Lesson video

Hello, there, I'm Mr. Forbes, and welcome to this lesson on the particle explanations of density and pressure unit.

This less is called "Upthrust," and it's all about the force that allows objects to float in fluids.

By the end of this lesson, you're going to be able to describe how pressure changes with depth in a fluid and how those differences in pressure at different depths cause an upthrust to act on an object inside a fluid.

The keywords you need to help you through this lesson are shown here.

The first is pressure, and that's produced by the forces from particles within a fluid acting on each other or on a surface.

Particles, which is the term we use for atoms or molecules that make up matter.

Upthrust, which is the force acting upwards on an object that's in a liquid or a fluid due to pressure differences between the top and bottom surfaces.

And density, which is the mass per unit volume of a substance, and we should know that a less dense substance will float on top of a more dense substance as well.

The lesson's in three parts, and in the first part, we'll look at the differences in pressure at different depths in a fluid and why that happens.

In the second part of the lesson, we'll look at the upthrust, which is the force that'll act on an object submerged in a fluid and why that's caused by differences in pressure between its surfaces.

And in the final part, we'll look at the different factors that affect the floating and sinking of an object and its density in terms of the types of particles that are in it and the spacing between them.

So when you're ready, let's start by looking at pressure and depth.

The pressure under water is caused by the weight of the water acting downwards on objects submerged in it.

So if I've got a submarine here, there's going to be a force of the water acting downwards.

The weight of all that water's gonna act on that submarine, and it's gonna create pressure.

Because it's quite high up in the water there, there's gonna be lower pressure, but as the submarine goes deeper in the water, there's going to be more water and more weight of water above it, and that's gonna generate a higher pressure on the submarine.

The extra weight is increasing the pressure on that submarine.

We can demonstrate that idea with a can full of water.

So we start with an empty can and then fill it to the top with water, and there's a small hole in the side of the can.

Well, what's gonna happen is fairly obvious, is the water is going to escape through that hole.

So when the can is filled with water, we'll get water jetting out, and it's gonna go quite far because there's going to be a high pressure 'cause there's quite a lot of water above the level of that hole.

But as that can slowly empties and the water level decreases, then the water's not gonna fly out at the same speed.

It's gonna be a bit slower because the pressure's lower now.

There's less water above the hole, so the weight of the water above the hole is decreased.

The pressure's decreased, and the water doesn't travel as far.

Let's see if you understand that idea.

I've got three identical cans here, but you can't see into them to see the water level, and they've each got a small hole in the side at the same height.

In which of those three cans is the water level deepest? So pause the video, make your decision, and restart, please.

Welcome back.

Hopefully, you selected C.

The water's going out the furthest here, and the pressure increases with depth, so that water's gone out furthest because the pressure is greatest in that can, so that must mean that the water depth must be greatest in that can as well.

Well done if you got that.

Now, the reason the water pressure increases with depth is because there's a greater weight of water pushing down, and at greater depths, the particles are gonna be pushed closer together by that greater force, so there's gonna be bigger forces between them.

So let's say I've got some particles in shallow water.

These particles are very close together, but there's still some gaps between them, but if I go deeper into the water, deeper below the surface, the forces are gonna be greater.

The particles are gonna be compacted up, pushed closer together, so we've got a higher pressure in all directions deeper in the water.

So in the shallow water, I've got fairly small forces between the particles.

They're not pushed together as much, but deeper in the water, I've got larger forces, so a greater pressure, and that pressure acts in all directions on all the particles.

So a question for you now, which diagram most accurately shows the direction of pressure at a point in a fluid? So I've got three possible answers there.

I'd like you to select one.

Pause the video, make your selection, and restart, please.

Welcome back, and you should have selected answer C, and that's because pressure acts equally in all directions.

In the other two diagrams, the pressure just seems to be acting in one direction, which is incorrect.

So well done if you got that one.

Now, as we've seen, the pressure increases with depth in a liquid, but we can derive an equation that will give us a value for that pressure based upon the properties of that liquid and the depth.

So if we imagine column of liquid like this with a base area of A, so I've labelled that as A, and a depth of D, and that's labelled as well.

And so I've got that column of liquid.

We can find the volume of that column of liquid by multiplying the depth by the area.

That'll give us the volume of that cylinder.

The mass of the liquid, then, can be found using its density and its volume.

