Hello there, I'm Mr. Forbes and welcome to this lesson for measuring and calculating motion.

In this lesson we're going to be looking at the results of an investigation into acceleration and trying to analyse them to see if there's a pattern in them.

In this lesson we're gonna look at an acceleration investigation and try and find out if there's a relationship between acceleration and the force acting on the object.

And to do that we'll need to take into careful consideration the control variables and how we make sure that they stay the same to make the test fair.

We're also gonna process a set of results to see if there's a pattern, and reach a conclusion, and then we'll look at making a range of improvements to the experiment to make it better.

Here's a list of the keywords that will help you throughout the lesson.

The first of them is compensated ramp.

And a compensated ramp is a ramp with a very slight tilt on it to compensate for the effect of friction.

And there's final velocity.

And that's the velocity of the object after it's accelerated.

Next is light gate and a light gate is a device that we use to measure the speed of an object.

When the object passes through the gate, we can measure the time it takes to pass through.

And repeatable, measurements are repeatable if you can repeat the experiment and get very similar results.

And finally, uniform acceleration, which is a term we use for a constant amount of acceleration.

And here's the definitions of those keywords again, and you can return to this slide at any point during the lesson.

This lesson is in three parts and in the first part we're gonna look at how we can make the investigation into acceleration fair by identifying and controlling the key variables.

In the second part, we're going to use the data we've collected to see if there's a relationship between the force acting on a dynamic trolley and the acceleration it experiences.

And in a third part we'll focus on identifying a range of improvements for the experiments to get more accurate results.

So when you're ready, let's start with looking at how to make the experiment fair.

So throughout this lesson, we're going to be discussing an experiment where we've accelerated a dynamics trolley by using a range of forces generated by hanging some masses from the end of a desk.

So a setup similar to this.

As you can see, I've got a dynamics trolley on a horizontal or flat track.

It's attached by a piece of string to some hanging masses.

What that does is the hanging masses produce a downwards force that's transferred by the spring to the dynamic trolley causing it to accelerate.

And by varying those hanging masses, I can vary the force acting on the trolley.

There is a very small frictional force that acts on the trolley as well and we'll discuss that later in the lesson.

And what we do is we measure the increase in velocity of the trolley over a period of time and we can use that to calculate the acceleration.

As we're trying to find a relationship between the force acting on the trolley and the acceleration of the trolley, it's very important that we try a fair test.

We look at all the other factors that could influence the acceleration of the trolley and we try and keep those constant.

Now there are two important factors in this experiment that are clearly identified.

And the first of those is we need to eliminate the effect of other forces acting on the trolley because we just want to look at the effect of that accelerating pulling force through the string.

To do that, we'll need to find a way of reducing any frictional forces that might be slowing the trolley down during the experiment.

The second one is not quite as obvious, but we're looking at the effect of the force on the trolley and we need that to stay the same.

We've been adding and taking away masses on the string attached to the trolley and those masses are actually part of the moving object.

So we need to keep the mass of the accelerating object the same throughout the experiment.

And that's an issue because we're taking masses off the end of the string and putting masses back on and that's going to alter the mass of the overall moving object.

So we're gonna look at the effect of both of those and how we can eliminate those problems. Let's start by looking at the first of them.

As the trolley rolls across the surface, there's more than one force acting on it.

So we actually want just this force, just this accelerating force making the trolley move because that's the force we can measure quite easily 'cause we're controlling the masses on the end of the string and we know what force each mass produces.

But we've got forces like friction and drag affecting the trolley as it accelerates.

And what we want to do is to try and eliminate those two forces to make this a fair test.

Now those forces are small, but they could have an effect and we really want to make them as small as possible or ideally take them out the equation completely.

One way to reduce the effect of friction is to actually use a slightly tilted ramp like this one.

This one's tilted by just a couple of degrees.

What that's going to do is the frictional force is going to be acting to try and slow the trolley down, but because I've got a very slightly tilted ramp that's going to actually provide a very small force on the trolley as well, a constant force.

And that force, if I get it just right, balances the effect of friction.

So by carefully tilting the ramp, I can eliminate some of the effects of friction and get just the accelerating force that I'm measuring from the masses.

