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

In this lesson, we're going to be carrying out a practical to measure the acceleration of a dynamics trolley.

By the end of this lesson, you're going to have planned and carried out an experiment where you can measure the acceleration of a dynamics trolley when it's pulled by a range of different forces.

There are three keywords that you'll need to understand to get the most from this lesson.

First of them is acceleration, and the acceleration of an object is how much faster it's getting each second, the change in velocity per second.

The second keyword's velocity, and that's the change in displacement every second, so how many metres it travels per second, and the third is dynamics trolley, and a dynamics trolley is a small wheeled vehicle that we use in experiments to measure motion, and we use it because it's got a very low friction.

It moves very easily over flat surfaces, and here's an explanation of those keywords, and you can return to this slide at any point during the lesson.

There are two parts to this lesson, and in the first part, we're gonna explain and plan and then carry out an experiment into measuring the acceleration of a dynamics trolley as it moves across a flat surface.

We're gonna use different forces to make the trolley accelerate at different rates.

In the second part of the lesson, we're going to use the data we've collected to actually calculate the acceleration of the trolley for those different forces.

So when you're ready, we'll begin with planning the experiment.

Let's start by looking back at the definition of acceleration, and acceleration is the rate of change of velocity.

That means how much the velocity is changing every second.

Mathematically, we represent that by this equation.

Acceleration is the change in velocity divided by time, or if we're using symbols, a is delta v over t.

That delta symbol there means change.

So a is acceleration.

It's measured in metres per second squared.

Change in velocity, delta v, is measured in metres per second, and the time is measured in seconds, as you'd expect.

So in this experiment, we're going to be measuring the acceleration of a dynamics trolley on those little wheeled vehicles, and to do that, we need to put a force on the trolley to cause it to accelerate, and what we want to use is a measurable force, a force that we know the value of.

So we're gonna place a dynamics trolley on a horizontal track, just a flat surface or a desk or something like that, and to put a force in it, what we're going to do is attach some hanging masses over a pulley, piece of string, connect that to the dynamics trolley.

What that does is it produces a downwards force.

The hanging masses have got a weight, and that produces a downward force, and that's transferred via the string to give a horizontal force acting on the dynamics trolley.

It's going to be pulled.

So when I release those masses, they're just going to be pulled downwards and it's gonna make the trolley moved.

So the accelerating force is produced by those masses, and we can change the number of masses to change the size of that force.

As the trolley moves, there's also going to be a very small frictional force that acts on it, reducing the overall pull.

So that frictional force is very small because the dynamics trolley is specifically designed to roll easily.

So in this experiment, we need to generate different sized forces acting on the trolley, and we can do that by changing the size of the pulling force by adding extra masses.

So if I've just got one small mass hanging on the edge of the pulley there, then I'm gonna get a small pulling force on the trolley.

If I add a second mass onto there, I'm gonna get a larger pulling force, and of course if I add a third mass, I'm gonna get a larger pulling force again.

So adding more masses will allow me to increase the size of that accelerating force, and I can add four or five masses in total.

Okay, the first check now.

What I'd like you to do is to have a think about the relationship between forces and what they do on objects and decide which of those identical trolleys will have the greatest acceleration, and as you can see, they've all got different forces acting on them.

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

Welcome back.

Hopefully you chose answer b.

The larger force is acting on the trolley there, and the larger force will give the greatest acceleration, and we'll see if we can confirm that too in the experiment.

So well done if you got that.

In the experiment, we're gonna use the dynamics trolley and accelerate it through a measured distance, and I've chosen the distance of about 50 centimetres.

That'll give it enough space to accelerate to a measurable amount, but not so large that we haven't got space on the desk to actually carry out the experiment.

So I'm gonna mark two points.

I'm gonna mark a start point where I'm gonna position the dynamics trolley, and there's going to be an end point, and it's the end point I wanna measure the speed at or the velocity.

To measure the velocity, you might have used this technique before, I'm gonna place two markers, and those two markers are gonna be either side of the end point.

I'm gonna time how long it takes for the trolley to pass between those two markers, and that'll allow me to calculate the time.

I'm gonna position them 10 centimetres each end of the end line.

So one's gonna be at 40 centimetres from the start and one's gonna be at 60 centimetres from the start, and in all, I'm gonna take three measurements of time as the trolley passes each of the markers, marker one and marker two, and as it passes the end line as well.

