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I am currently studying IGCSE Physics, and have the following question: Why aren't upthrust and normal reaction force not the same.

I understand that upthrust only occurs in fluids, and normal reaction forces only occur on a surface, but what is the actual, theoretical difference?

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At the beginning I found this question a bit naive. But now I think it is worth to think a little bit about it.

They definitely share some properties, at least at the microscopic level. Both have the same microscopic origin: the electromagnetic interaction. The upthrust requires gravity to create a pressure gradient on the fluid, resulting in an upwards net force. The normal force that a surface does on a body resting on it also has gravity as a "trigger", though this is not always required. If someone presses the body against the surface then the correspondent parcel of the normal force has nothing to do with gravity.

From the macroscopic point of view they are quite different. The upthrust has always the direction of the pressure gradient. The direction of the normal force can be any, defined by the normal to the surface. The upthrust on a (completely immersed) body of volume $V$ depends only on its volume and the density of the agent (fluid). The normal force acting on the same body when resting over a surface depend on its mass instead and does not depend on physical properties of the agent (surfaces).

I think this is enough to see differences and similarities.

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  • $\begingroup$ Thanks for this great answer! I could, slightly, see how people can see this question as a little naive, as I am a GCSE student, but thanks for looking outside of the box. $\endgroup$ – Annabelle Sykes May 5 '16 at 22:21
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To some extent I agree with @diracology : The question does at first seem naive, but on reflection it is insightful. And there are similarities at the microscopic level, in that both are contact forces which originate from the same electromagnetic repulsion between the outer electrons of atoms or molecules which are forced together. However, I am not convinced that

From the macroscopic point of view they are quite different.

  1. Both are contact forces arising at the interface between two bodies. In the fluid this interface might be irregular, and it completely surrounds a submerged object. For a solid it is usually a single flat surface - but it can be a collection of surfaces, which do not need to be flat or regular, and which can surround the object.

  2. Both forces are the resultant (sum) of all microscopic contact forces, summed over the area of contact. In the case of upthrust there is a convenient way of doing this, thanks to Archimedes' Principle, because the fluid is homogeneous. However, if there are several solid contact surfaces, we don't usually combine the normal forces into one.

  3. Upthrust occurs at a fluid-solid interface whereas normal reaction occurs at a solid-solid surface. However, it is possible to generate the same fluid-like phenomenon of upthrust by immersing a solid object in sand or small beads and agitating them to simulate the pressure of atoms. With sufficient vibration to reduce the density of the artificial fluid and allow the sand/bead particles to move around the solid object, the object will float or sink. (This also happens in quicksand : struggle and you will sink, but lie still and you can rest on the surface.)

  4. The opposite can also happen : a fluid can behave like a solid. For example : cornstarch and water (known in the USA as 'Oobleck'), and silly putty. On short time-scales they behave like solids, retain their shape and exert normal forces. But given sufficient time they flow, take the shape of the container and provide upthrust on immersed or floating objects.

  5. That upthrust requires gravity (in order to create a pressure gradient) is not strictly true. The pressure gradient can be created otherwise, eg in a centrifuge. Gravity comes into it only by defining which direction is "up". Normal force does not require gravity either : it arises also from a collision, or a human push.

  6. Both forces (fluid pressure and normal reaction) are always normal to the interface. But that is because it is how we define them. Solid surfaces can withstand tangential contact forces which we classify as solid friction. Real fluids can also exert tangential forces (viscous drag) as well as other normal forces (lift, compression).

  7. All of these forces originate from the same electronic repulsion between atoms or molecules. It is for our own convenience that we divide them or their components into categories such as upthrust, normal force, friction, lift, drag, etc.

Conclusion : On the atomic scale the force is essentially the same (in origin at least). On the macroscopic scale also there are many more similarities than differences.

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