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

This lesson's called force, mass and acceleration.

And in it, you're going to be carrying out an investigation, which links those three factors.

By the end of this lesson, you're going to have planned and carried out two investigations, which link force and mass to the acceleration of an object.

You're going to use the results of those investigations to discover the relationship between those variables.

The keywords you need to help you understand the lesson are here.

And the first is air track and an air track is a stretch track which uses small jets of air to lift up a glider and allow it to float friction free.

Directly proportional, which is a relationship where one value is a constant multiple of the other.

Inversely proportional where the relationship between a variable is one value halves each time the other variable doubles.

And finally, Newton's second law of motion, which states that the acceleration of an object is directly proportional to the resultant force acting on it and also inversely proportional to its mass.

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

The lesson's in three parts.

And in the first part, we'll discuss the basic setup of the experiment and then describe how we can carry out an investigation linking acceleration and mass.

In the second part of the lesson, we'll do a very similar experiment, but this time, we're going to try and find the link between acceleration and the resultant force acting on an object.

And in the third part of the lesson, we'll bring all the results together to discover Newton's second law of motion.

So when you're ready, we'll start with our investigation of acceleration and mass.

During these experiments, we're going to be using something called a linear air track.

Linear just means a straight line and an air track is basically a hollow tube with small holes in it and air is pumped into it so that it produces small jets of air upwards that affect a glider that will float on top of it.

So here's a simplified image of one here.

And as you can see, I've got a glider on top of it and that's just basically similar to a trolley.

It's a small mass that moves to the left or right.

The linear air track produces small jets of air through these holes that lift that glider upwards.

So it actually hovers slightly above the track and that basically eliminates the frictional forces.

There are still some drag forces on the trolley, sorry, the glider as it moves, but they're very small.

So the glider floats on top of the air track and we can use a small mass to accelerate it by hanging that mass on the end of a pulley.

So as you can see here, I've got the glider floating on top of the linear air track and then through a small piece of thread, I can attach some masses over that pulley.

And what that's going to do is the masses are going to be pulled downwards by gravity and that's going to cause the string to have a tension in it and that's going to pull the glider across.

So the glider is gonna slide to the right in that diagram.

It's going to accelerate in the direction of the arrow.

You can change the mass of the glider by adding small masses to its side or top, depending on its exact design.

In my design, I've got a little attachment at the side and I can put 20-gram masses on it.

We can also change the size of the accelerating force by adding extra masses on the end of the pulley there.

So putting another mass on that mass holder will give a greater accelerating force.

We'll need to measure the speed of the glider after it's been accelerated for a while.

So to do that, we're going to use a light gate and the light gate's gonna be positioned towards the end of the track.

So the glider has had some time to accelerate and reach a reasonable velocity.

So the small light gate is placed there towards the end of the track and the light gate operates when the glider passes underneath it, and a piece of card cuts the beam, triggering a timer and then allows the beam to rejoin again after the card's passed and that stops the timer.

So I need a small piece of card on top of the glider of a measured length so it's positioned there in my diagram.

We also need to measure the time it takes for the trolley to reach the light gate after it's been released.

And to do that, we can use a manual timer, such as a stopwatch.

So the first task of the lesson, why is the light gate used to measure the speed instead of using some sort of manual timing system to measure the speed? Is it A, the light gate can measure slower speeds than a human? B, the light gate eliminates human reaction time.

C, the light gate measures both distance and time.

Pause video, make your selection and restart, please.

Welcome back.

Well, the light gate eliminates human reaction time.

So the answer is B.

Well done if you got that.

We're going to be able to find the acceleration of the glider using the acceleration equation.

And as you should recall, it's like this.

Acceleration is change in velocity divided by time or acceleration is final velocity minus initial velocity divided by time.

Now, we're going to be starting the glider from rest.

So it's gonna be stationary at the start.

So its initial velocity's gonna be 0 metres per second.

So that allows us to simplify the equation there slightly because u is going to be zero.

So now we can just say acceleration is final velocity divided by time or a is v divided by t.

To find the acceleration of the trolley then, we need two measurements.

We need to find the acceleration from velocity and time.

The time taken for the glider to reach the light gate, that's the time t.

