# Lesson video

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

This lesson's all about balancing, and in it, you're going to carry out an investigation to see what factors affect the balance of a beam and to do calculations involving balance.

By the end of this lesson, you'll have carried out an investigation into the factors that affect how a beam balances.

For that, you're going to use a rule and some masses.

You have discovered something called a principle of moments and then used that in a range of calculations.

The first is equilibrium.

And an object is in equilibrium when there are no resultant forces on it and no resultant moments.

A moment is a turning effect of a force and we measure that in newton metres.

And the principle of moments is a statement that states when the clockwise moments acting on an object are equal to the anti-clockwise moments, the object will be balanced.

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

The lesson's in just two parts.

In the first part, you're going to carry out an investigation that will allow you to discover the principle of moments using a balance beam.

And in the second part of the lesson, you'll be using that principle of moments to solve a range of problems involving balance.

Let's get started with planning the investigation.

You have studied moments in previous lessons, but as a recap, the moment caused by a force is given by this equation, moment X force times distance, normal to the direction of the force or right angles to the direction of the force.

In symbols, we can write that as M equals F times D, and where M is the moment measured in newton metres.

F is the force measured in newtons and D is the distance in the direction of the force and that's measured in metres.

Let's try an example to see if you can remember how to calculate moments.

So I'm going to calculate the moment caused when a force of 5.

0 newtons acts 1.

5 metres from a pivot.

And to do that, I write out the equation, moment equals force times distance.

I substitute in the two values from the question here.

The force is five newtons, the distance 1.

5 metres and that gives me a moment of 7.

5 and I need a unit for that and that's newton metres.

Okay, let's see if you can calculate a moment.

I'd like you to calculate the moment for the data in this question please.

So pause the video, do that calculation and restart.

Welcome back.

One, you should have written the equation, substituted the two values in that list, 25 newtons and 1.

2 metres, and that gives you a moment of 30 newton metres.

Well done if you got that.

So in this lesson, we're going to try and find out what factors affect the balancing of a beam and we're going to use a metre rule for that beam, on top of a triangular wedge, something like this.

So we've got a metre rule there and it's on top of a pivot, which is a triangular piece of wood or plastic, something like that just on top of a flat desk.

The wedge is placed halfway along the length of the rule so that the rule balances.

So we've got the weight of the rule acting down and there's going to be a reaction force from the pivot acting up right at the centre.

And that will give a balance rule.

You might find that your rule doesn't balance perfectly in the middle, so you'll have to find that balance point for yourself sometimes.

You'll also find that it's easier to balance the rule if the pivot's not a perfect triangle, if it's slightly flattened at the top to find as a simpler balance point.

So try and find a pivot that's not perfectly pointy at the top.

If you place a small mass on one side of the metre rule, then the metre rule rotate until it touches the desk and it'll stop rotating then.

So you'll get a situation like this where the weight of that mass is acting downwards on the rule, causing it to rotate in this case clockwise.

So the clockwise moment produced by that mass is causing that rotation.

You can get the rule to balance again by placing an identical mass the same distance from the pivot on the other side of it.

So a situation like this where I've got two masses, I've placed some 30 centimetres from the pivot, their identical masses producing identical downward forces and the beam balances again.

The beam isn't accelerating and there's no resultant force acting on it and it's not starting to turn in any way.

The wedge in the centre, that pivot must be causing an upwards force on it that counteracts the down force of those two masses and the weight of the rule.

So I've got a situation where the reaction force is equal to all of those three down forces added together, the weight of the two masses and the weight of the rule.

Now it's time for the first check for the lesson.

A balance rule has a weight of two newtons.

Two masses of weight one newton are placed on it as shown in that diagram.

I want to know what is the size of the upward force R.

So pause the video, make selection from the list there on the left and restart please.

Welcome back.

Hopefully you chose four newtons.

There are four newtons downwards.

We've got one newton and two newtons and another newton, and that gives an upward force of four newtons as well if the rule is balanced.

So well done if you've got that.

You can also balance the rule when you place a single mass on one side and two masses on the other side of the rule.

For that to happen, the single mass needs to be placed further from the pivot than the two masses on the other side.

So you can see in this situation, I've got a mass on the right hand side.

It's got a weight of W and it's 40 centimetres from the pivot.

