Lesson video

Hello, I'm Mr. Forbes and welcome to this lesson from the Hidden Forces unit and it's all about turning forces.

In the lesson, we're gonna look at the effect of a force on an object like a seesaw and see how we can balance that seesaw by applying turning forces to both sides.

In it you're gonna carry out an investigation to find out the mathematical relationship between the force on both sides and the distances to the pivot.

By the end of this lesson, you'll have carried out an investigation into the turning forces acting on a balance beam, and you'll find a relationship between those forces and distances that cause that beam to balance or be unbalanced.

You'll also have calculated the turning effect or moment of the force.

These are the keywords you'll need to understand to get the most from the lesson.

The first is balanced and an object is balanced if it's not starting to rotate or not rotating already.

The second is newton-meter and that's the unit we use to measure the turning effect of a force for a large force or a large distance.

A newton-centimeter, which is also used to measure turning effects, but usually for smaller distances that we've measured in centimeters.

And finally, moment and moment is the name we use for the turning effect of a force on the size of it.

And here's some explanations of those keywords.

You can return to this list at any time during the lesson if you become confused about them.

This lesson's in two parts, and in the first part we're gonna lead up to an investigation into the turning effect of force and when a balanced beam actually becomes balanced.

In the second part, we're going to look at calculating the turning effect of the forces and see that there's a mathematical relationship for when an object is balanced.

So let's get on with the first part where we start the investigation.

So we'll start the lesson by thinking about a seesaw.

Now if you've seen a seesaw, you've probably seen that sometimes it's balanced and sometimes it's not.

And whether it's balanced or not depends on a range of factors.

You could have two people who are roughly the same size on each end of the seesaw and it'd be balanced.

But sometimes you can have one person on one side and two people on the other and they're very different in size.

And sometimes the seesaw is balanced when you're sat closer to the pivot and sometimes it's balanced when you're further from the pivot.

So, the balance of that seesaw depends upon the weight of the people on each side and also perhaps the distances they are from the center.

So we've got some pupils who've got ideas about what makes a seesaw balanced or not.

The first one is this.

I think it will be balanced when the weight on each side is the same.

Or we could have this suggestion.

I think the position of the weights is the important factor.

Or perhaps it's the third one where I think it's both the weight and the position that affects the balance.

And there's only one way to find out and that is to carry out a test.

So we'll think about a test with a model seesaw.

So this can be the simple model of the seesaw here.

I've got a lever balanced along a pivot in the center and I can use a stiff ruler to be that lever or that seesaw.

And I can place a pivot point in the center, a simple triangular wedge for example here.

And instead of putting pupils on it, I'm obviously gonna put something a bit smaller.

So I'm gonna put some masses on each end representing the weight of the child.

And what I can do then is I can adjust the distances between those masses and the pivot and slide them back and forth until I get them balanced.

So, I can find different situations where I've got a balanced seesaw just by using those masses.

So when the students carried out that experiment, they found that the seesaw would balance for certain combinations of masses and distances but not for others.

They found it was balanced like this when I had two masses the same size and they're equal distances from the pivot.

But they also found out that you could balance the seesaw with one mass on one side and two masses on the other side.

As long as the two masses were closer to the pivot than the one mass.

They found it was unbalanced when you had two equal masses, but they weren't equal distances from the pivot and they found it was unbalanced as well when you had one mass further from the pivot and two masses too close to the pivot.

So it didn't always balance when there's one mass on each side or even unequal numbers of masses on either sides.

So, thinking back to those predictions we saw earlier, which prediction about the seesaw was correct? And I've shown you an example of a balanced seesaw and an unbalanced seesaw to help you with that.

So was it A, I think it would be balanced when the weight on each side is the same? Is it B, I think it's just the position of the weight that's important? Or was it C, both the weight and the position affects balance? So pause the video, make your selection, and restart please.

Okay, welcome back.

Hopefully you selected C.

The weight and the position both affect balance.

You can have unequal weights on opposite sides and still get balanced as long as you get the positions correct.

So, the answer is C, well done if you've got that.

So in this lesson we're gonna try and investigate that relationship in a bit more detail.

And to do that we're gonna use a balance beam.

A balance beam is something like this.

It's a simple plastic beam balanced in the middle around the pivot.

So, the pivot's exactly in the center and the beam naturally balances, so it's naturally horizontal.

But the beam's got these set of pegs.

And on those pegs we can put small masses hanging from each side.

And we've got one on each side in this diagram here.

And those pegs are equal distances apart on each side.

So, peg one is the same on each side and peg two is the same on each side.

They're typically about four centimeters apart.

And we can use this to investigate whether or not masses on each side are balanced because it'll be tilted when it's not balanced and straight when it is balanced.

What we can do then is place combinations of masses on each side of the beam at the same distance or different distances and then decide if the beam is balanced or unbalanced.

So as I said, if it's balanced it'll be horizontal, as in the diagram on the left.

And if it's unbalanced, it'll be tilted to one side or the other as shown in the diagram on the right there.

