Archimedes vs Newton?

Question

Lets divide 2 liters of space into two interwoven regions of two equal volumes, and fill the regions with one liter of oil (ρ = 0.9g/ml) and one liter of water.

Force of buoyancy acting on water is equal to the weight of displaced oil, that is 0.9kg.
Force of buoyancy acting on oil is equal to the weight of displaced water, that is 1.0kg.
But according to 3rd law of Newton the two forces must be equal.

Answer 1

Forces only counterbalance if there is no net force in a direction causing a change in position.

In this case - at the time of the initial conditions (the initial conditions being that the oil and water are interwoven) - the forces acting upward on the oil are greater than the forces acting upward on the water (water being denser than oil) - the oil therefore rises - until the net forces on the oil are the same as the net forces on the water. This happens when the oil is floating entirely on the surface. Then for forces on the water equal the weight of the oil and vice versa.

None of the oil is below the surface of the water - so none of the archimedean "weight of displaced water" rules apply. The oil floating entirely above the surface of the water is not the same as an iceberg floating in the water with part of the iceberg being exposed and supported by a force equal to the weight of displaced water.

The weight of the oil acting down on the water is countered by the supporting force of water pushing up on against the oil.

In the "weight of displaced water" problems - the solution is demonstrated by summing the forces acting on all of the parts of the submerged portion of the floating thing. The result, it turns out, is equal to the weight of the displaced volume.

Here - the sum of forces is just the weight of the oil. Surface tensions of the water and or oil may affect the shape of the oil in the water - but all things being equal - the oil would just stay on top of the water.

If you actually put oil on a lake - the oil may stay in one blob - the blob will extend down somewhat into the water - and the top of the blob will be above the water. The weight of the volume of displaced water will equal the weight of the blob.

Answer 2

For equal volume of of fluid the oil is less dense than water.
So the force(weight per unit volume) is less for the oil.
The buoyancy is proportional to the weight of the volume displaced(density),this is Archimedes principle. Therefore the oil would displace less volume of water. That would be less than one liter volume.
The weight pushing down on the water is still equal to the weight pushing up(newton's 3rd law)
Newton's 3rd law of motion states =for every action there is and equal and opposite reaction. That also means to every power applied there is an equal and opposite power reacting. Or to every energy acting there is an equal an opposite energy reacting.

Answer 3

The fluids do not fully displace each other. Oil will float on water so that only 90% of its substance is below the surface of the water, causing the volume of displaced water to have a weight equal to the weight of the oil.

Answer 4

Buoyant force is the force acting upward.

The buoyant force is due to water alone and there is no buoyant force due to oil on water.

Each unit volume of oil experiences a force upward due to the surrounding water.


If you consider a small volume δv of oil δv σ g is the force that the gravity exerts on this oil drop. [σ is the density of the oil]

The buoyant force that acts on this oil drop is δv d g which acts upward. d is the density of water.

Since d is greater than σ, the net force is acting up ward and oil goes up as long as it is surrounded by water.

These two forces are not action reaction pair referred by Newton's third law.

Action reaction pair must be acting on two different bodies.

For the upward buoyant force δv d g which is exerted by water on oil drop there is a corresponding reaction force = δv d g acting on the water which is exerted by the oil.

This force tends to make the water down ward.

For the force δv σ g which is exerted by gravity there is a corresponding upward reaction force acting on the earth.

Think of the displacement of water which cannot happen unless a force acts on it.

However in this case it is proper to consier the pressure rather than force.

Answer 5

Newton would win, he was much younger than Archimedes.

Answer 6

so the oil would float.