And to balance that, I can place two masses.

So that gives a weight of two W on the left hand side, but that's only 20 centimetres away from the pivot.

The rule can also be balanced when the two masses are not placed on top of each other.

You have a single mass here on one side with the weight of W and the other masses on the other side, two W's got a different distances.

Both of those masses on the left are closer to the pivot than the one on the right in this situation.

I've got my distances marked at here.

And again that rule, rule of balance.

What you are going to do is carry out an investigation to try and find out different situations where the rule of balance is.

So you're going to place masses on either side of the rule and see if you can get positions where those balance against each other and the rule doesn't start tilting to each side.

You use different combinations of masses and you're placing them on opposite sides of the rule at different distances.

Some of the combinations that you'll find will balance and most will not.

So I've got situations like this, this situation balances if I position one weight 40 centimetres on one side and two weights 20 centimetres on the other.

But this situation doesn't balance.

So you are basically trying to find out different positions where the will balance and rule out once where it won't.

It can be difficult to get the rule to balance perfectly, so you are going to have to judge a little bit whether or not you think the rule is balanced.

If it's starting to tilt very slightly, you might judge that that's approximately balanced.

I've got Andeep and he's trying to balance a rule as shown in the diagram here.

I've got three masses on it and as you can see it's not balanced, it's tilted to the right side here.

Which of the following changes do you think would cause the beam to balance? And I've got three possibilities there.

Welcome back.

Well, you should have chosen these two, move mass X further from the pivot to the left or move mass Z closer to the pivot on the right.

And the reason that that will cause it to balance is in the first situation, that's going to increase the anti-clockwise moments to cause a bit more tilting to the left side there.

And in the second one, you're gonna be decreasing the clockwise moments and both of those modifications would make that rule of balance a bit better.

So well done if you selected those.

And now it's time for you to carry out the investigation.

So what you're going to do is set up the fairly simple apparatus like this.

You've got a wedge or pivot, the rest are on a desk and you've got a balance rule on top of it and you've got a selection of masses to move to different positions along the left hand side and the right hand side of the rule.

So balance the metre rule with its centre on top of that triangular wedge.

Carefully position different combinations of up to five 0.

5 newton weights.

You don't want to have too many weights on masses on there.

And adjust those positions until you get the rule of balance.

Record any combinations of masses and distances which cause the rule to balance.

You don't need to record all of the possibilities that do not cause it to balance.

I want you to repeat that process until you find at least five different balancing combinations.

You're going to record your results in a table like this.

I've already recorded one set of results for the other, but I'd like you to find at least five combinations where you'll get the rule to balance with different masses on different sizes.

Sides, sorry.

So when you're ready, carry out your experiment and then restart the video.

Welcome back.

Well, your results should look something like this.

I've got a completed table here with five different combinations of masses at different distances and for that, the rule of balance for each of those five.

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

And now we're gonna move on to the second part of the lesson.

And in it, we're going to discuss the principle of moments using the data we collected from the investigation and then try to apply that principle in a range of situations.

So let's go on with that.

What we're going to do is analyse the situations where they're being balanced.

So we're gonna look at the combinations that cause that rule to balance by finding the total clockwise moments and the total anti-clockwise moments.

What I mean by that is I'm going to calculate the moments trying to turn it clockwise and anti-clockwise separately and compare them.

So the anti-clockwise moments in this diagram would be the sum of the moments caused by each of those weights.

So I've got two weights of W and they're different distances away from the pivot that are right here.

So my anti-clockwise moments would be W times D two added to W times D three.

My clockwise moments were a bit simpler because I've only got one distance involved there and a weight of two W.

So my clockwise moments would be two times W times D one.

So let's do a few examples of that.

So here, I've got a balance rule and we're gonna calculate the clockwise and anti-clockwise moments.

So my anti-clockwise moments, I write out a statement of what I'm doing and then I sum the anti-clockwise moments.

And as you can see, I've got two separate masses at two different distances and I like to put each mass in distance in brackets for clarity here.

So I've got N 0.

5 newtons times N 0.

1 metre because that's the distance away from the pivot.

And I add that to N 0.

5 metres times N 0.

3 metres.

And calculate that, that gives me two separate moments, 0.

