# Are these sandals floating due to surface tension or buoyancy?

Having an argument. If the sandals are wet (which I think we can assume they are), then they have broken the surface, correct? And if they’ve broken the surface, then that leaves only buoyancy to hold them up.

I reason that they appear to be floating “on” the water because they are incredibly light, foam sandals, and only need to displace a very small amount of water to float.

The angle from which the photo was taken also hides any under-the-surface view of the sandals.

So, is it buoyancy or surface tension? Or both? Or neither? (A higher power?)

• What happens when you release sandals like this from below the surface? If they sink, then it's likely surface tension. If they float, then it's likely buoyancy. – probably_someone Jul 17 '18 at 20:36
• Unfortunately I don’t have the sandals. But isn’t it true that if the reason is surface tension and you lift the sandals up the bottoms will be dry? You only get wet if you break the surface, right? – Buttle Butkus Jul 17 '18 at 20:38

It must be buoyancy, since even under very favorable assumptions, the force associated with the surface tension would not be sufficient to keep the sandals from sinking.

Let's assume that the sandals are made out of styrofoam with density $30kg/m^3$ and have dimensions $300mm\times100mm\times10mm$, which translates to about $10g$ weight - not much.

For a sandal to float, the minimum surface tension force would have to be equal to that weight of the sandal, i.e., $\sigma L cos(\theta)=mg$.

With the perimeter, $L=800mm$ $(2\times 300mm + 2\times 100mm)$ and the surface tension coefficient of water $\sigma=73mN/m$, we can find that $cos(\theta)$ would have to be about $1.7$, which says that it must be buoyancy.

• Lovely math! Thanks for confirming my intuition with numbers. I would also add that the choppy surface of the pool would cause a significant increase in the maximum force of the sandals pushing against the water, making surface tension even less plausible. – Buttle Butkus Jul 17 '18 at 22:22
• Also, do you know if the bottoms of the sandals would come out dry if they had in fact not broken the surface of the water? Or would they be wet? – Buttle Butkus Jul 17 '18 at 22:24
• @ButtleButkus Dry sounds right to me. – V.F. Jul 17 '18 at 22:25
• @V.F. I'm not sure about that. Surface tension is a function mainly of the cohesion of the water, whereas wetting is a function mainly of its adhesion to the sandal. Those are two independent variables, as far as I know. – probably_someone Jul 17 '18 at 22:27
• @probably_someone "The degree of wetting (wettability) is determined by a force balance between adhesive and cohesive forces." Wikipedia. – V.F. Jul 17 '18 at 22:33