When we put a little pin on the surface of water, it floats; is this because of surface tension or buoyancy? Can somebody also draw a force diagram for me to explain how surface tension of water supports an object.
And anybody has any advise for me that I can do any simple experiment to demonstrate water-surface tension?
[Physics] water surface tension and buoyancy
buoyancysurface-tension
Related Solutions
Introduction
That is an interesting subject. Quotation (my emphasis):
sedimentation holds novel surprises [...] showing that a simple external field like gravity may induce mind-boggling, and theoretically challenging effects
from the paper The unbearable heaviness of colloids: facts, surprises, and puzzles in sedimentation.
I strongly suggest taking a look also at this paper, where they experimentally observe "unexpected effects, such as denser particles floating on top of a lighter fluid" in colloidal mixtures and provide a theoretical approach as well.
Notice, in particular, that "particles have settled" doesn't necessarily mean "they rest at the bottom", but rather that there's a vertical gradient of particle density in the fluid.
First question
Yes, using the average density of the (local) mixture is a good approximation and $F$ will be greater; but only if in the equilibrium state particles are still suspended at the float's height. The approximation is then good: a first correction to it would be to consider the effective volume of the float due to the finite size of the suspended particles, which is of course negligible for a big float.
If, on the other hand (and that actually seems to be the configuration you have in mind), by "macroscopic" you mean big enough to truly completely set at the bottom, then the float could not feel it: for only the total depth will have changed and the buoyancy would be unaffected (as it's determined by the pressure difference over the float).
Experiment
The float will therefore present the same or, if the dust is fine enough, slightly increased buoyancy. But the net result depends on what
once the cloud of particles fully covers the float
exactly means. Particularly, how strongly do these particles adhere to the surface of the floater?
If not at all, then the tension in the cord will accordingly stay the same or increase a bit.
If they do stick a lot to the float, then the combined (float+particles) density overcomes any extra buoyancy and the tension decreases.
Edit: Now the OP makes clear that the particles do not stick to the float, so the answer to the first question is enough to predict the outcome of the experiment:
If the particles completely set at the bottom, leaving only plain water in the bulk of the fluid, then the tension stays the same;
If a colloid is formed, then the tension will increase by an additive factor proportional to the particles density and concentration.
A conceptual trap
It might be tempting to think that "when the float is inside of the dust cloud then it is the same as if it were in a liquid with density higher than plain water", but that doesn't happen.
This becomes clear once you remember that the microscopic mechanism behind pressure is simply moment transfer from innumerable collisions with the fluid constituents: and for particles not in equilibrium with the fluid, for particles with are mostly moving downwards, these collisions can't transfer a net upwards moment (the origin of buoyancy), on the contrary, actually, as pointed out in Car Lei's answer.
You can also consider the effect of holding a big piece of lead next to the float: even if the the average density around the float is now how higher, there's obviously no increase in buoyancy. Denser particles mostly falling next to it have exactly the same effect (none, and they push it downwards when falling on top of it).
Separating molecules requires work to be done against the attractive forces. So because molecules in the surface don't have molecules above them, they need less energy to move down into the bulk of the liquid than is needed for molecules to move from bulk to surface. Therefore the rate of movement of molecules due to their random thermal energy is greater surface to bulk than bulk to surface. [Compare Boltzmann factors exp$\left( -\frac{E_{S\ to\ B}}{kT}\right)$ and exp $\left(-\frac{E_{B\ to\ S}}{kT}\right)$.] This tends to deplete the surface layer, which in turn reduces the movement of molecules from surface to bulk, re-establishing (dynamic) equilibrium (equal rates of movement to and from the surface layer).
But with this 'new' dynamic equilibrium, the molecules are further apart in the surface layer than their usual separations so, recalling the intermolecular force curve, they attract each other, in other words the surface is under tension, like a stretched balloon-skin.
Best Answer
The pin floats on the surface of water because of water's surface tension. When a pin is delicately placed on the surface of still water, it creates a small depression on the water's surface. If the pin is of unit length, then through out its length, the water's surface experiences a force T. If $\alpha$ is the angle of depression, then there is a net upward force $2T\sin\alpha$ that balances the pin's weight. You may refer to the figure for the meaning of symbols.
The blue circle is the transverse section of the pin. That is, the pin is placed perpendicular to the screen.
The force $2T\sin\alpha$ is analogous to the normal reaction of a solid surface.