That type of ramp with a very slight tilt on it where I've adjusted it to be just right is called a compensated ramp.

It compensates for the effect of friction.

I can tilt the ramp to any angle, but to compensate for friction, I've got to actually tilt it at exactly the correct angle.

If I've got a ramp that's too steep, then the force it's going to produce on the trolley is going to be larger than the frictional force as shown in this diagram here.

What that's going to do is gonna cause the trolley to accelerate more than it should.

So I've over tilted the ramp in that situation.

But on the other hand, if I don't tilt the ramp enough, I'm going to get a force that's gonna compensate for some of the friction but not all of it.

So in this case, I've got a ramp that's too shallow.

What I've got to do is adjust the ramp so it's just right so that the frictional force exactly matches the force produced by the ramp.

Now I need to know that the ramp is tilted to exactly the correct angle and if it is then any trolley that I place on it, if I don't put on those forward forces via the string, then the trolley would roll down the ramp at a constant velocity.

It wouldn't be speeding up or slowing down so it's not accelerating.

And I can check that by checking the speed of the trolley near the top of the ramp and near the bottom of the ramp.

And if the trolley's moving at the same speed in those two sections, then it's not accelerating.

I can check that by doing some timing measurements like this.

So I've got start marker and an end marker near the top of the ramp and a start marker and an end marker near the bottom of the ramp.

And I've timed how long it takes the trolley to pass between those two markers.

And what I can do then is calculate its velocity at the top of the ramp and its velocity at the bottom of the ramp to see if it's the same.

So I can do this calculation on this, taking the measurements from the table and I can see near the top of the ramp it's going at 0.

5 metres per second and near the bottom of the ramp it's going at 0.

59 metres per second.

That means that the trolley's actually speeding up.

So I've over tilted my ramp, it's too steep, so I need to adjust it and make it a bit shallower.

What I'd like you to do now is to use a set of data to see if a ramp is too steep, too shallow, or just right.

So I've got a trolley and it's being released on a ramp and the time it takes to pass between two markers 10 centimetres apart near the top and near the bottom has been measured and recorded in that table there.

What I'd like you to do is to look at the data in that table and decide, is the ramp too steep? Is it too shallow, or is it just right to counter effect the forces of friction? So pause the video, work out that, and then restart please.

Welcome back.

Well hopefully you selected the ramp is too shallow.

If you look at the timing there, the time differences increased, so the trolley's actually slowing down as it moved down the ramp.

So I need to tilt that ramp a little bit more to counteract friction.

Well done if you've got that.

Let's have a look at a second example.

So it's the same scenario.

I've got a trolley released on the ramp and I've got the timings it took to pass between markers 10 centimetres apart near the top and near the bottom there.

And I'd like you to use that data to decide if this ramp is too steep, too shallow, or just right.

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

Welcome back.

Well, that ramp was just right.

If you look at the time difference at the top of the ramp, the time difference at the bottom of ramp, it's 0.

11 seconds in both cases.

So the trolley's moving at constant velocity.

Well done if you spotted that.

Now let's look at the second problem associated with this experiment.

And that's to do with the mass of the trolley.

In the experiment we sort of consider the trolley moving down the ramp, but actually it's not just the trolley that's moving, it's the trolley and the masses that are attached to it.

So we have to take into account the total mass of the system, the trolley and the masses in order to reach some sort of conclusion in this experiment.

So what I want to do is to try and make the mass of the whole system constant.

So when I've got the trolley attached to the masses, both of them are accelerating and the problem is if I take one of the masses off to reduce the force on the trolley, then I've reduced the mass of the whole system.

I've made it lighter and that's not very fair.

If I then add another mass on, then again I've increased the mass of the system and again, it's not a fair test because I've changed the mass.

So I need some way of keeping the total mass of the system constant.

Right, let's have a look if you can calculate the overall mass of this system based on some data.

I've got a dynamics trolley and the dynamics trolley has a mass of 0.

60 kilogrammes and it's being pulled by a metal block and that metal block weighs 2.

0 Newtons and it hangs over the pulley at the end of the desk.

What I'd like you to do is to try and work out the mass of the whole system, all the moving parts of that.

And to do that you'll need to use the gravitational field strength g, which is 10 Newtons per kilogramme for this question.

