Lesson video

Hi there.

My name is Ms. Lambell.

You've made a superb choice deciding to join me today to do some maths.

Let's get cracking.

Welcome to today's lesson.

The title of today's lesson is Compound Measures for Pressure, and this is within the unit, compound measures.

By the end of this lesson, you'll be able to use compound measures for pressure.

Two key words that we'll be using a lot in today's lesson are pressure and force.

Pressure is the perpendicular force applied to the surface of an object per unit area over which that force is distributed.

A force is a push or a pull on an object.

A force is an influence that can cause an object to change its speed.

Today's lesson is in two learning cycles.

In the first one we will concentrate on calculating pressure and in the second one we will look at solving problems with pressure.

Let's get going with that first one, calculating pressure.

Which do you think would hurt more if they stood on your foot? An elephant or someone wearing a high heeled shoe? Hmm.

Laura says, "Well, that's easy.

A person as they have a much smaller mass than an elephant." Jun says, "I am not so sure.

Look at how spiky that heel is on the shoe." What would you prefer? In this situation we need to consider the pressure exerted on your foot.

Pressure is measured in Newtons per centimetre squared and Newtons per metre squared, and it takes into account the force measured in Newtons and the area this force is distributed over.

Let's use this information to help us answer this question.

The person wearing the shoe exerts a force of 500 Newtons.

The area of the heel is 0.

5 centimetres squared.

We can set this up with a ratio table.

We know that the shoe exerts a force of 500 Newtons and the area of the heel is 0.

5 centimetres squared.

In order to find the pressure, we need to work out how many Newtons, so the force per 1 centimetre squared.

Therefore, I'm going to divide by 0.

5 and I'm gonna divide my force by 0.

5, giving me 1,000.

The pressure of the person wearing the shoe on your foot is 1,000 Newtons per centimetre squared.

The elephant exerts a force of 10,000 Newtons.

The area of the elephant's foot is 275 centimetres squared.

Again, we can set this up in a ratio table with our force and our area of the elephant's foot.

In order to calculate the pressure, we want to know the force per square centimetre.

We're going to divide 275 by 275 to get 1, and we're gonna do that to the force, which is 36.

4, and I've rounded that to one decimal place.

The pressure of the elephant on your foot is 36.

4 Newtons per centimetre squared.

The pressure of the person wearing the shoe is 1,000 Newtons per centimetre squared.

The pressure of the elephant is 36.

4 Newtons per centimetre squared.

Laura says, "You were right Jun, the pressure of the high heel is much greater than the pressure of the elephant." Jun says, "Although the elephant is much heavier, because it is distributed over a much larger area the pressure is much lower." Therefore we would prefer the elephant to stand on our foot.

I wonder if that's what you decided to start with.

A box is placed on a table.

The area of the base of the box is 1.

25 metres squared.

The force exerted by the box on the table is 42 Newtons.

Calculate the pressure exerted by the box on the table.

We've got our force is 42 and we've got our area.

We are working out how many Newtons per, this time, per metre square.

We're dividing by 1.

25, giving us 33.

6.

And again, I've given that to one decimal place.

The pressure exerted by the box on the table is 33.

6 Newtons per metre squared.

The cuboid has a mass of 108 Newtons and the cube has a mass of 75 Newtons.

Which exerts the greater pressure on the ground? Laura says, "Pressure is measured in Newtons per centimetre squared." Jun says, "Yes, Laura, that's right.

I can see where the N comes from.

And the centimetre squared must mean we need to find an area." "This must be the area of the base as that's the part that is in contact with the ground." We know the cuboid has a mass of 108 Newtons.

In order to work out the pressure, we need to know the force per centimetre squared.

Therefore, we need to know the area of the base of the cuboid.

The base of the cuboid has dimensions of 9 centimetres and 4 centimetres.

To find the area, we multiply those together, we find the product of those, giving us 36 centimetres squared.

Now we can fill in the missing information.

We've divided by 36, so we divide by 36 giving us 3.

The pressure of the cuboid is 3 Newtons per centimetre squared.

Now let's take a look at the cube.

Again, we've got our force is 75 Newtons and we're trying to work out the force per square centimetre.

This time it's a cube, therefore the base has dimensions of 5 centimetres and 5 centimetres, giving us an area of 25 centimetres squared, and dividing by 25 giving us 3.

