Posted by **HELP ASAP** on Monday, May 12, 2014 at 11:01pm.

(i) A 20m chain with a mass-density of 3kg/m (coiled on the ground). How

much work is performed lifting the chain so that it is fully extended (and

one end touches the ground)?

(ii) How much work is performed to lift 1/4 of the chain?

- Calculus -
**MathMate**, Tuesday, May 13, 2014 at 7:05am
This sounds like a physics problem:

Work done = increase in potential energy (PE)

Let

PE at ground = 0

After lifting, the centre of gravity of the chain is at h=10 m above ground, so

potential energy

=mgh

=(3 kg/m * 20m)*9.8 m/s²*10m

= 5880 joules

Using calculus,

Let

ρ = length density = 3 kg/m

x=distance of top of chain from ground in metres

then

length of chain off ground = x

mass of chain off ground = ρx

weight of chain off ground = ρxg

lifting the chain through a distnce dx does work of

ρxg*dx

Total work done through a length of 0 to L metres

=∫ρx;gdx [0,L]

=14.7L²

For L=20m,

Work done = 14.7(20²)=5880 joules

as before.

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