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October 22, 2014

October 22, 2014

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

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 7:05amThis 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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