Area density - Wikipedia
Pressure & Density. • Pressure is defined as force divided by area (force/area). santoriniinfo.info Kurtus. • One can also assume that pressure = weight/area. To apply density relationships in problem solving. INTRODUCTION. Remember the relationship between mass and volume of the substance. If the density of a . The areal density of a two-dimensional object is calculated as the mass per unit area. The SI derived unit is: kilogram per square metre (kg·m−2). In the paper.
How do you calculate mass using density and volume? | Socratic
What's the volume of the liquid? The volume of the liquid is going to be the cross-sectional area of the cylinder times the height. So let's call this cross-sectional area A. A for area-- that's the area of the cylinder or the foil that's floating within the water. We could write down that the downward force is equal to the density of the fluid-- I'll stop writing the l or f, or whatever I was doing there-- times the volume of the liquid.
The volume of the liquid is just the height times the area of the liquid. So that is just times the height times the area and then times gravity. We've now figured out if we knew the density, this height, the cross-sectional area, and the gravitational constant, we would know the force coming down. That's kind of vaguely interesting, but let's try to figure out what the pressure is, because that's what started this whole discussion.
What is the pressure when you go to deep parts of the ocean?
This is the force-- what is the pressure on this foil that I have floating? It's the force divided by the area of pressure on this foil.
So I would take the force and divide it by the area, which is the same thing as A, so let's do that. Let's divide both sides of this equation by area, so the pressure coming down-- so that's P sub d.
The downward pressure at that point is going to be equal to-- keep in mind, that's going to be the same thing as the upward pressure, because the upward force is the same. The area of whether you're going upwards or downwards is going to be the same thing.
The downward pressure is going to be equal to the downward force divided by area, which is going to be equal to this expression divided by area. Essentially, we can just get rid of the area here, so it equals PhAg divided by A-- we get rid of the A's in both situations-- so the downward pressure is equal to the density of the fluid, times the depth of the fluid, or the height of the fluid above it, times the gravitational constant Phg.
As I said, the downward pressure is equal to the upward pressure-- how do we know that? Because we knew that the upward force is the same as the downward force. If the upward force were less, this little piece of foil would actually accelerate downwards.
The fact that it's static-- it's in one place-- lets us know that the upward force is equal to the downward force, so the upward pressure is equal to the downward pressure. Let's use that in an example. If I were on the same planet, and this is water, and so the density of water-- and this is something good to memorize-- is 1, kilograms per meter cubed.
For example, 10 grams of freshwater has a volume of 10 milliliters. Unlike mass and volume, increasing the amount of material measured does not increase or decrease density. This makes density a useful property in identifying many substances.
However, since volume deviates with changes in temperature and pressure, density can also change with temperature and pressure. Specific Gravity One derivative measurement of density is specific gravity.
Worked example finding area under density curves (video) | Khan Academy
Specific gravity compares the density of a substance with the density of a reference material. In the case of gases, the reference material is standard dry air, or air without water. In the case of liquids and solids, the reference material is fresh water. Specific gravity is calculated by dividing the density of a substance by the reference substance's density.
For example, gold has a density of This yields a specific gravity of And so this is going to give us as it should have, 0.
So the area under the entire density curve is one which we need to be true for this to be a density curve. Now let's think about what percentage of that area is represented in blue right over here. Well we could do the same thing. We could say all right, this is a trapezoid.
We want to take the average of this side and this side and multiply it times the base. So this side is 0. Well the base going from two to three is only equal to, is equal to one.
And so this is going to give us 1. And what is that going to be equal to? Well that would be the same thing as zero point what?
Did I do that right, Yep. If I multiply two times this, I would get 1. So the percent of the area under the density curve where x is more than two, this is the decimal expression of it.