Is Newton's 3rd law sufficient to explain buoyancy force?

[PhysicsNowApple]

I assigned a question: Explain the physics mechanism that results in the buoyancy force.

Some students replied: The floating object is interacting with the water. Therefore it exerts a downward force on the water. The water then exerts an upward force on the object due to Newton's Third Law. This force balances the weight of the object. I was looking for the standard: variable depth pressure causes a pressure differential that results in the buoyancy force.

Now I feel that their explanation is not sufficient but I was wondering how to go about addressing their answer because I feel like if I am not careful I might obfuscate their understanding of Newton's 3rd Law.Thank you,

 

[anorlunda]

Wikipedia has a good article on buoyancy forces. https://en.wikipedia.org/wiki/Buoyancy Read that first and then if you still have questions, come back here.

 

[Orodruin]

The 3rd law just states that the force of the water on the object is the negative of the force of the object on the water. To actually explain buoyancy you need the pressure differential, which in turn results from assuming a hydrostatic situation in a gravitational field.

 

[PhysicsNowApple]

The 3rd law just states that the force of the water on the object is the negative of the force of the object on the water. To actually explain buoyancy you need the pressure differential, which in turn results from assuming a hydrostatic situation in a gravitational field.

Hmmm, so perhaps to address this I should point out that technically the water is exerting a force along all points on the object, so using Newton's third law I cannot find a net force upward. Only by using the pressure differential, do we see that the forces exerted on the top of the object are not as large as the forces exerted on the bottom of the object and then we are able to get a net buoyant force?

 

[anorlunda]

The buoyancy force exerted on a body can now be calculated easily, since the internal pressure of the fluid is known. The force exerted on the body can be calculated by integrating the stress tensor over the surface of the body which is in contact with the fluid:

The surface integral can be transformed into a volume integral with the help of the Gauss theorem:

where V is the measure of the volume in contact with the fluid, that is the volume of the submerged part of the body.

 

[sophiecentaur]

The water then exerts an upward force on the object due to Newton's Third Law.

It is vital not to confuse the idea of third law pairs and Forces in Equilibrium (which is a special case).