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Hello there, I'm Mr. Forbes, and welcome to this lesson from the "Forces make things change" unit.

This lesson's called Newton's Second Law, and that's the law that links force, mass, and acceleration together.

By the end of this lesson, you're going to be able to apply Newton's Second Law of motion, and that law is force equals mass times acceleration.

You're to use that law to perform a range of calculations.

Here are the key words that will help you with this lesson.

The first is resultant force, and that's the overall effect of the forces acting on an object.

The next is acceleration.

An acceleration is caused by a resultant force and it results in a change in speed and/or direction of movement.

And finally, mass, that's the amount of matter in an object that's measured in kilogrammes.

You can return to this slide at any point in the lesson.

This lesson's in three parts, and in the first part we're going to be looking at what Newton's Second Law is, and applying it in a wide range of situations.

And the second part, we'll look at the concept of mass and what that is.

And in the final part, we'll look at the motion of objects that have been accelerated by gravitational forces.

So when you're ready, we'll start by looking at Newton's Second Law.

Isaac Newton described the relationship between acceleration, force, and mass in his Second Law.

And the Second Law is stated as this, "The acceleration of a body is directly proportional to the resultant force acting on it and inversely proportional to its mass." If we measure force in newtons, that gives us an equation like this, where acceleration is force divided by mass.

Newton's Second Law is usually written out this way, force is mass times acceleration, or in symbols, F equals ma, where F is the force measured in newtons, m is the mass measured in kilogrammes, and a is the acceleration measured in metres per second squared.

Let's see if you understand that relationship.

Two identical spaceships travel through space with the forces shown, which of the following statements is correct? And you can see the two spaceships there.

I've got spaceship P, and that's got a force of F acting on it.

And I've got spaceship Q, and that's got force of two times F, two F on it.

So, read through the three statements, decide which is correct, and then restart the video please.

welcome back.

The answer to that one is C.

Spaceship Q has twice acceleration of spaceship P, and that's because doubling the force doubles the acceleration as long as the mass is constant.

So well done if you've got that.

Now when we use Newton's Second Law of motion, we're using the resultant force acting on the object.

So we need to find that resultant force sometimes in order to find the acceleration.

So we can find the resultant force in these stages, adding the forces acting in the same direction, so every force acting in the same direction adds together, and then we subtract all the forces acting in the opposite direction.

So let's see a quick example of that.

I've got a space shuttle taking off here, and I've got some forces acting on it.

I've got its weight acting downwards of 20 meganewtons, 20 million newtons, and upwards, I've got two forces, from the rockets, 12 meganewtons, and another 12 meganewtons.

So I can find the resultant force like this.

Resultant is the upward forces minus the downward forces.

So that's 12 meganewtons plus 12 meganewtons, they're both upwards, and take away the downward force of 20 meganewtons, that gives me a resultant force of 4 meganewtons upwards or 4 million newtons upwards.

Let's see if you can find the resultant force.

So I'd like to know what's the size or the magnitude of the resultant force acting on the car shown in this diagram.

So pause the video, work out the resultant force, and restart please.

Welcome back.

You should have found the resultant force of 380 newtons.

So we've got 600 newtons in one direction and we take away the two forces in the other direction, so we take away 80 newtons and we take away 140 newtons, and that leaves us with a resultant of 380 newtons.

Well done if you've got that.

We can apply Newton's Second Law to any acceleration including decelerations.

So we'll look at an example of one of those.

I've got a resultant force acting on a van that's in the same direction as the van is moving.

What's gonna happen there is the van is going to speed up.

If I've got a resultant force acting on a cyclist, and that's opposite to the direction that they're moving, that term cyclist is going to slow down or decelerate.

And we can try examples that involve calculation.

So I've got a car of mass 1,200 kilogrammes, it's decelerating at 4.

0 metres per second squared.

Calculate the magnitude of the resultant force active on the car.

And so, to do that, I would write out the equation, force is mass times acceleration, and substitute the values in from the question, that's 1,200 kilogrammes times 4.

0 metres per second squared, and that will give me the resultant force acting on the car, which is 4,800 newtons.

I'd like you to have a go now.

So I'd like you to calculate the magnitude of the resultant force acting in this situation.

So pause the video, work out the resultant force, and restart please.

Welcome back.

Well, your answer should look something like this.

