An anchor weighing 105 lb in water is attached to a chain weighing 3 lb/ft in water. Find the work done to haul the anchor and chain to the surface of the water from a depth of 35 ft.

The weight of the anchor is 105 lb

The chain weights  3 lb/ft

The length of the chain to be hauled up  be y

Therefore the total work done is 5336 ft-lbs

Explanation:

The weight of the anchor is 105 lb

The chain weights  3 lb/ft

The length of the chain to be hauled up  be y

So the combined weight is

==> (3)(35-y)+100=(205-3y)

Consider a small section of chain of length Δy

The work done by a small section is (205-3y)(Δy)

Total work done to haul up the anchor and the chain can be calculated as

W=∫₀³⁵(205-3y)Δy

  =(175y-3y²/2)²⁵

  =(205(35)-3(35²-0)/2)

  =5336

Therefore the total work done is 5336 ft-lbs