05 newton metres and N 0.

15 newton metres and add those together to get a total of 0.

2 newton metres anti-clockwise.

The clockwise moments are a bit simpler because I've only got one mass on that side.

So I've got N 0.

5 newtons downwards and N 0.

4 metres and I multiply those together.

And I get my clockwise moments of N 0.

2 newton metres.

Okay, I'd like you to try and calculate a moment.

I'd like to know the total clockwise moments of this balance rule.

So I don't need to know anything about the anti-clockwise moments, just the total clockwise moments please.

So pause the video, work that out and restart.

Welcome back.

25 newton metres.

If you calculate the clockwise moments, I've got two masses on that side.

I've got N 0.

5 newtons and it's N 0.

30 metres away from the pivot.

And I've got another N 0.

5 newtons and that's not N 0.

20 metres from the pivot.

So calculating that gives me a total of N.

25 newton metres.

Well done if you got that.

If you analyse all of the results from your experiment, you'll find that the rule is balanced when the total clockwise moments are equal to the total anti-clockwise moments.

So every one of your results should show that.

So I've got a situation like this and in this situation if I calculate the clockwise and the anti-clockwise moments, they're both N 0.

4 newton metres.

And in this situation, that rule will be balanced.

But if I put another mass on and that changes the moment, so I've still got N 0.

4 anti-clockwise, but now I've got N 0.

8 newton metres clockwise, that rule is not balanced.

So if the moments are different, the rule is unbalanced.

If the moments are equal to each other in opposite directions, then there's no overall change.

So there's a balanced rule.

What I'd like you to do is to use the idea to decide which of the following beams are balanced and these figures aren't drawn to scale.

So I've got different forces and different distances from the pivot and some of these are balanced and some are not.

So I'd like you to decide that by calculating the clockwise and anti-clockwise moments and seeing if they're the same or not.

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

Welcome back.

Hopefully you selected beams A and C as being balanced.

So let's have a look at the moments for each of them.

In the first one, the situation A, I've got one newton metre clockwise and one newton metre anti-clockwise.

So that one's balanced.

And in situation C, again, I've got two newton metres clockwise and two newton metres anti-clockwise.

So that one's balanced.

But in situation B, I've got different moments in different directions.

So I've got clockwise moments of 4.

8 newton metres and anti-clockwise moments of 4.

2.

And they're different so that rule isn't balanced.

Well done if you selected A and C.

That idea leads us to the principle of moments.

And the principle of moments tells us when a beam is balanced.

And I've got it written out here in a box.

If an object is in equilibrium, the sum of the clockwise moments is equal to the sum of the anti-clockwise moments.

So I've got this situation, I'll mark all the distances and forces on it and that means that if I do the clockwise moments and anti-clockwise moments, you can see that they're equal.

So F one D one, the force times the distance one added to the force two times distance two is equal to force three times distance three.

We mustn't forget that to be an equilibrium as well, the forces in opposite directions must be balanced.

So I've got three downward forces, the F one, F two and F three.

So there must be an upwards force that counteracts them for it to be in equilibrium.

So there's no resultant force acting on the beam as well.

And that must mean that this.

That those three forces plus the weight of the rule must be balanced by a normal reaction force from the pivot.

And I've drawn that on the diagram as are there.

So R is equal to the weight plus the three forces of the masses on top of the rule.

We can use the principle of moments to find unknown forces or distances.

So I've got an example here.

I've got a balanced beam, but that balanced beam has one of the pieces of information missing from it.

That's the distance I've placed one of the forces from the pivot.

So what I'm going to do is to try and find that distance X.

And to do that, I follow these stages.

First thing I do is I can calculate the anti-clockwise moments because I've got a force and a distance in the anti-clockwise direction.

So I can actually calculate that moment.

I write down my equation, substitute in the two values, and that gives me an anti-clockwise moment of 16 newton metres.

Now I know that the beam is balanced.

So the next stage is to use that anti-clockwise moments to say that the clockwise moment must also be 16 newton metres.

We can use that fact for the beam being balanced and use it to find the clockwise moment to find the distance.

So I write up the equation again, but this time I rearrange it.

But I rearrange it to give X is equal to M divided by F.

So the distance is the moment divided by the force.