And we're going to measure that manually with the stopwatch.

And the velocity of the glider when it reaches the light gate is v, and that's going to be measured by the light gate and a connected computer system.

So let's have a look at calculating an acceleration based upon some example data before we start the experiment.

A glider is released and it takes 9.

66 seconds to reach the light gate where it's travelling at 9.

98 metres per second.

Calculate the glider's acceleration.

So pause the video, Decide which of the four answers is correct and restart, please.

Welcome back.

Well, the answer was 1.

5 metres per second.

Again, here's the equation.

If we substitute the values for velocity and time into that, we get an acceleration of 1.

48 metres per second squared, which rounds to 1.

5 metres per second squared.

Well done if you got that.

In the first experiment, you're going to try and find the relationship between the mass of the glider and the acceleration when there's a constant force acting on it.

And for that, to keep the accelerating force constant, we need to keep the total mass on the holder the same for each run.

So we're keeping that accelerating force constant by having the total mass the same on the end of that string.

The mass of the glider system needs to be varied for each run.

So we're going to add small masses to the side of the glider each time we run the experiment so that we are changing the mass of the glider, the mass that's moving.

And finally, we need to measure the acceleration of the system by getting the final velocity and the time and doing the calculation.

Let's check that you understand the type of variables in the experiment.

I'd like you to decide which of these is the independent, the dependent, and the control variable, please.

So pause video, decide which is which, and then restart.

Welcome back.

Well, the mass of the glider system, that's the independent variable.

That's the thing we're changing during the experiment.

The size of the accelerating force or the number of hanging masses is the control variable.

We're keeping that constant throughout the experiment, and the dependent variable, the thing that's going to change because we're changing something is the acceleration of the glider system.

So that's the dependent variable.

Well done if you got all three.

Okay, now it's time for you to actually carry out the experiment to find the relationship between acceleration and mass.

All of the instructions are here.

So I'm going to ask you to follow through each of those steps in turn and I'll show you a brief video to see the idea in practise.

So here's that video.

The linear air track is used to reduce friction.

The balance is used to measure the mass of the glider and any masses attached.

The glider is placed on the air track attached to a string which will pull it.

Masses are hung over a pulley to provide a constant pulling force.

A light gate is used to measure the velocity of the glider near the end of the track.

And the timer is used to measure the time taken for the glider to reach the light gate.

The glider is released and its velocity and the time it takes to reach the light gate is recorded.

Add a 20-gram mass to the glider and repeat the process.

Continue adding masses until 100 grammes has been added and collect your results in a table.

An example results table is shown here.

Okay, and I'm gonna ask you to follow each of those steps in turn, but you're going to need a results table as well.

So here's the results table and I'll need you to complete that.

Looking at the start, remember, you have to measure the mass of the glider and the mass holder and fill it in, and then complete this results table for the total mass and final velocity and time.

And we'll calculate the accelerations as well using that equation.

So by the end, you'll have a fully completed results table.

So pause the video, you can go back to the instructions if you need to and then complete this table.

And once you're done, restart this video.

Welcome back.

Well, this is my completed results table for a set of experiments I did.

And as you can see, I've completed it in, I've calculated the acceleration based upon the time and the final velocity.

And I've got a set of data there, and it looks like there's a fairly obvious pattern and we'll analyse that a bit later in the lesson.

So well done if you got results like this.

Okay, now it's time for the second part of the lesson and in it, we're going to do a very similar investigation to collect more data about a slightly different relationship.

We're going to investigate the relationship between the acceleration and the force that's causing that acceleration.

So let's have a look at that.

So as I mentioned, the acceleration is also gonna depend upon the force acting on the glider.

So I've got my basic setup here and what I want to do in this experiment is change the size of the force that's acting on the glider and see if that has any effect on the acceleration.

The size of the accelerating force can be changed if we add masses to the end of the mass holder over the pulley there.

So we want to actually change the size of that force by adding masses there.

But there is a slight issue with that that we'll need to think about.

So adding that mass increases the force.

Adding another mass increases the force further.

But if I add masses to the end of the pulley like that, what I've actually done is change the total mass of the system.

I've changed the mass of the glider and everything put together, a system that's moving and that's unfair.

