# Amount of work

• Oct 12th 2008, 05:36 PM
amiv4
Amount of work
An anchor weighing 100 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
• Oct 12th 2008, 06:05 PM
Jhevon
Quote:

Originally Posted by amiv4
An anchor weighing 100 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

again, as i said in your last thread, the work here is going to be $W = \int_0^{35} F(x)~dx$.

so we need to find $F(x)$.

Hint:

there is a constant force of 100lb being hauled.

there is also a variable force at play, that is, the weight of the chain. as we lift some of the chain, the force decreases, as we have to lift less weight. the chain weighs 3lb/ft, so for every foot we pull, we have 3lb less force to haul.

let x be the distance we already hauled it
• Oct 12th 2008, 06:10 PM
amiv4
so F(x) = 100 - 3x dx
?????
• Oct 12th 2008, 06:22 PM
Jhevon
Quote:

Originally Posted by amiv4
so F(x) = 100 - 3x dx
?????

nope. remember, there is a constant force of 100lb

now, in addition, there is a 35ft cable, that weighs 3lb/ft. it is the force from this cable that is decreasing.

also, another tip, it helps to draw a diagram
• Oct 12th 2008, 06:57 PM
amiv4
k how bout 100 - 3x/35