So what I'd like you to do is try and work out the overall mass of the system there from that list on the right.

Pause the video, make your selection and restart.

Welcome back.

Well, you should have selected 0.

8 kilogrammes there.

And the way we work that out is we need to work out what the mass of the metal blocks pulling the system is.

And I've got the weight, that's 2.

0 Newtons, so I need to use the equation that links weight and mass.

So the weight of the metal is the mass times the gravitational field strength as I've written there.

I substitute the values in and the metal blocks have a mass of 0.

2 kilogrammes.

So I need to add that to the mass of the trolley, which gives a total of 0.

8 kilogrammes.

Well done if you've got that.

What I need is a way of keeping the total mass of the system the same.

So I've got a trolley here and I've attached it to five metal blocks, five small masses to make it accelerate.

But if I take a mass off those, then I'm reducing the overall mass of the system.

What I can do instead though is take the mass off and instead of just removing it and putting it to the side, I can carefully place it on top of the dynamics trolley so it's still part of the moving system and that will mean that the overall mass stays the same.

So what I mean is this, I've got a trolley here and I've taken two of the masses off and instead of putting them to the side, I've put 'em very carefully on top of the trolley so they move with it.

And that means that in the first example I've got five masses and the trolley mass moving.

But in the second one I've got five masses and the trolley mass moving as well.

So I've not altered the mass of the system even though I've changed the size of the force causing it all to accelerate.

So that's how we can maintain a controlled amount of mass moving in the system.

Okay, I'd like to check your understanding of what happens if the overall mass of the system wasn't kept the same.

So what effect would reducing the overall mass of the system have on the acceleration of the trolley when there's a constant force acting on it? Is it A, it will have no effect? B, it will cause the acceleration to increase, or C, it will cause the acceleration to decrease? So pause the video, make your selection and restart please.

Welcome back.

Well the answer to that was it will cause the acceleration to increase.

If I've got a smaller mass that I'm pulling with the same size force, it's going to accelerate at a greater rate.

Well done if you got that.

Now it's time for the first task of the lesson.

And what I'd like you to do is to write a method that will allow a student to investigate the relationship between force acting on a trolley and its acceleration.

So I'd like you to write that method that will allow the people to perform that test fairly reducing the effect of friction and keeping a constant mass moving.

The method should include an equipment list, a diagram, and step-by-step instructions.

Now that's quite a large task, so I'd like you to pause the video, write out your method, equipment list and diagram and then restart please.

Welcome back.

Well your equipment list should look something like this with the dynamics trolley and a ramp and that's the important a addition here with an incline and adjustable slope.

You need the mass holder a hundred gramme masses pulley and string and you'll also of course need a timer, a tape measure and to get those timing measurements accurate, some sort of video recorder.

The diagram is shown there.

As you can see, I've got a trolley rolling down an incline ramp, so it's a slightly adjustable slope there and I've got all the distances measured out.

The second part of the task was to write the instructions and here's a set of instructions.

I'm not gonna read through them all.

You can pause the video and check through them if you like, but if your method looks something like this, well done.

Now we've reached the second part of the lesson and in it we're going to look at a set of data that links acceleration of force and see if there's a relationship between those two variables.

As I've said, we've collected a set of force and acceleration data for a moving trolley along a compensated ramp.

We're going to see if there's a pattern between those, a link between force and acceleration.

And the best way of finding a link is by plotting a graph based on the data to see what that relationship is.

So we're going to plot a graph of force against acceleration and see if there's a shape in there, like a straight line or curve.

And that'll give us some indication of the connection between force and acceleration.

Before we plot the graph, let's have a brief recap of how we can calculate acceleration based on velocity data.

So I've got a table of data here with accelerating force, velocity, and time and I need to calculate acceleration and to calculate acceleration, I use this equation A equals delta V over T where delta V is changing velocity.

We can also write that as final velocity V minus initial velocity U divided by time.

And in this experiment, the initial velocity was zero, remember.

So if I want to calculate the acceleration for the 0.

5 nuisance here, the highlighted row of the table, I can substitute in the velocity of 0.

47 metres per second.

That's the final velocity minus the initial velocity of zero, divide it by the time and that gives me an acceleration of 0.