We've got an equation for that, and the mass is going to be equal to the density times the volume.

And if I combine those equations together, then I'll get an equation like this.

The mass of the liquid is the density times the depth times the area.

So the mass of the liquid in the column is given there by that expression, but we can also find the weight, and we can find the weight by using the gravitational field strength, G.

So the weight of any object is its mass times the gravitational field strength.

So the weight of that column of liquid will give us an expression like this.

The weight is the density times the depth times the area of the base times G, the gravitational field strength.

So we have an expression for the weight of that liquid column, and that's going to be the force acting on the base of that cylinder.

So the force acting on the base of that cylinder is weight times density times depth times area times gravitational field strength.

So now, we can have an expression for the pressure.

The pressure is given by the force divided by the area.

So we write that out.

We've got a pressure is equal to that force that we expressed before divided by the area, and as you can see in the top and bottom rows, I've got area, so those two will cancel out, and that'll give us a final expression for the pressure at the bottom of a column of liquid.

The pressure is the density times the depth times the gravitational field strength.

Okay, so let's write that out formally.

The pressure at a certain depth or height in a fluid is given by this expression: pressure equals density times height times gravitational field strength, and that can be written like this in symbols, where pressure, P, is measured in newtons per square metre, density is measured in kilogrammes per cubic metre, height is measured in metres, and gravitational field strength is measured in newtons per kilogramme.

So let's try and use that equation to calculate a pressure.

The submarine here is travelling at a depth of 200 metres in fresh water, which has a density of 1,000 kilogrammes per metre cubed, and I'm gonna calculate the pressure on the submarine.

The gravitational field strength, though, is 9.

8 newtons per kilogramme, which is the gravitational field strength on Earth.

So the first stage is to write out the equation.

I'm gonna write it out like this: pressure equals density times height times gravitational field strength.

We just substitute in the values from the question now.

So I've identified them here, and I can just put those into the equation like this, and the final stage is just simply solving it.

So I can solve it by putting those values into my calculator, and I get a pressure of this, 1,960,000 newtons per metre squared.

That's a fully sort of awkward number, so I'm gonna change that into meganewtons per metre squared there, so 1.

96 meganewtons per metre squared.

Okay, I'd like you to try and calculate the pressure on something else, so I've got a diver below the surface of the sea, and I'd like you to calculate the water pressure acting on them, and I've given you all the data you need there.

So pause the video, calculate the pressure, and then restart, please.

Welcome back.

Hopefully, you selected the bottom option, 1.

1 meganewtons per square metre, and here's the mathematics that shows that, so well done if you got that.

And now, it's time for the first task of the lesson, so what I'd like you to do is to answer this question again about a diver.

You're describing the cause of pressure, what would happen if they went to a greater depth, and finally, calculating the pressure acting on them.

So pause the video, answer those three parts to the question, and then restart, please.

Welcome back.

Here's the answers to the first part.

You can see the first one should be an explanation based upon water particles and the weight of the water acting on them, and then the second part, the pressure is going to increase because there's a greater weight of water as they go further into the ocean.

And here's the answer to the third part.

There's a calculation involved, so you use the equation there.

You calculate the pressure at 20 metres, and that gives a value of 196,000 newtons per square metre.

The pressure at 30 metres, that's 294,000, and then the increase in pressure is the difference in those two pressures, which is 98,000 newtons per square metre.

Well done if you got that one.

And now, it's time to move on to the second part of the lesson, and in this one, we're going to explain why there's an upthrust first acting on an object that's in water.

So let's go on with that.

If you try and push a ball further underwater, you'll feel like there's an upward force acting on it, pushing on it and bringing it back to the surface when you let go, and that's because when you submerge a ball in water, there'll be pressure acting on it in all directions, and that pressure will act inwards on a ball, but as we'll see, that pressure is not equal in every direction.

And so the pressure on a submerged ball is not equal in all the directions.

If we look at the pressure on the sides of the ball here, the pressure's equal on the two sides, and that's because they're at the same depth within the water, so those two pressures act on each other, and they sorta cancel each other out, but the ball is being compressed by those.

But at the top of the ball, that's higher up in the water, so there's actually gonna be a lower pressure there because it's at less depth, so I've got a lower pressure there.