The pressure of the cube is 3 Newtons per centimetre squared.

The pressure is the same for both of those objects.

Your turn to have a go at this check for understanding, I'd like you to match each with its correct pressure.

Pause the video, draw out your ratio tables.

You may use your calculator, show all steps of your working and when you come back, I'll be here ready waiting for you so that we can check those answers.

Good luck.

Okay, first one was 240 Newtons per metre squared.

The second one, 4.

8 Newtons per metre squared.

The third one was 48 Newtons per centimetre squared, and the final one was 120 Newtons per centimetre squared.

And now you're ready to have a go at the first independent task of today's lesson and that is Task A.

I'd like you please to calculate the pressure of each of the following.

Good luck with these, pause the video and then come back when you're ready for question two.

And question number two.

Which of the following exerts the most pressure on the floor? Draw a ratio table to support your answer.

You'll need to draw a ratio table for each of the three items. Pause the video and then come back when you're done.

And we'll check those answers.

Question number one.

The first one was 660 Newtons per metre squared.

The second one, 6.

5 Newtons per centimetre squared.

Third one, 54 Newtons per metre squared.

Fourth one, 65 Newtons per centimetre squared and the last one was 0.

54 Newtons per centimetre squared.

How did you get on? Of course, yeah, five out of five, I knew you would.

And question number two.

The pressure for the first shape was 26.

4 Newtons per centimetre squared.

The second one was 25 Newtons per centimetre squared, and then the cylinder, the final one was 26.

5 Newtons per centimetre squared, meaning the cylinder exerted the most pressure on the floor.

And now we can move on to that second learning cycle.

We'll look at solving problems with pressure.

The pressure exerted by a cube with side lengths of 8 centimetres on a table is 1.

4 Newtons per centimetre squared.

Find the force exerted by the cube on the table.

We know that the force is 1.

4 Newtons for every centimetre squared.

That's where that first line in our ratio table comes from.

We need to calculate the area of the cube which comes into contact with the table.

What is the area of the base of the cube? Well, it's 8 squared, which is 64 centimetres squared, so we can now put that into our table.

My multiplicative relationship is multiplied by 64.

I'm gonna multiply by 64, giving me 89.

6.

The force exerted by the cube on the table is 89.

6 Newtons, remember to give the correct units here.

We're just talking about the force, which is in Newtons, represented by that capital N.

This box exerts a pressure of 95 Newtons per metre squared and a force of 171 Newtons on the ground.

How wide is the box? Here's our ratio table.

We put our pressure on the top row and we know the force of the object on the ground is 171.

We're going to find the missing value with multiplier.

Remember, if it's not obvious, we can do 171 divided by 95 gives us that multiplicative relationship of multiplied by 1.

8.

I'm going to do 1 multiplied by 1.

8, which is 1.

8.

Laura says, "So the answer is 1.

8 metres squared?" Jun says, "No, that is the area of the base of the box." Remember, it was the area.

If we look at our ratio table, we can see it's 1.

8 metres squared, which is an area.

Laura says, "To find the width we need to divide the area by the length." "Yes, so the width of the box is 1.

2 metres." A 15 centimetre tall cylindrical candle exerts a pressure of 0.

1 Newtons per centimetre squared and weighs 4.

9 Newtons.

Will the candle fit in this gift box? Our pressure is the force 0.

1 and that's per centimetre squared because if we look at the units we can see it's per centimetre squared.

We know the force of the candle is 4.

9 Newtons.

I can now look for that multiplicative relationship.

I've multiplied by 49.

I get the area is 49.

That's the area of the base of the candle.

We are told that the candle is cylindrical.

The area of a circle is pi r squared.

We know that the area of the cylindrical candle is 49.

We've just worked that out using the pressure and the force.

49 equals pi multiplied by r squared.

We need to now solve this equation.

r squared is 49 over pi, dividing both sides of the equation by pi.

Then I need to take the square root of both sides, giving me r equals the square root of 49 over pi, which is 3.

95 centimetres.

That's the radius.

If the radius is 3.

95 centimetres, then the diameter is going to be double that.

It's going to be 3.

95 multiplied by 2, which is 7.

9 centimetres.

Therefore the base of the box is 8 by 8 centimetres.