So, the balance combinations can be recorded in the table and then later we can look at those peg measurements and mass measurements and see if there's a pattern between them.

So we can record something like this, a table showing the force downwards, which depends on the mass, and the distance from the center.

And compare both sides and see if there's a relationship between the two.

So, I've got a very simple check here.

I'd like to look at the three pictures and decide which one shows a beam that is balanced.

So pause the video, make a selection, and restart.

Welcome back.

Well that was a fairly easy one.

B is balanced.

So I've got balanced beam, it's horizontal there.

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

And what you're gonna do is set up the empty balance beam as you saw earlier.

You're going to measure and record the distances between the adjacent pegs 'cause you'll need that distance later.

Then you're going to try different combinations of masses and differences, sorry, distances on each side and identify which ones cause the beam to be balanced.

So, you only really need to record the combinations that cause the beam to be balanced, not the ones that don't.

So we can watch a video showing that sort of experiment now.

Balance beam is a plastic rod and it's balanced around pivot in the center as shown here.

And there are a series of numbered pegs from which you can hang small masses or weights all along the sides.

The balance beam tilts when a mass is added, a 10 gram mass produces a force of 0.

1 newtons on the beam.

Beam's unbalanced.

When a 10 gram mass is placed the same distance on the opposite side, the beam is balanced again.

Removing the mass unbalances the beam again, but then adding two masses on the right can balance the one mass on the left.

The beam is balanced.

A single mass in position eight can be balanced by four masses added to position two.

The beam is balanced.

You should test different combinations of masses on the left hand side and the right hand side and record which combinations cause the beam to balance.

Try as many combinations as you have time for.

Here is a set of example results you can use if you don't have enough time or the right equipment.

Hopefully that video showed you exactly what you needed to do.

So what I'd like you to do is to pause the video, follow these instructions, and collect a set of data for balanced beams and then restart the video when you've done that.

Good luck.

Okay, welcome back.

Hopefully you've got results similar to these.

I've calculated the force times the distance using a distance between pegs that's one centimeter.

Your balance beam might have been different so, your results might look a little bit different, but they should show the same sort of pattern.

Well done if you've got something like this.

Now it's time for the second part of the lesson which is about calculating turning effects.

And in this section, we're gonna look at the results of the experiment and see if there's a relationship between the force and the distance on the left hand side and the force and the distance on the right hand side when the beam was balanced.

That'll lead us into doing calculations of something called moments, which is the turning effect of a force.

Okay, so we're gonna start by looking at the data I collected during my experiment and seeing if there's a pattern there.

So, here's a table of data I collected and what I asked you to do was to multiply the force by the distance from the pivot.

So we'll do that for each set, for each balanced set anyway.

So, for the first one I can do the calculations here.

The second one, the third balanced position, fourth, and fifth.

And hopefully what you can see is there's a very clear connection between the force times the distance on the left side and the force times the distance on the right side.

So this set of numbers here.

And in fact, they're both identical.

The force times the distance on the left and the force times the distance on the right is always the same for any balanced beam.

So we've got a conclusion already.

Okay, so let's see if you know what that conclusion was.

What conclusion can you make from this balance beam data? We've got a table of data there, we've got forces and distances on the left and forces and distances on the right.

I wanna know which of these conclusions was correct.

Is it, it balances when the distances are the same? It balances when the force is the same on each side.

Or it balances when the force multiplied by the distance on the same on each side.

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

Welcome back.

Well, as you saw in my example table before, it balances when the force multiplied by the distance is the same.

So if you multiply the force by the distance on the left for any row of that table, then it'll be the same for the left side and the right side.

Well done if you've got that.

Okay, let's see if you can apply that knowledge to another scenario.

I've got a wooden ruler that's balanced here.

It's got masses on the left and the right and they're place at different distances.

So, is that beam balanced? Pause the video, make your selection, and restart.

Welcome back.

The answer you should've selected was true, but why is that? I'd like you to justify your answer.

So, is it because the total forces are the same size in each direction or is it because the product of the forces and the distances are the same size? So, pause the video, make your selection, and restart.

Hello again and the answer was the product of the forces and the distances.

So that's the forces multiplied by the distances are the same size.

Well done if you chose that.

Right, it's time to look at the turning of effect of a force in more detail.

So, the overall turning effect of a force is calculated by multiplying the force by the distance to the pivot.

And you can see a diagram of that here.

So, I've got a force trying to turn this lever anticlockwise and it's a certain distance from the pivot.

And to find the overall turning effect of that, I'd multiply the force by the distance.

Now because I'm multiplying a force which is measured in newtons by a distance that will be measured in meters or centimeters, I've got these units that I can measure the turning effect in.

So it's measured in newton-meters if I use distances in meters or it's measured in newton-centimeters if I use distances in centimeters.

So I'm gonna show you an example of calculating the turning effect of a force here and then I'm gonna ask you to have a go at one.

So, calculate the turning effect caused when a force of five newtons is acting 1.

5 meters from a pivot.

So what I do is I write up that relationship we saw on the last slide.