15 metres per second.

I can repeat the process with the second row of the table writing the values into the equation and getting a value of 0.

12 metres per second.

And I can continue with that with the other two until I've completed my data table.

So now I've got accelerating force and acceleration and I can use those two columns to plot my graph.

Let's check if you can calculate the acceleration for a trolley here.

I've got a similar table of data to the one I've just used and I'd like you to just calculate the acceleration.

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

Welcome back.

You should have selected 0.

45 metres per second there.

And here's the mathematics behind that.

I've got my acceleration equation, substitute the values and it's 0.

45 metres per second squared.

Well done if you got that.

So now as we've got our table of data, we've got our accelerating force and we've got our acceleration.

They're the two variables we're gonna plot in the graph.

So let's go through the procedure to plot a graph again.

So first of all we're gonna draw the x and y axis on a sheet of graph paper.

So I've got a simple sheet of graph paper here and I've got the axis drawn at the left and at the bottom.

Next I'm gonna add the scales and those scales don't have to be the same as each other.

We choose the scales based upon the data.

So you can see you've got a scale along the bottom and a scale at the side.

Along the bottom I've got the axis labels there, force in Newtons on the bottom and acceleration in metres per second squared on the y axis or of the side there.

And the next stage is to plot the points using small crosses.

So they've gotta be accurately plotted and clear.

So let's start adding those small crosses onto the diagram one at a time.

And as usual, I like to sort of tick them off as I go through each one.

So I'm gonna plot the first one, the second, the third.

And I've only got four pieces of data here.

So there's only four crosses.

The next stage in the procedure is to see if there's a line of best fit that I can do.

And there's two styles of lines of best fit that you should be aware of.

The first one is a single straight line that we'd draw with a ruler.

So a perfectly straight line that passes close to the points but it doesn't have to pass exactly through them.

Or the second type is a smooth curve that passes close to the points.

To judge whether this is a straight line or a curve, I'm gonna place a ruler and see if it looks like a straight line to me.

So if I place a ruler onto my set of points, I can see immediately that these line up really, really well in a straight line.

So I'm gonna assume this is a straight line graph and I'm going to draw a straight line of best fit through it and I've drawn it there.

So I end up with a force and acceleration graph that looks like this and I try and analyse it and I can see straight away all the points are in a straight line and that straight line I've drawn as well passes through the origin of the graph.

And that's quite an important feature.

The reason those two features are important, the straight line and passing through the origin is it shows a mathematical relationship between acceleration and force.

The acceleration of the object is directly proportional to the size of the resultant force acting on it.

So I can use that relationship to predict what the acceleration would be at any sized force.

So there's our conclusion.

I've highlighted in the box there, acceleration of the object is directly proportional to the resultant force acting on it.

So I'd like you to look at this graph now and decide which of these statements best describes the relationship.

So which of these is the best description of the relationship between the acceleration and the force acting on an object? So pause the video, make your selection and restart please.

Welcome back.

You should have selected the acceleration is directly proportional to the force.

I've got a straight line passing through the origin and that indicates direct proportionality.

Well done if you selected that.

It's now time for the second task of the lesson and I've got a set of results for an experiment with a compensated or sloped ramp used to collect data about the force acting on a trolley and its acceleration and all the calculations have been done.

I've got accelerating force and acceleration in the table.

So what I'd like you to do is plot a graph showing the relationship between force and acceleration solely based on that data.

Then when you've got your graph, I'd like you to write out a conclusion, again just based on the data collected by this pupil.

And finally I'd like you to try and have a think about what that data shows and suggest what the results show about the steepness of the ramp used in the experiment.

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

Welcome back and here's the answers to those questions.

I've got my graph plotted here and as you can see I've got a nice straight line or linear relationship there.

Your conclusion should be something like this.

The acceleration increases linearly with the force.

You'll notice I've not put it's directly proportional to the, this line does not pass through the origin so I can't make that conclusion.

So the acceleration increases linearly with force.

The acceleration is not in direct proportion to the force as the line does not pass through the origin.

And what that indicates to me about the results is, well, when there was no force acting on the trolley, there was still an acceleration.

