δx between the boundaries of 0 and 650
Thus;
W_ca = 4x² between the boundaries of 0 and 650
W_ca = 4(650²) - 4(0²)
W_ca = 1,690,000 lb.ft
Workdone on the 900 lb of coal will be calculated as;
W_co = 900 × 650
W_co = 585000 lb.ft
Thus,
Total work done = W_ca + W_co
Total workdone = 1690000 + 585000
Total workdone = 1690000 + 585000
Total workdone = 2275000 lb.ft