You write out the expression, force is mass times acceleration, put in the values from the question, and that gives you a resultant force of 3,900 newtons.

Well done if you've got that.

As usual with equations, we can rearrange 'em to find other values.

So, you might want to find acceleration or mass based upon Newton's Second Law.

So, if we wanna find acceleration a, we can start with the original equation, force equals mass times acceleration.

Then we can divide both sides of this equation by m or mass.

So we'll write it out like this.

And as you can see there's two masses on the right-hand side there, so the next stage would be to cancel those masses on the right side, and we're left with the expression force divided by mass is acceleration, which we can write out just the other way around, acceleration is force divided by mass.

To find the mass, again, we start with the original equation, force is mass times acceleration.

This time, we can divide both sides by the acceleration or a, and that gives us this expression.

And again, you can see there's two a's on the right-hand side there, a divided by a, so we can cancel those two accelerations, that gives us this expression, force divided by acceleration is equal to the mass, or mass is equal to force divided by acceleration.

So let's try and use those rearranged equations here.

I've got a force of 300 newtons acting on a skateboarder of mass 60 kilogrammes.

Calculate the acceleration of the skateboarder.

So I write out the version of the equation that's appropriate, and that's acceleration is force divided by mass.

I substitute in the values from the question, 300 newtons and 60 kilogrammes, and finally, I can write out the answer by doing that calculation, and it's 5.

0 metres per second squared.

I'd like you to try and calculate deceleration here, please.

So, I've got a bowling ball of mass 6 kilogrammes, calculate the deceleration when the frictional force is 1.

5 newtons.

So pause the video, work up that deceleration, and restart please.

And welcome back.

And you should have got a calculation something like this.

So the acceleration is 0.

25 metres per second squared, or you may have found acceleration of -0.

25 metres per second squared if you used a negative force in that calculation.

Well done if you've got those.

And the third version of the equation is used to calculate mass.

So we'll try a couple of examples of that.

So, I've got a force of 15 newtons that causes a ball to accelerate at 5.

0 metres per second squared.

Calculate the mass of the ball.

So I write out the expression for it, mass is force divided by acceleration, substitute the values in, and that gives me a mass of 3.

0 kilogrammes for the ball.

And you can have a go as well, so I'd like you to read this question and then calculate the mass of the ball, please.

Pause the video, calculate that mass, and restart.

Welcome back.

Well, substituting those values in, you should have noticed it's 30 kilonewtons, so 30,000 newtons, and you're dividing it by 0.

20 metres per second squared, and that gives an answer of 150,000 kilogrammes.

Well done if you got that.

Now we're gonna combine our techniques to find the resultant force, and then use that to find an acceleration.

So, I've got my spaceship taking off again here, at this time, I've got a few more forces on it.

I've got three upward forces from the rocket motors at 12 meganewtons, 6 meganewtons, and another 12 meganewtons.

And I've got the weight of the whole thing as well as 20 meganewtons.

And we're going to find its acceleration.

So the first step is to find the resultant force, and the resultant force is going to be the upward forces minus the downward forces.

So I'll write all those values in and I've put all my upward forces in a bracket there to keep 'em together so I can see that I'm talking about all of those together.

And then I've got the downward force of 20 meganewtons as well.

So that gives me a resultant force of 10 meganewtons upwards, 10 million newtons upwards.

The next thing I can do is find the acceleration using that resultant force.

So I'll write out my equation for acceleration, acceleration is forced divided by mass, and I substitute in my resultant force of 10 million newtons or 10 meganewtons and 2 million kilogrammes there, and that gives me an answer of 5.

0 metres per second squared.

Okay, I'd like you to calculate an acceleration.

I've got cyclist of mass 80 kilogrammes.

You can see there's a range of forces acting along them.

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

And welcome back.

And the answer to that is 2.

1 metres per second squared.

We can find the resultant force, it's 168 newtons to the right, and we can use that in the acceleration calculation, and that gives us an answer of 2.

1 metre per second squared.

Well done if you've got that.

And now we've reached the end of the first part of the lesson, and we've got to our first task.

So what I'd like you to do is to carefully read through these four questions and answer them for me, please.

So pause the video, work through the questions, and once you've got your answers, restart.

Welcome back.

And here's the answers to those.

