Oh boy.
“Bouyancy is there, but bouyancy only really makes the difference for the part of the mattress which are not saturated by water.”
Big Red, you keep confusing “bouyency” with “positive bouyency.”
Bouyency force is a result of the density of an object compared to the density of the fluid it is in. Positive bouyency refers to the state where bouyency force is stronger than the force of gravity. Bouyency acts to reduce the effects of grvity felt on an object. Hence, my example of a rock thrown into water. It greatly slows down when it enters the water due to the resistance of the fluid against motion, but also due to the fact that the rock “feels” a reduced gravity.
Definition of Bouyency So, no matter what kind of object I am talking about, within a fluid, there exists a force acting against gravity. Further clarification
“A stone can’t be saturated by water, so it’s not the same example.”
It does not matter what I am talking about. Everything in a fluid is acted upon by a bouyency force.
“The mattress isn’t displacing a lot of water if it is saturated, therefore, it’s buoyancy force won’t make it “as easy to lift as in air”. I base the entire bouyancy argument provided that the mattress does not displace more water than it absorbs.”
It does displace slightly more water than it absorbs. To show this, and to distinguish the two processes involved here, let’s imagine two scenarios, then combine them.
Scenario 1.) the mattress has all air removed from it, without increasing the density of the fabric. (i.e. it is squeezed such that fibers and springs, etc have no air in and around them, but individual fibers have not been compressed to the point where we alter their molecular structure.) There is no air space left in this squished mattress for it to absorb any water. This squished mattress is then placed into a pool and promptly sinks. How much force will be required to lift the mattress while it is submerged in the pool?
Answer: Weight - [(density of water)*(volume of the squished mattress) *(acceleration due to gravity)] … or less than it’s weight.
Scenario 2.) we create a box out of a plastic with identical density as our pool water. This box has an identical volume as (our original mattress) - (the volume of our squished mattress). This box gets some holes puched in it so that water can move, but slowly, through it. The box is placed in the pool and allowed to fill with water. Now, how much force do we need to apply to the box to lift it (while it is still submerged)?
Answer: only enough to overcome drag. Our box is neutrally bouyant. The water in the box makes no difference whatsoever to the force required to lift the box, as long as it is submerged. Move slowly enough, and drag is negligable.
Combination: We place the submerged squished mattress on top of the submerged and water-logged box. What force do we need to apply to lift this combined system to lift it, so long as it is submerged? Same as in scenario 1. (Weight of the mattress) - (bouyency force of the displaced water). We are not lifting the water in the box. The water in the box is immeterial.*
“I never claimed that pressure was “unidirectional””
You’re right; you never stated it that way, but your arguments stem from this misunderstanding. Your equation is correct, but you are applying it incorrectly. If the pressure is the same on all sides, the will be no pressure force. The concept of a pressure creating a force is called Pressure Gradient Force, because you need a difference in pressures in order to create a force. Simply having pressure does absolutely nothing for the weight of an object and nothing for the directional force it feels.
“just that it is also under the weight of the water above it now as well.”
True, but either this has nothing to do with the force as I’ve stated, or you need the weight of the water to be acting in one direction only. One of the properties of fluids is that the pressure is transfered to all sides equally. Thus, there is no “pressure of the water on top of it pushing down” (emphasis mine)
“But hey, if you want to take my words out of context, and patronise me with some stupid real-world example, go right ahead.”
I haven’t taken your words out of context; you’re applying the concepts incorrectly. Pressure does not push down. And how can it be patronizing if it is a real-world example? Wouldn’t it just be an example of how your explination does not correctly match reality?
*just to make sure I am clear here: I don’t mean that if we removed the water and replaced it with air it would make no difference. I only mean that for the purpose of lifting the system while submerged, the presence of that amount of water has no effect on the force required to move it.