It makes the test unfair because I've altered a factor besides the force.

I've changed the force but I've also changed the mass at the same time.

Okay, I'd like to see if you can come up with a solution for that problem of keeping the mass constant while changing the force.

And I've got three options for you to choose from here.

So which of these would keep the overall mass of the system the same while changing the accelerating force? So have a read of those three options and make your decision.

Pause the video and then restart when you're done.

Welcome back, the correct answer though was taking mass off the top of the glider and moving it to the mass holder.

If you're taking the mass off the glider and putting it onto the holder, then the overall mass of the system hasn't changed.

You've still got the same amount of moving mass.

If you chose the first option, well, that would increase the overall mass of the system and that wouldn't be a fair test.

And that second option would decrease the mass of the whole system and that wouldn't be a first test either.

So well done if you chose option C.

And now it's time for you to carry out the second experiment where you investigate the relationship between acceleration and force.

And I can show you a quick Video that outlines the process.

Here it is.

The linear air track is used to reduce friction.

The balance is used to measure the mass of the glider and any masses attached.

The glider is placed on the air track attached to a string which will pull it.

Masses are hung over a pulley to provide a constant pulling force.

A light gate is used to measure the velocity of the glider near the end of the track.

And the timer is used to measure the time taken for the glider to reach the light gate.

The glider is released and its velocity and the time it takes to reach the light gate recorded.

Take one of the small masses off the glider and add it to the mass holder.

This will increase the accelerating force but not change the mass of the system.

Repeat the experiment with this new accelerating force and record the velocity and the time again.

Use a range of accelerating forces and record all of your results in a table.

An example table is shown here and as usual, I've got a full set of instructions here that you can follow.

So you can come back to this slide to see the instructions if you need to.

You'll also need a results table, which looks like this.

And again, I'd like you to fully complete that table.

I'd like you to get the final velocity and the time for different accelerating forces and also calculate the acceleration column for me using the equation there.

So pause the video, carry out the experiment, and then restart when you're done.

And welcome back.

Here's my completed table for an experiment I carried out.

And as you can see again, the acceleration is different for different accelerating forces and we'll look for a pattern in those results in the final part of the lesson.

Well done if you got something like this.

And now we've reached the final part of the lesson and in it, we're going to look at the results of both of the experiments we've carried out and come up with something called Newton's second law of motion to see if our data matches it.

So let's look at that.

Let's start by looking at the relationship between the accelerating force, the size of the force acting and the acceleration.

And I've got a table of data here based on my results and I think we can see a fairly simple relationship.

As the accelerating force increases there, you can see the acceleration is also increasing, so it can reach a simple conclusion like the results show as the acceleration increases as the force of the glider increases.

So a greater force is causing greater acceleration.

I think we should look at a graph to see if there's a more formal relationship between those two variables.

So I'm gonna plot all that data on a graph and this is the graph I come up with.

I've plotted each of those points on a force against acceleration graph here.

And as you can see, I've drawn a line of best fit there in blue and that line of best fit shows me that it's a straight line and it passes through the origin.

Now, I can reach a conclusion based upon those two things and that conclusion is acceleration is directly proportional to the force.

So when I increase the force, the acceleration increases by a constant multiple of it.

And I can write that as acceleration is proportional to force like this.

Let's see if you understand that with the true and false question and some justification.

So I've got a graph here, I'd like you to decide if this statement is true and which of those justify your answer.

So pause the video, make your decisions and restart, please.

Welcome back.

Well, that relationship is true, it's directly proportional and the reason that it's directly proportional is well, that's true and that's true.

Both of those have to be true for us to say that the relationship is of direct proportion.

Well done if you selected all of them.

And now it's time to look at the relationship between the mass of the glider and the acceleration.

And this one's not quite so obvious, so we'll go through that carefully.

I've got the total mass of the moving system there.

It goes from 320 grammes up to 420 and the acceleration.

And as you can see, as the mass of the system increases, these numbers are decreasing.

So the acceleration is getting less when the mass of the system is increasing.

So I can say something like the results show that the acceleration decreases as the mass of the glider system increases and therefore, the acceleration can't be in direct proportion to the mass because we're not going to get a line that passes through the origin or is straight for this sort of relationship.

