What work must be done to lift a marble slab weighing 540 kg, lying on the seabed at a depth of 20 m

What work must be done to lift a marble slab weighing 540 kg, lying on the seabed at a depth of 20 m, aboard the ship. Depth above water 3 m. Disregard water resistance.

1) Raise under water
The work is done here against the resultant force of gravity and Archimedes. We must find this power:
F = mg – P0hV = mg – ρ₀gm / ρ = mg (1-ρ₀ / ρ)
Where ro is the density of water, ro is the density of marble (which is 2700).
2) Find a job A
A1 = FS = mgH (1-ρ₀ / ρ)
We raise again above the water, but in this case there is no Archimedes force, therefore: A2 = FS = mgh
3) Looking for a job
A = mgH (1-ρ₀ / ρ) + mgh = 540 * 10 * (20 * (1-1000 / 2700) +3) = 84200
Answer: 84200



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