What work must be done to lift a stone weighing 10 kg from the bottom of the lake to the surface of the water? The depth of the lake is 3 m, the density of the stone is 2500 kg / m3. Neglect water resistance.
m = 10 kilograms is the mass of a stone lying at the depth of the lake;
h = 3 meters – the depth of the lake;
ro = 2500 kg / m ^ 3 is the density of the stone;
ro1 = 1000 kg / m ^ 3 – water density;
g = 10 N / kg – acceleration of gravity.
It is required to determine the work A (Joule) that needs to be done to raise the stone.
Let’s find the volume of the stone:
V = m / ro = 10/2500 = 0.004 m ^ 3.
Then, the buoyancy force acting on the stone is equal to:
Fa = ro1 * g * V = 1000 * 10 * 0.004 = 40 Newtons.
The weight of a stone in water will be equal to:
P = F gravity – Fa = m * g – Fa = 10 * 10 – 40 = 100 – 40 = 60 Newtons.
To lift a stone, you need to apply to it a force equal to its weight, that is: F = P = 60 Newtons.
Then the work will be equal to:
A = F * h = 60 * 3 = 180 Joules.
Answer: you need to do work equal to 180 Joules.