So actually there must have been a force acting on the trolley and what I suspect is that the ramp was tilted too much, it was too steep, so it was producing an extra force in the trolley causing it to accelerate when it shouldn't be accelerating.

So well done if you've got answers like this.

Okay, we're now onto the third part of the lesson, which is all about improving the acceleration experiment.

As you've seen, there are some issues with the experiment and we can try and take measures to control the variables, but there are still some things we could do to make the experiment better and get more accurate results.

So the main issue with the experiment that remains is the timing.

We can take three timing measurements to an experiment as the trolley passes through three separate markers and that's very difficult to do.

So we've got the trolley set up here at its start point and then when we release it, it will accelerate towards the left and it'll pass three sets of markers.

And in each of those we need to actually record the time it was at when the trolley reached that marker.

So we've got it at this first marker and we've gotta record that time.

The second marker, we need to record that time and the third marker, we need to record that time as well.

And each of those are going to give us some timing measurements.

But any errors that we record, any timing errors we've got are going to be incorporated into our calculation and give us an inaccurate measurement of acceleration.

Measuring those times accurately without some sort of assistance is impossible.

And one way of recording those times is to actually video the experiment.

And you may well have done this.

We take video recordings and then we can pause the video at certain points and see what the time is on the screen and where the trolley is and that will help us to some extent.

So I've got two photographs I've taken during my experiment here and as you can see in the first photograph, the one on the left there, I've got a time of 1.

20 seconds just as it reaches the purple marker.

And then in the second one it reached the second marker, the light blue one, and it's at two seconds.

So I could use those two photographs reading them off the screen and calculating the time it takes the trolley to pass between those two markers.

And it's the difference in those two times.

So it's 0.

8 seconds.

But the accuracy of those measurements is limited.

You can see that the video is slightly blurred, it's not capturing enough frames every second for me to get a very accurate measurement.

So I'm gonna get some limitations even though I'm using video recording.

So the precision of the measurements I can take even in videos can be quite low depending on how many frames per second I can capture.

But there is a piece of equipment specifically designed for very precise timing measurements and that's a light gate.

And a light gate is a system that uses an infrared beam that's transmitted between a transmitter and then received by a receiver.

So I've got a simple diagram of it here.

We've got a transmitter and a receiver.

And normally when I turn them on there's an infrared beam that I've drawn in red here between the two.

And as long as that signals the light gate, it doesn't do anything.

But when an object passes between and breaks the beam, then it can't be received by a receiver and the light gate triggers a timer, it activates it and starts it.

So as soon as the object breaks the beam, the timer starts.

And then what happens is as the object passes through the transmitter and receiver gap and then the beam can go back across like this, the object's completely passed through and the timer is stopped.

So what's happened there is that the timer has measured precisely how long it took the object to pass between the transmitter and receiver.

So that gives a very accurate time for the object to move through those two systems. To measure the time it takes a trolley to pass through the light gate very precisely and I can do that by getting a trolley and attaching a piece of card to the top of it.

So if you imagine our set up is like this from above, I've got a ramp and I've got the light gate position precisely where I want it and there's the infrared beam going across it.

Then I've got a trolley that's rolling down the ramp from the left to the right.

And here in this image it's just about reached the light gate and that piece of card which is placed on top of the trolley is just about to cut the beam.

So when it does that, it's gonna start a timer, then the trolley will continue moving and pass through the beam.

And as soon as it's completely passed through the beam and the card is no longer breaking the beam, the timer's going to automatically stop.

So what I've got there is a very precise measurement of the time it took that piece of card attached to the top of the trolley to pass through the light gate.

So the trolley's moved forward by the length of the card in the time it took for the light gate to measure.

Okay, let's see if we can use timing information and length of information to calculate the speed of a trolley.

So I've got a dynamics trolley here and it's got a piece of card attached to it.

And as you can see it's five centimetres tall and 20 centimetres wide.

And this trolley passes through a light gate in a time of 0.

5 seconds.

So it cuts the beam and then rejoins the beam 0.

5 seconds later.

And I'd like you to use that information to calculate the speed of the trolley.

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

Welcome back.

Hopefully you selected 0.

4 metres per second.

And the reason for that is well, we can calculate the velocity or the speed of the trolley using this equation.