So yes, the candle is going to fit into that box.

Now there's quite a lot of information there and you may feel at this point that you just want to go back through that question.

So if you do, rewind the video, go back and check each of those steps as you go, and you might want to do it at a slightly slower pace, that's absolutely fine remember.

What's most important is that you are able to apply this yourself in a moment.

You can now have a go at this check.

The pressure exerted by a cube with side lengths of 10 centimetres on a table is 3.

65 Newtons per centimetre squared.

Find the force exerted by the cube on the table.

Pause the video, draw me that ratio table, get me the force exerted by the cube on the table.

Good luck.

I'll be waiting when you get back.

Right then, let's check that answer.

We've got our pressure is 3.

65 Newtons per centimetre squared.

We now need to work out the area of the base of the cube, which is 100 because it's 10 multiplied by 10 or 10 squared.

The multiplicative relationship multiplied by 100, so I end up at 365.

The force exerted by the cube on the table is 365 Newtons.

And now we can move on to Task B.

You're gonna pause the video, complete the missing values in the table below.

Good luck with this and I'll be waiting when you get back.

And moving on to question two and three.

Question two, a cube exerts a pressure of 0.

2 Newtons per centimetre squared and a force of 5 Newtons on the ground.

How many of these cubes will fit into this box? And question three, a 6 centimetre tall cylindrical candle exerts a pressure of 0.

03 Newtons per centimetre squared and a force of 4.

8 Newtons on a table.

Will the candle fit into this gift box? Remember that final question, it is not okay just to say yes or no.

You need to be able to back that up with your wonderfully set out method using the information given to you in the question.

And I suggest for both of these, you draw a ratio table.

You can pause the video now, good luck with these and I'll be waiting when you get back and we'll be ready to check our answers.

Okay, let's check those answers.

Question number one.

The missing force was 570 Newtons.

The second row, the missing area was 16.

2 centimetres squared.

The third row, you were missing a pressure of 62 Newtons per metre squared.

The fourth row, we were missing a force of 3,996 Newtons.

And the final row, we were missing an area of 11.

3 centimetres squared.

Now let's take a look at question two.

We knew that the force was 0.

2 Newtons per centimetre squared and we knew the force that the cube was exerting on the ground.

So at the moment, I'm ignoring that diagram, the box.

We find the area at the base of the cube is 25, and we do this by looking at the multiplicative relationship between 0.

2 and 5.

That's where our 25 comes from.

The length of the cube is the square root of 25, which is 5 centimetres.

The volume of the cube therefore is 5 cubed, which is 125 cubic centimetres.

I've worked out the volume of the box that we are packing the cubes into as 720,000 cubic centimetres.

Which leads us to the number of cubes that will fit in the box is the volume of the large box.

So 720,000 divided by the volume of one cube, 125, which gives us 5,760.

We will be able to fit 5,760 cubes into that box.

And question number three.

Using the information given in the question about the pressure and the force, we can work out by multiplicative relationship is multiplied by 160.

We know then that the area of the base of the candle is 160 centimetres squared.

We were told in the question that it is a cylindrical candle, so we then know that the area of the circle, pi r squared is equal to 160.

We now need to solve this equation for r, r squared is 160 over pi, so r is the square root of 160 over pi, which is 7.

136.

to show that that continues.

We need to find the diameter because obviously it's the diameter that needs to fit in the box, so we're going to take that and multiply it by 2, giving us 14.

27 centimetres.

The base of the box is 14 by 14, so unfortunately, no, the candle will not fit into the box.

Well done if you've got all of those right.

There were some really challenging questions towards the end of that lesson, fantastic.

Now let's summarise our learning from today's lesson then.

Pressure is the perpendicular force applied to the surface of an object per unit area over which that force is distributed.

The main units of measurement of pressure are Newtons per cubic centimetre and Newtons per cubic metre, represented by N/cm cubed and N/meters cubed.

A force is a push or a pull on an object.

A force is an influence that can cause an object to change its speed.

Ratio tables are an excellent way to solve problems involving force and pressure, and there's an example there of one of the questions that we looked at during today's lesson.

Well done, you've worked fantastically well today and like I said, there were some really quite challenging problems towards the end of that Task B.

Well done for sticking with me.

Hopefully I will see you again really soon.

Take care of yourself.

Goodbye.