Question

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

Answer 1

`work \ done= 45937.5`

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-(x^2)/(2)  \right ]_0^(175)`

`work \ done= 3\left [175^2-(175^2)/(2)  \right ]`

`work \ done= 3\cdot (175^2)/(2)`

`work \ done= 45937.5`