Question

Find the work done in winding up a 175 ft cable that weighs 3 lb/ft.

Answer 1

Answer:

$work \ done= 45937.5$

Step-by-step explanation:

Work done is given by

$work \ done=\int_a^b w(d-x) \ dx$ , where d = length of cable and w = weight of cable.

Here, d = 175 ft and w = 3 lb/ft

Now, $work \ done=\int_0^{175} 3(175-x) \ dx$

$work \ done= 3\left [175x-\frac{x^2}{2} \right ]_0^{175}$

$work \ done= 3\left [175^2-\frac{175^2}{2} \right ]$

$work \ done= 3\cdot \frac{175^2}{2}$

$work \ done= 45937.5$