Let's see if you can calculate a speed.

I've got a dynamics trolley.

It takes 0.

25 seconds to pass between two markers that are 20 centimetres apart, and I'd like you to calculate the average speed of the trolley as it passes between those two markers please.

So pause the video, make your selection, and then restart.

Welcome back.

Hopefully you selected answer b, 0.

8 metres per second, and to show that, we can do the calculation.

Speed equals distance divided by time.

The distance there was 0.

20 metres.

That's 20 centimetres, 0.

2 metres, and divided by the time of 0.

25 seconds gives a speed of 0.

8 metres per second.

Well done if you got that.

So the goal of this experiment is to find out a relationship between acceleration and the size of the accelerating force acting on the trolley.

So we're gonna set up the trolley like this as we've seen before with the markers towards the end and the trolley starting on the start line, and it's starting from rest, so we're gonna release it while it's not moving, and when we release it, the masses are gonna pull that trolley forward, accelerating it until it reaches the end line.

We're gonna measure the velocity at that point.

We can change the number of masses acting on the trolley.

So we've got two masses in the diagram here, but I can use one, two or up to five masses to cause different accelerating forces on it, and I can easily calculate those accelerating forces as well, as we'll see later, and we're going to measure the velocity at that 50 centimetre point as it passes between those two markers or average velocity there.

To see if you understand the experiment, I want you to have a think about the types of variables.

I would like you to match each variable to the type of variable.

Is it a dependent variable, independent, or control? So as you can see, I've got five factors there, and all I'd like you to do is to mark each one of them with the letter D for dependent, I for independent, and C for control.

So pause the video, read through those, put down the letter, and then restart please.

Welcome back.

Let's have a look through each of those.

So the mass of the trolley is a control variable.

It's something we don't want to change throughout this experiment because we're looking for, for a test, we just wanna see the relationship between acceleration and accelerating force.

We don't wanna involve changes in masses.

The distance for the acceleration to happen in is also a control variable.

We don't want that to change throughout the experiment.

We are changing the size of the accelerating force.

That's the independent variable, the thing that we are altering deliberately to see its effect.

The distance between the speed markers is a control variable as well, and what we're looking for, we're looking for the dependent variable, the acceleration of the trolley.

So you should have written those letters.

Well done if you got them.

Now we're going to be measuring the time at which the trolley passes each of three separate markers, and that's quite difficult to do.

We need to measure the time on the trolley is at the 40 centimetres mark, the first of the markers, then as it passes the 50 centimetres mark, and finally as it passes the 60 centimetre mark.

Now, trying to measure those manually with a stopwatch is going to be impossible.

They're too small for manual timing to happen.

So in order to do that, we're going to be using some video recording techniques.

We're going to place a large timer behind those markers and we're gonna film the trolley passing them, and that's going to allow us to pause the video and look at the position of the trolley.

So as it passes the first marker, we can wind through the video until that point, pause it, and look at the timer and then get a reading.

Then we can let the recording move on in slow motion for a while, pause it as it passes the 50 centimetres mark and look at the timer, and pause at the 60 centimetre mark as well.

So video recording is essential to get accurate measurements in this experiment.

Okay, now it's time for you to actually carry out the experiment.

So what I'd like you to do is to set up the equipment as shown in the diagram here, and it's very important that we get the measurements of these distances correct.

So make sure you use the metre rule to measure out all those distances and put markers in the correct points.

We're gonna place 50 grammes on the end of the string over the pulley, and we're gonna release the trolley, but importantly, we're going to be recording the motion of that trolley so we can take some accurate measurements of time.

Once we've done that roll, we can analyse the video, pausing it and measuring the time the trolley was at 40, 50, and 60 centimetre positions.

Then we can repeat that for a second time with the same pulling force, and finally, we're going to alter the mass that's pulling to alter the force.

So we're gonna repeat those steps with 0.

4 newtons, 0.

3 newtons and 0.

2 newtons.

To show you how that's done, let's watch a quick video of somebody carrying out that experiment.

<v Instructor>In this investigation,</v> we're going to measure the acceleration of a dynamics trolley.

We're going to start it from rest and accelerate it over a distance of 50 centimetres.

To accelerate it, we're going to pull it using these hanging masses.