But at the bottom of the ball, that's deeper in the water, where the pressure's higher, so I've got a higher pressure on the ball, so overall, those pressure differences are going to produce a force that acts upwards because there's a higher pressure at the bottom of the ball than at the top of the ball.

The resultant force pushing upwards due to those pressure difference is called the upthrust, so we've got the two forces on here.

I've got the upthrust acting upwards to accelerate the ball upwards, and I've got the weight of the ball acting downwards.

And if we find the resultant of those two forces, it allows us to find out which way the ball is going to accelerate.

Is it gonna sink downwards, or is it gonna float upwards? That depends on which is bigger, upthrust or weight, or if they're equal.

So let's see if you can decide which way an object's going to accelerate when it's in the water.

I've got three balls here all in the water, and I've marked the size of the upthrust and the weight for each of them, and I want you to decide if the ball will accelerate upwards, downwards, or not at all.

So pause the video, make your decisions for each of the ball, and then restart, please.

Welcome back, so going through each of them, the first one, that's going to accelerate upwards because the upwards force, the upthrust, is greater than the weight.

The second ball is not going to accelerate at all.

The upthrust and the weight are equal, so there's no acceleration.

And then, the final one, well, that's going to accelerate downwards.

It's going to sink because the weight is greater than the upthrust.

Well done if you got those three.

The size of the acceleration can be found using Newton's Second Law of motion, which is this: the acceleration is the resultant force divided by the mass, or we use symbols a = F over m, where acceleration, a, is measured in metres per second squared.

Force is measured in newtons.

That's the symbol F, and mass, m, is measured in kilogrammes.

So we're gonna try and use that expression to calculate some accelerations now.

So I've got a ball of mass 0.

5 kilogrammes and a weight of five newtons, and there's an upthrust force of seven newtons acting on it.

I'm going to calculate the vertical acceleration of the ball.

So the first thing I do is I find the resultant force, and the resultant force here is me taking one force from the other, and that gives me a force of 2.

0 newtons acting upwards because the upwards force is slightly larger than the downwards force.

Now, I can use that to find the acceleration.

The acceleration is force divided by mass.

Put those numbers in, two newtons.

Remember, I'm using the resultant force, and there's the mass, 0.

5 kilogrammes, and that gives me an acceleration of 4.

0 metres per second squared, and that's in the upwards direction.

Now, it's your turn.

I'd like you to calculate the vertical acceleration of the brick.

So a brick of mass two kilogrammes has got a weight of 20 newtons and an upthrust force of eight newtons acting on it.

So pause the video, calculate the acceleration, and then restart, please.

Welcome back.

Well, the resultant force here is found to be -12 newtons.

I've got force acting downwards, and I can then use that force to calculate the acceleration that's -6.

0 metres per second squared.

I've got an acceleration 6.

0 metres per second downwards, and that's what the minus sign indicated.

Well done if you got that.

Upthrust forces don't just act on objects within the water.

They'll act on an object floating on the surface of the water as well.

So I've got a raft here, and I've got its weight and its upthrust.

The pressure of the water on the bottom of the raft is greater than the pressure of the air on the top.

What that's going to do is allow the weight of the raft on the water be equal to the upthrust, provided that the water pressure is acting on the bottom.

Now, a question for you: I've got a boat of weight 50,000 newtons, and it's floating on the surface of a lake.

What size is the upthrust acting on it? So pause the video, make your selection from those three, and restart, please.

Welcome back.

It should be exactly 50,000 newtons.

The boat's floating, so there's no resultant force on it.

It's not rising up, and it's not sinking downwards, so the weight and the upthrust must be equal in size.

Okay, it's time for the second task, and what I'd like you to do is to answer these two questions.

I'd like you to explain why it's difficult to hold a beach ball underwater.

So if you ever tried it, it's very, very difficult.

And for part two, I'd like you to look at that submarine.

It's travelling forwards at a constant depth under the sea surface, and you've got its weight there.

I'd like you to state the size of the upthrust force and explain the cause of the upthrust force on the submarine as well, please.

So pause the video, answer those questions, and restart.

Welcome back.

Well, let's look at the first one.

Your explanation should be something about a very large upthrust force acting on the ball when it's underwater due to those pressure differences at the top and the bottom of the ball.

And for the second one, if you stated the size of the upthrust, it should be equal to the weight, so it's exactly the same value, two million newtons, and the cause of the upthrust force is the difference in pressure between the top and bottom surfaces of the submarine, and that gives a resultant force that acts in the upwards direction.