Velocity equals distance divided by time and the distance that passed through the light gate is that top edge of the card.

It was 20 centimetres long or 0.

2 metres in a time of 0.

5 seconds.

And that gives an answer of 0.

40 metres per second.

Well done for getting that.

The reason we take repeat measurements during the experiment is to check that the readings are repeatable, that we can get the same results each time we take a measurement when we don't change anything else.

So repeatable results are quite important.

I've got a set of repeatable results here.

And repeatable results are results taken by the same person or the same team trying to do the same experiment.

And you can, although there's a little bit of variation in my calculations of acceleration here, they're repeatable, they're fairly close to each other.

A set of results like that will allow mean values to be calculated and that will reduce the overall error by, you know, eliminating some of the smaller results and some of the higher results to get a mean value.

And I can calculate the mean of that like this.

We add the three values together, divide by the number of measurements I've taken, which is three.

And that gives me a mean of 0.

25 metres per second squared.

Now it's very common to take three measurements and calculate a mean, but that doesn't always need to happen, especially for longer experiments.

And I need to be able to judge whether or not I need to take more measurements from the data I've already collected.

So if I've got the first pair of results and they match closely, it shows that the experiment is repeatable and I probably don't need to collect a third value.

So in this instance, I've got two final velocities that I've measured and they're very similar to each other.

So I don't really need to take a third measurement 'cause the procedure I'm following is giving me repeatable results.

However, if I've got a set of results that look a bit like this, I've taken the first one and I've seen that the second result is quite a lot higher, so I've taken a third one and that's reasonable.

Then I've taken a fourth result and I've got something that's much, much lower.

There's quite a lot of variation happening there.

So taking a set of five results and eliminating any anomalous ones is probably a better approach.

So let's delete the anomalous results.

That one was too high and this one was too low.

And now by taking five measurements, I've got three useful ones and I can use that to calculate the mean.

Now I'd like you to decide whether or not it was worthwhile taking all of these measurements during the experiment.

I've got the same accelerating force and I've got final velocities listed out there.

How many results would you have collected during that experiment to show that it's repeatable? So pause the video, make a selection, and then restart please.

Okay, welcome back and hopefully you selected two.

As you can see after the first and second result, you can see that it's the same sort of result you're getting each time.

They're very similar to each other.

So it wasn't really necessary for me to collect the third, fourth, and fifth result there.

I could have stopped the experiment after two and moved on to my next sized accelerating force.

Well done if you selected two.

So now it's time for the final task of the lesson and we've got a pupil that's carried out the acceleration experiment and the results are shown in the table here.

What I'd like you to do is to calculate the accelerations based upon that data and then use the data to calculate the mean acceleration for each of the three accelerating forces.

If you look, you can see there was a 0.

1 Newton, 0.

2, and 0.

4 Newton accelerating forces used.

So I want the mean value for each of those please.

So pause the video, restart when you've done that.

And welcome back.

And here's a completed table.

As you can see I've calculated all the accelerations, that end column.

I've noticed that two of them don't fit the pattern very well, so I have crossed those out and counted them as anomalous results.

And then I've calculated the mean.

For the 0.

1 Newton force, all three acceleration values look similar.

So I've used all three of those to calculate the mean of 0.

19 metre per second squared.

For the 0.

2 Newtons one, because I crossed out one of them, I've calculated the mean just using the two values that remain.

And similarly for the 0.

4 Newtons ones, one of those was anomalous as well.

I've crossed that out.

So I've only got two left and I've calculated the mean there.

So well done if you've got an answer like this.

And now it's the end of the lesson.

So here's a quick summary.

For any investigation into acceleration, we need to keep the test fair.

And to do that we should use a sloping track and that will compensate for any frictional effects or as close as possible anyway.

We should also keep the total mass of the system constant by taking any removed masses and putting them on the trolley so we've got that constant mass.

We reached a conclusion and that conclusion was the acceleration is directly proportional to the applied force.

And finally, we don't always have to have three repeat measurements for everything.

Sometimes we can get away with just using two or sometimes we may need to make more repeat measurements depending on how repeatable the results were.

So well done for reaching the end of the lesson.

I'll see you in the next one.