Undergrad Is the Force Applied by an Object on a Fluid Equal to the Buoyant Force?

[UMath1]

If you place an solid object on a fluid, is the force it applies to the fluid equal to the buoyant force? I would have thought that it applies a force equal to its own weight but that would mean that the force applied to the object by the fluid, the buoyant force, would not be equal and opposite to the force the object applies to the fluid unless it has a density equal to the fluid. This would violate Newton's 3rd Law.

So does that mean the force an object applies to a fluid is equal to the buoyant force the fluid applies on it? And how would you physically explain this at the molecular level? This would be mean that as the object sinks it applies more and more force on the fluid. How does this differ from the situation where solid applies a force on a solid surface, like the ground?

 

[jbriggs444]

If you place an solid object on a fluid, is the force it applies to the fluid equal to the buoyant force? I would have thought that it applies a force equal to its own weight but that would mean that the force applied to the object by the fluid, the buoyant force, would not be equal and opposite to the force the object applies to the fluid unless it has a density equal to the fluid. This would violate Newton's 3rd Law.

So does that mean the force an object applies to a fluid is equal to the buoyant force the fluid applies on it? And how would you physically explain this at the molecular level? This would be mean that as the object sinks it applies more and more force on the fluid. How does this differ from the situation where solid applies a force on a solid surface, like the ground?

A solid object that floats on the fluid displaces its own weight in fluid. The upward buoyant force from the fluid and the down force from the object on the fluid are third law pairs and are equal to the weight of the object.

A solid object that sinks will have frictional forces as it sinks and, barring unusual conditions, will keep sinking until it hits the bottom.

 

[UMath1]

Yeah but before the floating solid reaches equilibrium, what force does it apply on the fluid? And what force does the sinking solid apply on the fluid?

 

[Dale]

The contact force exerted by the fluid on the object is called the buoyant force. Per Newton's third law it is equal and opposite to the contact force exerted by the object on the fluid.

The gravitational force exerted by the Earth on the object is called the weight. Per Newton's third law it is equal and opposite to the gravitational force exerted by the object on the Earth.

The weight and the buoyant force are not necessarily related, only in the special case of a floating vessel.

 

[UMath1]

How would you physically explain this at the molecular level? This would be mean that as the object sinks it applies more and more force on the fluid. How does this differ from the situation where solid applies a force on a solid surface, like the ground? What is going on with the molecules of the fluid and the object?

 

[russ_watters]

This would be mean that as the object sinks it applies more and more force on the fluid.

As it accelerates, drag increases, yes.

 

[Dale]

How would you physically explain this at the molecular level? This would be mean that as the object sinks it applies more and more force on the fluid. How does this differ from the situation where solid applies a force on a solid surface, like the ground? What is going on with the molecules of the fluid and the object?

I really dislike these kinds of questions. At a molecular level I would write the wave function for a few quintillion water molecules and the wave function for a similar number of metal atoms. Then I would get million dollar grant from some gullible government agency and build the worlds biggest supercomputer to be able to handle all of those wave functions.

I would use these wave functions to calculate the EM exchange of virtual photons between the metal lattice and the water molecules. In the end I would integrate all of that to come up with the usual result obtained by hand in every introductory physics course.

There is no value in asking about molecules here. This is neither a chemical reaction nor a quantum mechanical phenomenon.

 

[UMath1]

Okay. I was thinking that a visual idea would help me better understand how this works, but as you said perhaps that is not needed. However, I am having trouble understanding conceptually how much force an object applies on another. What is the difference between a hard solid surface and a fluid when it comes to how much force the object applies? Why isn't the object able to apply a force equal to its own weight on the fluid? What causes the force to be applied in the first place?

 

[jbriggs444]

Okay. I was thinking that a visual idea would help me better understand how this works, but as you said perhaps that is not needed. However, I am having trouble understanding conceptually how much force an object applies on another. What is the difference between a hard solid surface and a fluid when it comes to how much force the object applies? Why isn't the object able to apply a force equal to its own weight on the fluid? What causes the force to be applied in the first place?

What do you know about pressure in a fluid and the way that pressure varies with depth?

 

[UMath1]

Pressure in a fluid increases with depth. Pressure occurs due to the force of gravity on the fluid.

 

[Dale]

What is the difference between a hard solid surface and a fluid when it comes to how much force the object applies?

The main difference is in shear stress. In fluids the shear stress is proportional to the shear rate, whereas in solids the shear stress is proportional to the shear strain. This is what leads to a fluid flowing.

However, the buoyant force is due to normal stress rather than shear stress. In a fluid the normal stress is equal to the pressure. In a solid the normal stress is proportional to the normal strain.