A heavier person vs. a lighter person diving into a pool

[Haizakokaru]

Does the higher amount of force exerted onto the water's surface by the heavier person allow him to plunge deeper initially, and then they both sink afterward at the same speed due to same density? In other words, does the heavier person travel a greater distance than the lighter person in a first few seconds of sinking from the water's surface? Does the lighter person not plunge into the water as far as the other?

 

[A.T.]

Summary:: buoyancy and force question

Does the higher amount of force exerted onto the water's surface by the heavier person allow him to plunge deeper initially, and then they both sink afterward at the same speed due to same density? In other words, does the heavier person travel a greater distance than the lighter person in a first few seconds of sinking from the water's surface? Does the lighter person not plunge into the water as far as the other?

Buoyancy just gives you the static upwards force. The dynamic force while penetrating the surface and moving through the water is complicated, and depends on many factors. But it more likely scales with the cross-section, rather than volume (as the weight and inertia do). So assuming the same density (less than water) and uniform scaling the bigger body will sink deeper.

 

[Haizakokaru]

Thanks! A friend was saying how much he sinks shouldn't matter due to density and I disagreed, but kept quiet because I wasn't entirely sure about how buoyancy and other forces factored into it. I can finally be at peace now.

 

[PeroK]

Thanks! A friend was saying how much he sinks shouldn't matter due to density and I disagreed, but kept quiet because I wasn't entirely sure about how buoyancy and other forces factored into it. I can finally be at peace now.

You can read a bit about it here.

https://www.physicsforums.com/threads/does-density-affect-sinking-speed.809334/

It would be odd if all objects sank at the same rate, surely. Something very dense will have a large force of gravity on it compared to the small amount of water it displaces. It's bound to sink faster than something that almost floats.

 

[jbriggs444]

Something very dense will have a large force of gravity on it compared to the small amount of water it displaces. It's bound to sink faster than something that almost floats.

Of course, size and shape also play a role. A thin sheet of osmium will likely flutter downward in the water more slowly than a sphere made of ebony wood, despite the metal's dramatically higher density.

Huge ships sink at surprisingly high speeds despite near neutral buoyancy due to their large volume to cross-section ratio.

 

[AndreasC]

Gonna go slightly on a tangent here, the consequences of cross section vs volume ratio is one of my favorite of the very simple but slightly counter intuitive facts about physics that is relevant for many things. For instance, giants. People usually assumed that you could just scale up a person and maintain more or less the same proportions. But let's say you scale up someone's height by 10 while maintaining the same proportions. Then the cross section of their legs will be scaled up by 100, and their volume (and therefore their mass) by 1000. So the end result will be a person whose mass to leg (or spine) cross section ratio will be 10 times larger than normal, which should be pretty unpleasant to say the least.

So yeah I think that most of the resistance someone meets when they splash is dependent on the cross section, so that's the reason why heavier people usually manage to make it deeper, all other things equal. Although I am sure the effects are generally much more complicated than that in practice.

You can read some more about it here: https://en.m.wikipedia.org/wiki/Drag_equation

 

[Arjan82]

A heavier person will have acquired more kinetic energy before hitting the water. But its resistance once hitting the water is larger. How this pans out for how deep either will sink depends on a lot of things.