There are five masses, each weighing 0.

1 newtons.

So the total pulling force at the moment is 0.

5 newtons.

That's going to accelerate the trolley forwards when we leave go, and we're going to measure the average velocity at 50 centimetre mark, and to do that, we're going to measure its velocity between 40 and 60 centimetres.

So over a 20 centimetre distance, we're going to record the time and measure the average velocity, which will be the velocity approximately at the centre point.

<v Assistant>Three, two, one, go.

</v> <v Instructor>By freezing the video</v> and observing the timer, we were able to check the times that the trolley was at when it reached 40 centimetres, 50 centimetres and 60 centimetres.

We're going to use the times at 40 and 60 centimetres first to calculate the average velocity at the end of its journey at 50 centimetres.

So first of all, we need to take away those times to find the time between 40 and 60 centimetres, which is 0.

34 seconds.

And then to calculate the final velocity, we divide 0.

2 metres, which is the 20 centimetres, by 0.

34 seconds to get an answer of 0.

59 metres per second.

Now, because we know the final velocity of 50 centimetres and we know the starting velocity, which was 0, the increase in velocity is 0.

59 metres per second, and it took a time of 1.

34 seconds to reach that speed, that velocity.

So the acceleration is equal to 0.

59 metres per second, the increase in velocity, divided by 1.

34 seconds, the time it took to reach that velocity, and that gives us an acceleration of 0.

44 metres per second squared.

And now to check the results, we'll take a repeat reading.

<v Assistant>Three, two, one, go.

</v> <v Instructor>So let's put those new measurements</v> into the table and use them to calculate first of all the time between 40 and 60 centimetres in order to calculate the final velocity, and then we use the final velocity and the time taken to reach 50 centimetres to calculate the acceleration.

The next step is to take one of the weights off the hanging masses and to place it on the trolley.

That means that we've got only 0.

4 newtons now pulling the trolley forwards and accelerating it, but the total mass of the trolley and the mass hanger that's both being accelerated remains the same.

We take a set of results just as we did before.

<v Assistant>Three, two, one, go.

</v> <v Instructor>And we can add those results</v> to the results table as well and calculate the final velocity and the acceleration in the same way as before, and then we can take a repeat measurement for a pulling force of 0.

4 newtons, and then by removing one more mass each time off the mass hanger and placing it on the trolley, we can take further readings for the pulling force of 0.

3 newtons and 0.

2 newtons, and if we put all of those results into the table, this is what we end up with, and we can use the results again to calculate the acceleration for each of those trolleys.

<v ->Okay, hopefully that video helped you understand</v> how to carry out.

So what I'd like you to do now is to pause the video, follow the instructions and collect a set of results.

The results table you'll need is like this, and what I'd like you to do then is to pause the video, move back to the instructions if you need to, follow them, and complete the results table and then restart.

Okay, welcome back.

Hopefully you collected a useful set of results.

They should look something like these.

So I've completed the pulling force, time at 40 centimetres, time at 60 centimetres and time at 50 centimetres columns, and in the next part of the lesson, we'll analyse them, but if you've got something like that, well done.

Okay, now it's time for the second part of the lesson, and we've got a table of results, and we need to analyse those results in order to find the acceleration.

So let's get on with that.

In order to find the acceleration of the trolley, I need to find the velocity of the trolley as it passed the 50 centimetres mark.

So I'm gonna go through the process of finding that.

I need to find the time it took the trolley to travel between the two markers of 40 centimetres and 60 centimetres, and that's gonna allow me to calculate the velocity at the 50 centimetre mark.

So to find that, I need the time difference at the 60 centimetre marker and the 40 centimetre marker.

So I can do that for the first 0.

5 newton run, the top row of my table here.

The first 0.

5 newton run, the time difference is the difference in those two times, 1.

56 seconds minus 1.

22 seconds, and that gives me a time difference of 0.

34 seconds.

So the trolley took 0.

34 seconds to pass between my two markers.

I can do that for the second run as well after filling it in the table there, and I can find the time difference again, and it's 0.

32 seconds.

So calculating the time difference is the first step in calculating the velocity, and that's the first step in calculating the acceleration.

Okay, let's see if you can find the time difference now.

I've got a different table here, different set of results, and I'd like you to calculate the time difference between the 40 centimetres and 60 centimetre markers for both of those sets of readings please.

