00:01
So in this problem, we're going to be talking about buoyancy.
00:04
So if we have some fluid and an object dispersed in it, there are a couple of forces acting on this object.
00:10
One is its weight.
00:12
And that we could say is equal to its density times its volume, times the acceleration due to gravity, which is just an expansion of mass times gravity like we are typically used to, but we have some volume and density of this object.
00:26
Now, it's also experiencing a buoyant force, which in magnitude is a good.
00:32
To the density of the liquid times the volume times the acceleration due to gravity.
00:38
And then the relation between those tells us whether it sinks or flows.
00:43
But what we see here we're asking problem one is we're saying that density of the object is greater than the density of the liquid.
00:52
If we do new and second law, some of forces is equal to m a we have the buoyant force upwards and then the weight downwards and we can cross out row in v so basically, we're not equal to zero because it's equal to m .a.
01:13
So the density of liquid times the volume times gravity, minus the density of the object times the volume times gravity is equal to m .a.
01:21
And so if the density of the object is greater, then we're going to see acceleration is going to be negative.
01:26
And so the object would sink if we have here our positive direction for axis.
01:36
Now, the reason why that doesn't happen is because while the boat is made out of steel or the ship or the canoe out of concrete, that's not what it's exclusively made out of.
01:45
Of the entire boat, only the outer skin is a heavy material.
01:51
If you consider the whole boat, its density has to be lower because it's filled with air.
01:56
I guess it can be green because we already have the water to be blue.
01:59
And its density is very low.
02:02
The density of water is 1 ,000 kilograms per meter cubed.
02:10
Air is 1 .225 kilograms per meter cubed on the surface of earth and the density of steel or something or of rock or something crazy that may be something like 20 ,000 kilograms per meter cube so obviously the steel of concrete's a lot lot heavier but we see the boat's mostly air because the aircraft carrier wants aircraft and people to live and work in the boat so it's mostly air so those people can be in it and that air gives us a lot of buoyancy.
02:45
So that's kind of leading into point two is that can air create a buoyant force and yes it can because air is a fluid just like any other.
02:53
Like we said before though, the density of air is very small and so the buoyant force we create is not very large.
03:06
We can use archimedes principle to say that the buoyant force is equal to negative times the density of the air, times the volume of the object times gravity.
03:14
The negative sign is just telling us the direction.
03:17
So the reason why we didn't have it up here is because we already drew the point force in the opposite direction of gravity, where we assumed it to be downward by convention.
03:29
So if this is on earth, and what we're going to do is then just kind of get rid of this negative sign because we just kind of care about the magnitude.
03:36
I guess we could be specific and say the magnitude of the buoyant force.
03:40
The density of air, which we know is 1 .225.
03:43
The volume of the object, we don't know because we don't know what the object is.
03:47
But it accelerates to do gravity, 9 .81 meters per second times the volume.
03:52
And so the magnitude of the buoyant force is equal to 12 .02 times the volume in newton's.
04:05
So that's per meters cube, basically.
04:08
And so a meter cubed is a pretty large optic, right? if you have, you know, a typical person, a meter cubed box is something like this, maybe, pretty big.
04:21
So that's only 12 newtons, which is a pretty small force.
04:24
So it does create a buoyant force, but basically anything in air is heavier than the air...