So I've plotted a graph of that data here and I'd like you to say how does that graph show that the acceleration of the glider is not directly proportional to its mass? So pause the video.

Select correct options and restart, please.

Welcome back.

Well, you should have selected B, the line of best fit does not pass through the origin and we need that for direct proportion.

So that's not true there.

And also, the line of best fit is a curve.

If you look very carefully at that line, it is curving, it's not a straight line.

So those two are reasons that we can say it's not in direct proportion to the mass.

Now, there is another possible relationship and that's one of inverse proportionality.

In that case, we would find that acceleration is proportional to one divided by the mass.

So what I've done with my results is I've converted them to kilogrammes to make the mathematics a bit easier.

And then I've added a column that's one divided by the total mass, so one over the mass.

And when I look at that, I can see it is possible that that relationship is true, that the acceleration is inversely proportional to the mass.

So I'm going to plot a graph of one over mass compared to acceleration and see if it is true.

So I've plotted my results here and I've got acceleration on the -yaxis, but this time, I've got one divided by mass on the x-axis there.

And if I try and draw a line of best fit now, it is straight and it does pass through the origin so I can reach the conclusion that acceleration is inversely proportional to the mass.

So that's my second conclusion and I can write it like this.

Acceleration is inversely proportional to the mass or it's proportional to one divided by the mass.

So my two conclusions of the experiment are these: acceleration is directly proportional to the force.

And acceleration is inversely proportional to the mass.

And I can combine both of those relationships together to give me this single relationship: acceleration is proportional to the force divided by the mass.

So that's my final conclusion of both of those experiments.

Acceleration is proportional to the force divided by the mass.

Isaac Newton first proposed that relationship between acceleration, force and mass in his laws of motion.

In fact, his second law of motion, and he expressed it like this, he said, "The acceleration of a body is directly proportional to the resultant force acting on it and inversely proportional to its mass." And that's exactly the same conclusion we got from our experiment.

If we choose to measure the force in newtons, the relationship simplifies to this.

So acceleration is force divided by mass.

Newton's second law of motion is usually written in this format: force equals mass times acceleration or F = ma where the force is measured in newtons, the mass is measured in kilogrammes and the acceleration is measured in metres per second squared.

Let's check if you understand Newton's second law and how it's written out.

Which of these is a correct rearrangement of Newton's second law? So which of these can we find from the F = ma equation? So pause the video, make your selection and restart.

Welcome back.

Well, this is the rearrangement that you could have chosen.

There are actually three possible arrangements of the equation in terms of acceleration, force or mass.

And they're written out here.

Acceleration is force divided by mass, force equals mass times acceleration or mass equals force divided by acceleration.

Okay, now it's time for the last task of the lesson.

I've got a dynamics trolley pulled along a flat bench by falling weight.

I'd like you to predict what will happen to the acceleration if the mass of the trolley is doubled, the accelerating forces doubled by adding masses and both the mass and accelerating force are halved.

And then I'd like you to suggest why the result of this experiment might not exactly match Newton's second law.

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

Welcome back.

Well, the answers to those are if the mass of the trolley is doubled, the acceleration halves, it's inversely proportional to the mass.

If the accelerating force is doubled by adding masses, the acceleration doubles.

And if both the mass and accelerating force are halved, the acceleration stays the same.

One of them increases the acceleration and the other decreases it.

So the acceleration is the same as it was in the first place.

Well done if you got those.

And for the second one, why won't the results exactly match Newton's second law? Well, there's going to be a frictional force acting in this sort of scenario and that's going to alter the acceleration because it's going to reduce the resultant force.

So it's not going to be exactly the same.

And also, adding masses over the desk will increase the mass of the moving system.

So you'll not be carrying out a completely fair test.

So well done if you got answers like this.

We've reached the end of the lesson and here's a summary of the information.

The acceleration of an object can be investigated using a linear air track and that reduces the effect of friction.

And you can see a diagram of how we can set up the experiment there.

And we found from those experiments Newton's second law of motion and it states that the acceleration of an object is directly proportional to the resultant force acting on it and inversely proportional to the mass of the object.

So a is proportional to F divided by m.

Well done for reaching the end of the lesson.

I'll see you in the next one.