# Why do I sink then float in a swimming pool?

Was swimming this morning and observed something strange: if I stop treading water, hold my legs together, arms pressed against my sides, then I sink to about 3m below the surface, and then rise again and float. Tried different positions and still get the same effect, to varying degrees.

Does anyone know about the physics behind this?

• If you're above water, your weight is stronger than buoyancy and you sink. As you go down the two forces eventually cancel, but because of inertia you keep going down for a little bit. If water didn't cause drag you would oscillate around your equilibrium height. – Javier Jul 24 '15 at 18:12
• What Janvier says , also if you have little fat content your buoyancy will be less (muscle is denser). If you do not move you will sink. – anna v Jul 24 '15 at 18:13
• @Javier He is experiencing an oscillation of about 3 m, so that doesn't completely explain it. He must also take into account the air in his lungs and the involuntary muscle movements that must be affecting his oscillation. Otherwise, he would ( or should ) have said that he stopped oscillating while still underwater unless he kept all his breath in all the time. – Tetradic Jul 24 '15 at 18:19
• Probably he means his feet at 3meters. "treading" – anna v Jul 24 '15 at 18:25
• @Javier The sinking acceleration for someone who's exposing $.3$ m$^3$ outside of the water (the head basically) is about 4 $\frac{\text{m}}{\text{s}^2}$. You are more than likely correct. – Tetradic Jul 24 '15 at 18:57

If you are above the water you will get accelerated down until the weight of the water you disperse is equal to your own weight (calling this level $x$). As soon as you are completely submerged the gravitational force downwards will be $\rho Vg$ and by Archimedes principle the force upwards will be $\rho_w V g$, where $\rho$ is your density, $V$ is your volume and $\rho_w$ is the density of water. Thus the total downwards force is $Vg(\rho - \rho_w)$.
So depending on your density you will keep accelerating down ($x$ is never reached), or start accelerating up as soon as you pass level $x$. As humans are almost $90\%$ water, our density is very close to that of water (most people are a little more dense). Such that you probably can push your density to be higher than water if you complete exhale, then you will accelerate right to the bottom of the pool.
If you are less dense you will start accelerating up as soon as you reach level $x$ this acceleration plus the drag (which would depend on your position) will slow you down until your velocity is zero, then you will get accelerated upwards, and if you can hold your breath long enough you should oscillate around level $x$ with an exponentially decaying amplitude. And depending on your initial velocity at point $x$ and your density, the amplitude will vary.
It is basically a dapped harmonic oscillator, but not quite because the force for when you are higher then level $x$ is not linear in position.