What is 'doing the work' when Archimedes' principle is at play? I was watching a documentary about Greece, and at some point they showed a team 'cleaning' the seabed from lost fishing nets that litter some parts of the coast and are a danger to marine animals etc.
To do that, they used a large plastic sheet shaped roughly like a balloon. They dragged it down to the bottom of the sea, hooked the fishing nets to it using (I guess steel) cables, and then they filled the 'balloon' with air.
Once the balloon was sufficiently full of air, it lifted the nets to the surface, where they could be removed. They mentioned these nets can weigh up to 2 tons, if I understood correctly.
Initially I thought, that's clever.
But then it occurred to me: what is actually providing the energy for this to happen? At the end you have lifted 2 tons of stuff up the gravitational field by perhaps 10-50 metres, so that's quite an expenditure of energy.
Surely that's not the same energy that one requires to pump the air into the balloon, is it? You could even take a cylinder of compressed air down with you and just fill it from there.
Any ideas / pointers to other posts or literature describing this?
Thanks!
 A: It would take a great deal of energy to pump the air into the balloon.
The work done against the pressure is $W=P\Delta V$
and the pressure $30m$ down is from
$P=h\rho g$
For a dense object:
with the density of water of 1000kg per cubic metre, it's about $300,000J$ to pump in one cubic metre of air. You'd need 2 cubic metres to provide the upthrust, (from Archimedes principle), for a weight of two tonnes and the work needed is the similar to lifting the weight the same distance in air.
If the object to be lifted had a density only slightly more than water, then it wouldn't need so much air in the balloon and quite a heavy object could be lifted.  This is explained in energy terms as the object gains gravitational potential energy, but water drops into the space that the object left, losing some gravitational energy, so overall conservation of energy would still apply.
A: When the sheet is at the bottom and air is being pumped into the sheet to inflate the balloon the displaced water is "rising" up and so gaining gravitational potential energy which comes from the work done in pumping the air.
When the sheet is moving upwards the nets are gaining gravitational potential energy whilst the water around the balloon is "falling" and losing gravitational potential energy.