So pause the video, work out the time differences, and then restart.

Welcome back.

Well, your calculation should look something like this.

The first run, the 0.

5 newton run, the time difference is 1.

54 seconds minus 1.

10 seconds, or 0.

44 seconds as I filled in there, and for the second run there, the time difference was slightly different at 0.

43 seconds.

Well done if you got those two.

Now that I've got the time difference and I know how far apart the markers are, I can calculate the velocity of the trolley.

So I've got a data table here and I've got my time differences already filled in, and I'm gonna find the final velocity using that time difference, and I know the distance apart of those two markers.

They're 20 centimetres apart, or 0.

20 metres.

So for the first 0.

5 newton pulling force run, I can calculate the velocity of the trolley, and I write out the equation.

Velocity is distance divided by time.

Fill it in.

The distance is 0.

20 metres, and the time difference, as we worked out earlier, 0.

34 seconds, and that gives me a final velocity of 0.

59 metres per second.

So I can fill that into the table there, and I can repeat the process for the next row of the table using the time difference and the markers still being 0.

20 metres apart.

So I'll write out the expression again, fill in the values, and I get a velocity of 0.

63 metres per second like that.

Okay, it's time for you to try and find some example final velocities.

I've got a table of data here and I've got the times at 40 and 60 centimetres and I've already calculated the time differences for you.

What I'd like you to do is to use the process I've just used to find the final velocity, remembering the two markers are 20 centimetres or 0.

2 metres apart.

So pause the video, find the two missing final velocities, and then restart please.

Welcome back.

Well, your calculation should look something like this.

For the first run, we've got the equation written down.

We substitute in the values, and we find it's 0.

45 metres per second.

So well done if you got that one, and for the second run, very similar.

We put in the values from the table, and we find that the final velocity there is 0.

47 metres per second.

Well done if you got those two.

Now, the final stage of our processing of the data is to find the acceleration.

We know the velocity at the 50 centimetre mark, and we know the time it took to get to the 50 centimetres mark.

So we're gonna use that velocity and that time to calculate an acceleration.

So for the first run, again, in this data table, I'm going to write out my expression for acceleration.

Acceleration is change in velocity divided by time.

I can then substitute in the values from the table.

The change in velocity, well, the trolley started at 0 metres per second.

So the change in velocity is just the velocity, the final velocity there, so 0.

5 metres per second minus the starting velocity of 0.

Dividing that by the time it took to get to the 50 centimetre mark, that gives me an acceleration of 0.

44 metres per second squared.

Another example, so for the second run, I've got the expression for the acceleration there.

You can see that the change in velocity and it got up to a velocity of 0.

63 metres per second and it started at 0 metres per second.

We divide that by the time, and that gives us an acceleration of 0.

39 metres per second squared that we fill in here.

Okay, let's see if you can calculate acceleration.

I've got two rows of the table here, and I'd like you to calculate acceleration using the data for both of those rows please.

So pause the video, calculate the missing accelerations using the procedure I've just shown you, and then restart.

Okay, welcome back.

Well, for the first run, first row of the table there, you can write down the expression for acceleration, substitute the values, and we get 0.

35 metres per second squared.

Well done if you got that one, and the second calculation, it was very similar, slightly different values giving an acceleration of 0.

37 metres per second squared there.

So well done if you got those two.

Welcome back.

Well, hopefully you processed your data successfully and you've got a results table that looks similar to this.

So we've got a set of time differences filled in.

I filled in the final velocities, calculating that from the time difference and the separation of those two markers, and then I've used that final velocity and the time at 50 centimetres to calculate the acceleration and I filled in that column as well, and as we can see, there seems to be some pattern there, but we'll look at that in some future lessons.

So well done if you've got a table that looks like this.

We've reached the end of the lesson now, and a quick summary of everything we learned.

The acceleration of the dynamics trolley for different pulling forces can be found by measuring the velocity after it's accelerated for a measured time, and we use a setup as shown in that diagram to carry out that experiment.

To calculate acceleration, we needed to calculate the velocity at the 50 centimetres mark using change in displacement divided by time, and we needed to calculate the acceleration.

This is the change in velocity divided by the time.

Well done for reaching the end of the lesson.

I'll see you in the next one.