You can see in my calculations I've used different versions of the Newton's Second Law equation.

So the first one, I've calculated a force of 3.

0 newtons.

In the second question, I've been asked to calculate a mass, and I've come out with 40,000 kilogrammes.

And for the third one, I've been asked to find the acceleration, and that turned out to be 5.

4 metres per second squared.

Well done if you've got those three.

And for the final question, question four, we needed to, first of all, calculate a resultant force.

What I've done is looked down the slope and up the slope, and I found the resultant force is 5,600 newtons down the slope.

Then I've used that to find the acceleration based upon that value and the mass of the car, and it's 3.

7 metres per second squared.

Well done if you've got that one.

Now it's time for the second part of the lesson, and we're going to be looking at the mass of an object and what mass means.

We can think of the mass of an object as the amount of matter, or stuff, or material in it.

And that matter is made up of a collection of atoms joined together in different ways.

Even the very smallest piece of matter we can see it contains an enormous number of atoms. So, if I've got a very small sample of carbon, there'd be something like 1.

2 times 10 to the 24 carbon atoms in this small sample.

That's a huge number.

This single red blood cell or one of these red blood cells here would still contain almost uncountable number of atoms, 1.

2 times 10 to the 17.

So, a vast number of atoms even in a single blood cell, which is too small for the human eye to see.

We measure the mass of an object in kilogrammes.

Kilogrammes are a scale of quantity.

They can simply be added together.

So if you've got 1 kilogramme and you add it to another kilogramme of material, you've just got 2 kilogrammes.

So they're very easy to add together.

So, for example, I've got a collection of gold bars here, and each gold bar, even though it's quite small, it's got a mass of 5 kilogrammes.

So I've got a collection of 12 gold bars.

So there's 12 times 5 kilogrammes, I've got a total mass of 60 kilogrammes.

We can also measure mass in smaller fractions.

So we can have 1 kilogramme being 1,000 grammes.

And if I've got a small collection of gold, perhaps a couple of gold rings, and each gold ring's got a mass of 5 grammes, then the total amount of gold I've got there is two times 5 grammes, and that's 10 grammes or 0.

01 kilogrammes.

The greater the mass of an object, the harder it is to cause it to accelerate.

If you pull an empty sledge across some ice, then it's going to accelerate more than you pull a full sledge.

So, for example, I've got this sledge here, it's an empty one, I'm using a force through a rope of 20 newtons and I get a fairly small acceleration, 0.

8 metres per second squared.

But if I increase the mass of the thing I'm trying to pull by sitting somebody on it, so now it's 80 kilogrammes, and I'm still using the same sized force to try and pull it, I get an even smaller acceleration, 0.

2 metres per second squared.

So, a larger object is harder to accelerate than a less massive object.

Okay, let's check if you understand that idea.

Which of these three balls shown here will require the smallest force to accelerate it at 10 metres per second squared? Pause the video, make a selection, and restart please.

Welcome back.

Well, the object that's easiest to accelerate will have the smallest mass, so the golf ball will accelerate, it's got lowest mass, it's easiest to accelerate.

Well done if you got that one.

Okay, I'd like you to complete this task now.

I'd like you to fill in the blank spaces within those sentences, and then look at the objects at the bottom there, and starting with the greatest, place them in order, which will accelerate the most when I use a force of 30 newtons on each of them.

So pause the video, work out your answers, and then restart please.

Welcome back.

Well, the missing words to these, "The mass of an object is the amount of matter within it." Mass is measured in kilogrammes.

The greater the mass of the object, the greater the force needed to accelerate it per metre per second squared.

And the correct order that is shown on the bottom, the tennis ball is the first, the small rock of 5 kilogrammes there, that's the second, and the shopping trolley is the third, and the fourth, well, the smallest acceleration would be the car, which would hardly accelerate at all.

Well done if you've got those.

And now we're onto the final part of the lesson.

And in this part, we're going to look at gravitational acceleration.

How an object accelerates when a gravitational force acts on it.

So let's start that.

Earth produces a gravitational field that acts towards its centre.

So you already know that objects are pulled towards the centre of the Earth, and that's because Earth has a gravitational field around it.

When we look at just a small part of the Earth, we can imagine that the gravitational field is what we call uniform.

All of those arrows are pointing downwards in the direction of that gravitational field, and it's towards the ground and then further towards the centre of the Earth.

