Lesson video

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 get to use that law to perform a range of calculations.

Here are the keywords that will help you with this lesson.

And the first is resultant force.

And the resultant force is the overall effect of a set of forces acting on an object.

Acceleration, and that's caused by a resultant force acting and that results in a change in speed and/or direction of movement.

And there's mass and we can describe that as the amount of matter in an object, measured in kilogrammes.

And then we have another definition of mass, which is inertial mass and that's the mass as determined by Newton's second law of motion where the mass is the force divided by the acceleration.

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 are being 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 his second law is stated as this, the acceleration of a body is directly proportional to the result of force acting on it and inversely proportionate to its mass.

If we measure force in Newton's, 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 = 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 are correct? And you can see the two spaceships there.

We'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, 2F on it.

So read through these 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 a space shuttle taking off here and I've got some forces acting on it.

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

So I can find a result in force like this.

Resultant is the upward forces minus the downward forces.

So that's 12 mega Newtons plus 12 mega Newtons.

They both upwards, and take away the downward force of 20 mega Newtons and that gives me a resultant force of four mega Newtons 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 result of 380 Newtons.

Well done if you got that.

We can apply Newton's second law to any acceleration including decelerations.

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

I've got a result of force active on a van, that's in the same direction that the van is moving.

And what's gonna happen though 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 cyclist is going to slow down or decelerate.

And we can try examples that involve calculations.

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

0 metres per second squared.

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

And so to do that I would write up 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 at 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 we 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 for mass.

So we 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 forced 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 it 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 forced 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 a deceleration here please.

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

5 Newtons.

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

And welcome back, and you should have got a calculation of something like this.

So the acceleration is 0.

25 metres per second squared or you may have found acceleration of minus 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'll write out the expression for it.

Mass is forced 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 kilo Newtons or 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, this time I've got a few more forces on it.

I've got three upward forces from the the rocket motors, 12 mega Newtons, six mega Newtons, and another 12 mega Newtons.

And I've got the weight of the whole thing as well as 20 mega Newtons, 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 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 mega Newtons as well.

So that gives me a resultant force of 10 mega Newtons upwards, 10 million Newtons upwards.

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

So I write out my equation for acceleration.

Acceleration is force divided by mass and I substitute in my resultant force of 10 million Newtons or 10 mega Newtons 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 a cyclist of mass 80 kilogrammes.

You can see there's a range of forces acting on 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 metres 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.

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 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 a 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 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 and 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, I think too small for the human eye to see.

We measure the mass of an object in kilogrammes.

Kilogrammes are a scaler quantity, they can simply be added together.

So if you've got one kilogramme and you add it to another kilogramme of material, you've just got two 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 five kilogrammes.

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

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

We can also measure mass in smaller fractions.

So we can have one kilogramme being 1000 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 five grammes, then the total amount of gold I've got there is two times five grammes and that's 10 grammes or 0.

01 kilogrammes.

The greater than 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'd 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 size force to try and pull it, I'll 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 your 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've got that one.

We can define mass using Newton's second law of motion.

So instead of just saying it's the amount of stuff in it, we can actually have a more formal definition.

And that's based on a concept called inertia.

The inertia of an object is its tendency to resist acceleration, how difficult it is to accelerate.

So we have something we can call the inertial mass.

And that's based upon, as I said, Newton's second law of motion.

The inertial mass of an object is based upon this relationship: mass is forced divided by acceleration.

So if we have an object with an inertial mass of one kilogramme, it'll accelerate at one metre per second squared if we put a resulting force of one newton on it.

So here's an example of that.

We've got a ball, it's one kilogramme, I put one newton on it and it will accelerate at one metre per second squared.

'cause if you substitute all those values in the equation, they're all ones, and one equals one.

Okay, let's see if you understand the concept of inertial mass.

I've got three spaceships here.

They've all got different inertial masses, they've all got different masses, and I'm applying a force of 500 Newtons to each one of them.

And I've shown the resultant acceleration due to that.

So which one of those must have the greatest inertial mass? Pause the video, make your decision and restart.

Welcome back, the answer to that is B.

That one's got the smallest acceleration for the force of 0.

2 metres per second squared there, so it must have the greatest inertial mass.

You can measure the inertial mass of something by putting a force on it and measuring its acceleration.

So I could have a dynamic trolley system here and I'm using a string to put a force in it through some hanging weights.

I've got a trolley system here, it's result forces not 0.

40 Newtons.

I could then measure its acceleration, let's say it's not 0.

25 metres per second squared.

And then I could find the mass of the trolley system, that's the trolley and the falling masses as well.

And I could use the equation mass equals force divided by acceleration and that gives me 0.

4 Newtons divided by 0.

25 metres per second.

So the overall system would have a mass of 1.

6 kilogrammes.

It's now time for the second task of the lesson.

So what I'd like you to do is this.

Complete those statements there by filling in the blanks with single words and then use the information in question two to find the inertial masses for the rock and the car.

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

Welcome back, well let's have a look at the missing words.

We've got the mass of an object is the amount of matter within it.

Mass is measured in kilogrammes.

The inertial mass of an object is defined by Newton's second law of motion.

Well done if you've got those.

For the next ones, find the mass using mass is force divided by acceleration.

So the rock weighs eight kilogrammes and for the car you have to work out the resultant force acting on it.

So that's 500 Newtons minus 200 Newtons and divide that by the acceleration.

And that gives me a mass of 2,000 kilogrammes.

Well done if you 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 place a mass or any object with mass inside that gravitational field, there'll be a gravitational force acting on it, and 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 a 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 one 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 one kilogramme mass would have a 10 Newton force acting on it.

We can find the acceleration caused by earth gravity acting on different masses like this.

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

8 Newtons per kilogramme.

So if I write my expression for acceleration, acceleration is force divided by mass.

The force as I've just said, is one times 9.

8.

That's gonna be divided by the mass, which is one kilogramme.

That gives me an acceleration of 9.

8 metres per second squared.

Now imagine I've got two kilogrammes of mass.

Well now the downward force is going to be two times 9.

8 Newtons.

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

8 Newtons, divided by two kilogrammes.

That gives me 9.

8 metres per second squared again, because the twos are cancelling each other there.

I try again with three 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 downward force due to gravity acting on it no matter which way the ball's 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 going to be pulling the ball downwards and accelerating the ball downwards.

And 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 is 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's rising, it's going to 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 square 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 one 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 one 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.

When 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's stops accelerating, as it's falling it reaches a maximum falling speed.

But the stone in a 10 metre drop never actually reaches that maximum speed.

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 five 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 going to have to push the most air out the way as it's moving per second, and that's going to have the greatest drag 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 our top pan balance to measure the mass of the 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 going to do is I'm gonna drop the different balls from a height of two 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 two 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 drop 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 going to fall through different distances and obviously take different times.

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

And now we've reached the end of the lesson.

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

Newton's second lower motion states F equals ma.

Where force is measured in Newtons, mass is measured in kilogrammes, and acceleration is measured in metres per second squared.

The mass of an object is the measurement of the amount of matter in it or the inertial mass of the object is its resistance to acceleration given by M equals F divided by A where M is the inertial mass there.

All objects fall with an acceleration of G, which is typically given as a value of 9.

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

And that assumes there's negligible or no air resistance.

Well done for reaching the end of the lesson.

I'll see you in the next one.