Turning effect is force times distance.

I substitute in the values by looking in the question and find the force is five newtons, the distance is 1.

5 meters.

And that will give me a turning effect of 7.

5.

But again I need some sort of unit there.

I've multiplied newtons by meters so my answer is in newton-meters.

Now it's time for you to have a go.

I'd like you to calculate the turning effect caused when a force of 25 newtons is acting 1.

2 meters from a pivot.

So, pause the video, have a go at the calculation, and then restart and we'll check your answer.

Okay, welcome back.

Let's have a look.

You should have written down turning effect is force times distance.

Always write up the equation, it helps you remember it.

Then substitute the values in, 25 newtons times 1.

2 meters and that gives a turning effect of 30.

And again, newtons and meters were used so it's newton-meters there.

Well done if you've got that.

Let's do a second example.

And this time we're gonna look at distances in centimeters.

So, calculate the turning effect caused when a force of five newtons is acting 1.

5 meters from a pivot.

So, as before, I write out the equation.

I substitute the values in looking carefully at the question and then I put my answer down and it's 7.

5, but this time it's centimeters and newtons.

So newton-centimeters is what I need to give the answer in.

Now it's your turn.

I'd like you to calculate the turning effect caused when a force of 25 newtons is acting 1.

2 centimeters from a pivot.

So pause the video, carry out the calculation, and then restart.

And your answer here should be this, turning effect is force times distance.

Again, we've written out the equation.

Putting the values in there and finally the calculation gives 30 newton-centimeters because the distance was centimeters again.

Well done if you got that.

So we call the turning effect of a force a moment and we're gonna try and use that term to describe the turning effect from now on.

I've got a diagram here and I've got masses on both sides of a ruler and they're causing turning effects because their weight, which is acting downwards, is a distance from the pivot.

And we need to describe the directions of that turning effect as well because down isn't good enough 'cause one of those masses is gonna cause the beam to tilt one way and the other mass is gonna cause it to tilt the other way even though both of those forces are down.

So what we like to use to describe the direction of the turning effect are clockwise and anticlockwise.

So, on the right hand side of the diagram that 10 newtons is gonna cause the beam to try to rotate clockwise.

And on the left hand side of the beam that five newtons is gonna try and cause the beam to rotate anticlockwise.

That beam's balanced because if you calculate the moments on each side, you come up to the same value.

The balance beam has got equal clockwise and anticlockwise moments.

To check if any simple beam is balanced, all we need to do is just compare the moments on each side, the clockwise and the anticlockwise moments, and if they're equal to each other the beam will be balanced.

So let's do that for this example.

I've got some anticlockwise moments here.

The four newtons on the left hand side is gonna cause it to rotate anticlockwise.

And I can calculate the moments on that side using the mathematics we had earlier.

So the moments and the force times the distance, that's four newtons times 25 centimeters.

That's 100 newton-centimeters.

And on the other side, we've got those five newtons and that's gonna cause clockwise rotation.

So, I'll calculate moments there.

The moments is force times distance.

The moments five times 20 centimeters and that gives 100 newton-centimeters as well.

That beam's going to be balanced because the clockwise moments and the anticlockwise moments are the same.

And now it's time for you to check whether the moments on this beam are balanced.

So, I'd like you to calculate the clockwise and the anticlockwise moments and decide if that beam is balanced or if it will rotate.

So pause the video, carry out the calculations I did on the last slide to see if it's balanced, and then restart.

Okay, welcome back.

Let's have a look at the moments.

First of all, the anticlockwise moments.

If I multiply the force times the distance there, I get 135 newton-centimeters.

And then the clockwise moments, multiplying the force and distance again, I get 120 newton-centimeters and they're fairly close, but they're not the same.

So this beam is not balanced.

In fact, it's going to start to rotate anticlockwise because that's the side with the greatest moment on it.

Well done if you got that.

Okay, it's time for the next task and some pupils have completed an experiment with a balanced beam and have collected the data here in this table.

And what I'd like you to do is I'd like you to calculate the moments and fill in that table and then state whether the beam is balanced or unbalanced in each case please.

So, pause the video, carry out those two questions, and restart when you're done.

Okay, welcome back and I've completed the table here, so hopefully you've got answers like this.

If we look at the table, we've multiplied the forces times the distances in each case.

And when the moments on the left side and the right side are equal, that's when the beam is balanced.

So we've got two, three balanced beam, including the original ones and two unbalanced beams. Well done if you've got answers similar to that.

Now we've reached the end of the lesson and here's a summary of the information you should have learned during it.

Forces cause turning effects and those turning effects are called moments.

The size of the moment is given by the relationship here.

Turning effect is force times distance to the pivot.

The size of that turning effect can be measured in newton-meters if we're using meters as our measurement of length or newton-centimeters if we're using centimeters.

And a beam is balanced when the clockwise moments are equal to the anticlockwise moments.

And if they're not equal then the beam isn't balanced and is gonna start to rotate.

So well done for reaching the end of the lesson.

Hopefully I'll see you at the next one.

Goodbye.