We call that upthrust.

Well done if you got those.

And now, we're onto the final path of the lesson, and we're going to look at why some materials will float on water and some won't, so let's get on with that.

Any substance will sink in water if it's more dense than the water.

So a stone will sink in water because it's more dense there.

So if I place the stone in water, it will fall to the bottom of the water.

And that's because the stone has a higher density than water, and the reason the stone has got a higher density than water is this: it's made of particles which are heavier than water particles, so each individual particle in the stone is heavier than the one single water particle.

And the second reason is the particles are also packed more closely together in the stone.

So overall, the stone has more mass per cubic centimetre than the water, and that's what causes it to sink in the water.

Let's see if you understood that explanation.

I'd like you to complete these statements by using just the words greater and smaller to fill in the gaps.

So pause the video, decide which word fits which gap, and then restart, please.

Welcome back.

Let's go through those.

So rock has a greater density than water because it has a greater mass in a particular volume.

This is because each particle of rock has a greater mass than a particle of water, and the gaps between the particles in the rock are smaller than the particles in water.

So well done if you got those.

Now, let's see why a substance floats on water, and it floats because it's less dense than the water.

So we can have oil, and oil will float on the water because it's less dense, so if I spill oil on water, it'll float on the top like that.

The oil has a lower density than water because even though it's made of particles that have a greater mass than the water particles, they are much further apart.

They're spaced out more than the particles in water, so the individual particles are heavier, but they're more spaced out, and that means that the oil has less mass per cubic centimetre than water, and so it floats.

Now, let's look at a situation where the particles are identical, so we got liquid water and solid water, that's ice, are both made from exactly the same molecules, H20 molecules.

If you put a piece of ice in water, the ice will float on the water.

Now, ice is less dense than the water, even though it's made from the same particles, so particles, each individual one, has got the same mass, but the ice is less dense.

And the reason it'll float is the particles in the solid ice are spaced further apart than those in liquid water, and because they're further apart, there's less of them in each unit of volume, and so it's got a lower density.

Okay, let's see if you understood that explanation.

I'd like you to complete these statements by adding the words greater and smaller to each of the gaps.

So pause the video, read through them, and fill in the gaps, and then restart, please.

Welcome back.

Well, let's have a look at solutions.

Ice has a smaller density than water because it has a smaller mass in a particular volume.

That means that gaps between the particles in the ice must be greater than the gaps between the particles in the water.

Well done if you got those answers.

And now, it's time for the final task of the lesson, so I've got some pupils, and they're trying to make models to try and explain why some substances have a higher density than others, and they're using little balls with sticks between them to join them together.

So what I'd like you to do is to state three ways that they're good models for explaining density and three ways where they're not accurate models for explaining density, and then, try to use the particle model to explain why some substances have a higher density than others.

So pause the video, answer those three questions, and restart, please.

Okay, welcome back, and here's some explanations why they're good models.

I'm not gonna read through them all, but you've got several answers there that'll explain why they are good models, and it will give some ideas when it's done.

Welcome back, and here's some ways that that was a good model for explaining density, and you can see I've listed three of them there.

I'm not gonna read them all out.

You can read for yourself, but they can be used to explain some of the concepts of density, so well done if you got answers a bit like this.

And here are the limitations of the model, reasons why they're not an accurate model of density.

You got several examples there to read through.

Your answer could've contained any of those, so well done if you got those, and here's the answer to the final part using the particle model to explain why some substances have a higher density than others, and it's to do with the amount of mass in a certain volume, and that'll be to do with the size of the particles and their spacing, so well done if you got answers that look like this.

Okay, we've reached the end of the lesson now, so here's a quick summary of everything we've learned.

Pressure in a liquid increases with depth, and that's due to the additional weight of the liquid above, and that's causing the particles to be pushed closer together, increasing the forces between them.

The pressure at a height in a liquid can be calculated with this equation: pressure equals density times height times gravitational field strength.

Pressure differences between the top and the bottom of an object will produce an upthrust force, and that upthrust force acts along with the weight and can cause an acceleration depending upon the difference between the upthrust and the weight.

A less dense material will float on a more dense one, and the density depends upon the mass of the individual particles and the space in between them.

Well done for reaching the end of the lesson.

I'll see you in the next one.