So that's my gravitational field there.

If I placed a mass or any object with mass inside that gravitational field, there'll be a gravitational force acting on it that will act downwards.

So if I place this mass here, there'll be a force acting downwards due to gravity, and that force is going to try to cause the object to accelerate downwards.

So, the force accelerates in the direction of the gravitational field downwards, assuming there's no other forces on it.

If we place an object near the surface of the Earth, and by that I mean anywhere within a couple of hundred kilometres of the surface of the Earth, it's going to experience a force of about 9.

8 newtons acting downwards per kilogramme.

And that's towards the centre of the Earth.

So we say the gravitational field strength, the strength of gravity on Earth, g, is 9.

8 newtons per kilogramme, 9.

8 newtons for every kilogramme of mass.

And so I've got 1 kilogramme of mass here, and it would have a force of 9.

8 newtons.

That value of g, that 9.

8 newtons, will be given to you as part of any question because there can be slightly different values depending on how many significant figures are wanted.

So, for example, quite often we round that to just a single significant figure, and we give a value of g as 10 newtons per kilogramme.

So my 1 kilogramme mass would have a 10 newton force acting on it.

We can find the acceleration caused by Earth's gravity acting on different masses like this.

So, imagine I've got 1 kilogramme, it's going to have a force on it of 1 kilogramme times 9.

8 newtons per kilogramme.

So if I write my expression for acceleration, acceleration is force divided by mass, force, as I've just said, is 1 times 9.

8, that's gonna be divided by the mass, which is 1 kilogramme.

That gives me an acceleration of 9.

8 metres per second squared.

Now, imagine I've got 2 kilogrammes of mass.

Well, now the downward force is gonna be 2 times 9.

8 newtons.

So if I calculate the acceleration this time, I write it out, acceleration is force divided by mass, it's 2 times 9.

8 newtons divided by 2 kilogrammes, that gives me 9.

8 metres per second squared again, because the 2s are cancelling each other though.

I try again with 3 kilogrammes, and I get exactly the same result.

What's happening is, no matter what the mass is, the acceleration due to Earth's gravity, is always 9.

8 newtons per kilogramme.

It doesn't depend upon the mass of the object.

So, any object near the surface of the Earth will have an acceleration due to gravity of 9.

8 metres per second downwards.

And it doesn't matter what the motion of the object is or what the mass of the object is, all of the objects will be accelerated exactly the same way, 9.

8 metres per second squared downwards.

And that acceleration will affect objects thrown upwards.

So if I've got a tennis ball like this, there's always going to be a downwards force, due to gravity acting on it, no matter which way the ball is moving.

So I'm always going to have an acceleration that's downwards.

So even when the object's moving upwards, it's being accelerated downwards by gravity.

Let's have a look at what I mean by that by considering a ball at three stages in its motion.

So, initially, I've thrown the ball upwards and it's still moving upwards, but even though it's moving upwards, it's going to have a force acting on it, acting downwards, the gravitational force is gonna be pulling the ball downwards and accelerating the ball downwards.

What that's going to do is cause the ball to slow down.

So, that ball is moving upwards but slowing as it rises because of that downwards acting force.

So, the acceleration is down that way, the ball is slowing down.

The second part of the motion, I've got a ball where it's stopped, it's at the top of its motion so it momentarily stops, it's got no velocity, and at that point, I've still got that downward force acting on it and it's going to continue to accelerate downwards.

And obviously, what that's going to do is gonna start to make the ball fall downwards.

So a bit later in the motion, the ball is now moving downwards because it's been accelerated downwards and it's speeding up down towards the ground.

The ball's going to accelerate as it falls because that force is still acting, so it's still got an acceleration downwards, and the ball is speeding up in that situation.

Let's see if you can describe the motion of the ball then.

I've got Laura, she throws a ball straight up into the air.

As it rises, it slows down, as it falls, it speeds up.

And I'd like you to draw lines to match the part of the motion to the acceleration that the ball feels.

So pause the video, have a think about that, draw lines between those dots, and then restart please.

Welcome back.

Well, if you thought about it carefully, you'd see when the ball is rising, it's gonna be accelerating downwards because there's a force acting downwards, the force of gravity.

When it's reached its highest point, that force is still there, it's still accelerating downwards.

