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 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.

The 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 wheel vehicle that we use in experiments to measure motion, and we use it because it's got a very low friction, moves very easily over flat surfaces.

And here's an explanation of those keywords, and you can return to the 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 at a definition of acceleration, and the acceleration of an object is the rate of change of velocity, and all that means is it's how much the velocity of an object is changing every second.

If we write that mathematically, we get the expression here.

Acceleration is change in velocity divided by time or written in symbols A equals V minus U over T.

We'll define those symbols in the units here.

We've got acceleration that's measured in metres per second squared and has the symbol A.

Initial velocity and final velocity, well, that's the starting and end velocity of an object that's speeding up or slowing down, then measured in metres per second, and, as you'd expect, time is measured in seconds, and we use the symbol T for that.

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 on it, what we're going to do is attach some hanging masses over a pulley, piece of string, and 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 gonna be pulled downwards, and it's gonna make the trolley move.

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 going to 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 could 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 would 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 during 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 experiment.

So I'm gonna mark two points.

I'm gonna mark a start point where we're 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've used this technique before.

I'm gonna place two markers, and those two markers are gonna be either side of the endpoint.

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.

We're gonna position them 10 centimetres to 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, 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 a selection, and then restart.

Welcome back.

Hopefully you accepted 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 us speed of 0.

8 metres per second.

Well done if you've got that.

So the goal of this experiment is to find out a relationship between acceleration and the size of the accelerating force at the normal 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 in the start line, and it's starting from rest.

So we're gonna release it when it's not moving, and when we release it, the masses are gonna pull that trolley forwards, 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 or 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-centimeter point as it passes between those two markers at 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 what I'd like 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 a fair test.

We just wanna see the relationship between acceleration and accelerating force.

We don't wanna involve changes of 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-centimeters mark, the first of the markers, then as it passes the 50-centimeters mark, and finally, as it passes the 60-centimeter 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 and pause it as it passes the 50-centimeters mark and look at the timer and pause at the 60-centimeter 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 ones.

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, we can analyse the video, pausing it and measuring the time the trolley was at 40, 50, and 60-centimeter 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 on it, so 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 Experimenter>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-centimeter mark, and to do that, we're going to measure its velocity between 40 and 60 centimetres.

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

Three, two, one, go.

(trolley rattles) By freezing the video 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 each 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 zero, 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.

Three, two, one, go.

(trolley rattles) So let's put those new measurements into the table and use 'em 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 for the total mass of the trolley and the mass hanger that's both been accelerated remains the same.

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

Three, two, one, go.

(trolley rattles) And we can add those results 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 it 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, and if you've got something like that, well done.

Okay, now it's time for the second part of the lesson where 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-centimeter 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 at 40 centimetres and 60 centimetres, and that's gonna allow me to calculate the velocity at the 50-centimeter mark.

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

So I can do that for the first 0.

5 newton row.

The top row of my table here.

The first 0.

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

56, sorry, 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, a different set of results, and I'd like you to calculate the time difference between the 40 centimetres and 60-centimeter 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've 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 as we have the time difference for the trolley passing between the two markers, we can calculate its velocity.

So we're going to use the time difference, and the separation of the two markers define velocity, and the way we do it is like this.

So we know the markers were 20 centimetres apart or 0.

20 metres apart.

For the first run, we can find the velocity using the distance that the trolley's travelled and the time it took, and the distance between the two markers was 0.

20 metres, and the time it took is that time difference of 0.

34 seconds.

When we calculate that, we get a value of 0.

59 metres per second, and we fill it into the table here.

For the next row, we do the same procedure.

We write out expression, we take the values, 0.

20 metres, and the time difference, 0.

32 seconds, we calculate that, and it's 0.

63 metres per second, and fill it in here.

Let's see if you can calculate the final velocity for a pair of readings.

So I'd like you to follow the same procedure as I've done.

I've got a table here with a different set of data.

I've got the time differences worked out, and markers were still 20 centimetres apart.

So what I'd like you to do is to pause the video, find the two missing final velocities, and then restart please.

Welcome back.

Well, hopefully your calculations should look a little like this.

For the first run, we write out the expression velocity is distance divided by time.

We write in the distance at the time difference there, and that's 0.

45 metres per second, and we fill in that table, and for the second run, again, similar calculation.

This time, the time difference is 0.

03 seconds, and we get a slightly different velocity there of 0.

47 metres per second.

Well done if you've got those two.

Now as we have the velocity of the trolley at the 50-centimeters mark, we can calculate acceleration, remembering that the trolley started from rest or zero metres per second.

So we've got an almost completed table of data here, and I've got the final velocity and the time the trolley had taken to reach that 50-centimeters mark where we measured that final velocity, and I can use that final velocity and that time to calculate the acceleration.

So for the first run, I can write out the expression for acceleration.

The acceleration is V minus U, that's final velocity minus initial velocity divided by time.

For substituting the two values in the equation there, remember the final velocity was that end velocity we just calculated, 0.

59 metres per second, minus the initial velocity of 0 metres per second, and we divide that by the time.

It's 1.

34 seconds there.

Doing that gives us an acceleration of 0.

44 metres per second squared, and I can fill that in the table there.

I can repeat the process for the next row.

So again, writing out the expression for acceleration, filling in the two values taken from the table, and calculate an acceleration of a slightly different 0.

39 metres per second squared there.

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

Welcome back.

Let's have a look at the two calculations needed here.

So for the first row, we can write out the expression A equals V minus U divided by T, substitute the values we take from that first row of the table, and that gives 0.

35 metres per second squared.

Well done if you got that one, and similarly, for the next row, same sort of process, slightly different values.

Gives us an answer of 0.

37 metres per second squared.

Well done if you've got those two.

Okay, now it's time for you to process a complete set of results.

So hopefully you've got your own results, but I've got a table here you can use if you haven't got it.

So I'd like you to use the results you collected in your experiment to calculate the acceleration of the trolley, those different pulling forces.

If you don't have any suitable results, just use the set of data I've got in this table here.

So pause the video, work through all those calculations, and then restart when you're done.

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 got a table that looks like this.

Okay, we've reached the end of lesson now, and a quick summary.

The acceleration of the dynamics trolley can be found for different pulling forces if we can measure its velocity after it's been accelerated for a measured time, and we use the setup there of a dynamics trolley on a flat desk, and we used a pulling force generated by hanging masses.

That pulling force accelerated the trolley.

We measured its velocity after it passed the 50-centimeter mark.

We then calculated that velocity using change in displacement over time, and once we'd got that velocity, we could calculate the acceleration using change in velocity divided by time.

Well done for reaching the end the lesson.

I'll see you in the next one.