Final answer:
The total work done lifting 1200lb of coal and 600ft of cable up a mine shaft is 1350000ft-lb.
Step-by-step explanation:
In physics, the magnitude of work is defined as the force applied multiplied by the distance moved, expressed by the formula
W = Fd
. For this problem, where a cable is lifting coal up a mine shaft, there's work being done twice. First, the work is done in lifting the 1200lb of coal 600ft. This work,
W1
, is calculated by the weight of the coal times the distance,
W1 = Fd = (1200lb)(600ft) = 720000ft-lb
. Secondly, the weight of the cable must also be considered, but this changes as the coal is lifted because less cable is being lifted as it rises. This work,
W2
, is the integral from 0 to 600 of the weight of the cable per foot times the distance left to lift, which calculates to
W2 = 600^2/2 * 3.5lb/ft = 630000ft-lb
. Summing these two works give the total work done:
W = W1 + W2 = 720000ft-lb + 630000ft-lb = 1350000ft-lb
.
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