And as it's falling downwards, it's still gonna be accelerating downwards, so it's going to be getting faster as it falls.

Well done if you drew those three lines all to 9.

8 metres per second squared downwards.

So the acceleration of an object is the same size, no matter what the mass of the object is, they'll all fall at the same rate.

So if I've got a couple of objects and I hold 'em above the ground, so I've got some examples here, a 1 kilogramme block and a 10 kilogramme block, and they're 10 metres above ground level.

And if I drop them, they should reach the ground at the same time.

And it would take the 1 kilogramme block, 1.

4 seconds to reach the ground.

And similarly, with the 10 kilogramme block, it would fall at the same rate, accelerate at the same rate, and reach the ground at exactly the same time.

That's only true if there are no other forces acting though.

So, in reality, if I try to drop those two blocks, air resistance might make a small difference when I'm dropping something from 10 metres.

But if there's only a gravitational force, all the objects would fall at exactly the same rate and reach the ground at the same time.

As I mentioned, air resistance and drag will actually have an effect.

And so, that will alter the time it takes for an object to reach the ground as they fall through Earth's atmosphere.

The drag force actually increases as the object gets faster as well.

So, if we've got a more realistic example, I've got here a feather and a stone, and I'm gonna drop them from 10 metres, and I carry out an experiment.

It takes the feather 5.

2 seconds to reach the ground from that height, and the stone falls very quickly and it only takes 1.

4 seconds.

And that's because the drag on the feather matches the weight of the feather quite quickly 'cause it's very light and it stops accelerating as it's falling, it reaches a maximum falling speed.

But the stone, in a 10-meter drop, never actually reaches that maximum speed.

Okay, I'd like you to have a think about air resistance.

I've got three sports balls here, they've all got different diameters.

And I'd like you to have a think about which of them would have the greatest air resistance acting on it when they're all moving at 5 metres per second.

So pause the video, make your decision, and restart.

Welcome back.

The answer to that was the football.

It's got the largest diameter.

It's gonna have to push the most air out the way as it's moving per second, and that's gonna have the greatest (indistinct) force on it.

Well done if you've got that.

Okay, now it's time for the final task of the lesson, and it's about planning an investigation.

Izzy wants to find out if all objects are accelerated at the same rate by Earth's gravitational field, and she's going to use a set of different sports balls to do that.

So what I'd like you to do is to write a plan that will allow Izzy to find out if that acceleration is the same for all the objects.

And you can see the parts of the plan I want you to include there.

So, pause the video, write out a plan that would allow Izzy to verify that, and then restart when you're done.

Okay, welcome back.

Well, here's my plan.

Yours might not be exactly the same, but it should be something similar to this.

So we want balls of similar diameters but different masses.

We want a top pan balance to measure the mass of balls, and a ruler to measure and verify the diameter of the balls, a tape measure, and a timer.

I've got a simple diagram there, and it shows me what I'm gonna do is I'm gonna drop the different balls from a height of 2 metres, and I've used a line on the wall for that, and I'm gonna time how long it takes them to fall through that 2 metres.

The next part of the method should be something like this step-by-step instructions, and it should include these sorts of details.

I've measured a mark on the wall for a fixed height to drop them.

I dropped the ball from the height, timing how long it takes to reach the floor.

I repeat a few times so that I can get a mean time to eliminate some random errors there.

And I test the ball with different masses but similar diameters 'cause I need the test to be fair.

And I've got an example results table there where I've got three different times and a mean time calculated.

And the part about fair testing should be along these lines.

We need to use similar diameter balls so the air resistance is similar for them all.

And we've got to drop them from the same height, otherwise they're gonna fall through different distances and obviously take different times.

So, well done if you've got those parts of the plan.

Now we've reached the end of the lesson.

So here's a summary of everything we've learned.

Newton's Second Law of motion is stated as F equals ma, where force, F, is measured in newtons, mass, m, is measured in kilogrammes, and acceleration, a, is measured in metres per second squared.

The mass of an object is the measurement of the amount of matter or substance it contains.

And all objects fall within acceleration of g, which we use a value of 9.

8 metres per second squared or 10 near the surface of the Earth.

And that assumes that air resistance is negligible, there's no air resistance.

Well done for reaching the end of the lesson.

I'll see you in the next one.