And if I substitute the numbers there, I quite simply calculate X as being N 0.

5 metres.

Okay, now it's time for you to have a try at that.

I've got a beam here and this one's balanced.

And what I'd like you to do is find the size of the force W.

So I've got clockwise moments and anti-clockwise moments and they're equal to each other.

So I'd like you to find that missing force W please.

So pause the video, work out what that force is and restart.

Welcome back.

Hopefully you selected 6.

4 newtons.

And to work that out, what I did was calculate the clockwise moments using the information on the diagram.

And that gives me clockwise moments of 1.

60 newton metres.

And then I know the anti-clockwise moments must be equal.

So we can use the anti-clockwise moments to calculate W like this right out the equation.

The weight W must be equal to the moments, the anti-clockwise moments divided by that distance of N 0.

25 metres.

And that gives me 6.

4 newtons.

Well done if you got that.

You can use the principle of moments no matter how many weights and distances are involved in the balance beam.

So I've got a slightly more complicated situation here and I'm going to show you how to calculate the missing weight W.

So this is a balanced beam.

So to find the force W, I'm going to calculate the anti-clockwise moments first because I've got all the information in the anti-clockwise direction.

So the anti-clockwise moments, the moments must be equal to the forces times the distances.

So I've got 10 newtons and that's N 0.

5 metres away from that pivot.

And then I've got another five newtons, but that's N 0.

8 metres away from the pivot 'cause if you look careful at the diagram, it's N 0.

5 metres and another N 0.

3 metres.

So I've been very careful with that.

So I'm gonna calculate those anti-clockwise moments now and doing the math, that gives me anti-clockwise moments of nine newton metres.

Now the clockwise moments must be equal to that because they are equal and opposite for the beam to be balanced.

So the clockwise moments, I can use those to find the missing weight W.

So the force would be equal to the moment divided by the distance or W equals M divided by D, substituted that value for the moments I calculated earlier and the distance of N six metres.

And that gives me a missing weight of 15 newtons.

And now it's time for you to have a go at that process.

So I've got another balanced beam here.

I'd like you to find the distance X.

So remember you're calculating the moments on one side and using that to find missing values on the other.

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

Welcome back.

Hopefully you selected option B, N 0.

4 metres.

What I needed to do to find that was calculate the clockwise moments using all the information on the clockwise side of the beam, the right hand side there.

And that gives me a total clockwise moments of 3.

6 newton metres.

And I use that value for the clockwise moments to find X.

So that X, that distance X must be the moment divided by the force.

And I've got both of those, put those into the equation and I get N 0.

4 metres.

Well done if you got that.

And now it's time for the final task of the lesson.

And what I'd like you to do is this, I'd like you to state two conditions required for an object to be in equilibrium and then I'd like you to look at the two diagrams below and find the missing values.

So for the left end diagram it's find the distance X.

And for the right end diagram, I'd like you to find forces W and or the normal reaction force at the pivot there.

Welcome back.

Well, here's the two conditions required for an object to be in equilibrium.

The sum of the clockwise moments must be equal to the sum of the anti-clockwise moments.

And there must be no resultant force acting on the object.

Well done if you got both of those.

And here's the answer to the first of those scenarios about the beams in equilibrium.

We're finding the missing values here and finding the distance X.

So you find the anti-clockwise moments and use those to find the clockwise moments.

And that gives me a distance of 9.

5 metres.

Well done if you got that one.

And here's the second of those.

And again, we find the clockwise moments and that gives me a clockwise moments of 5.

2 newton metres and then the anti-clockwise moments.

So that gives me a weight W of 13 newtons.

But we also had to find the reaction force or that's the upwards force.

Well, if you add all the down forces together, that gives a total downward force of 32 newtons.

Sorry, 32 newtons.

So there must be an upwards force of 32 newtons and that's the reaction force.

Well done if you got both of those.

And we've reached the end of the lesson now, and here's a summary of all the information we've learned.

We've got the definition of a moment.

It's the force times the distance normal to the direction of the force.

And we found the principle of moments and that states that for an object in equilibrium, the sum of the clockwise moments is equal to some of the anti-clockwise moments.

Any unbalanced moments will cause an object to start to rotate and it won't be in equilibrium.

It'll rotate in the direction of the largest total moment.

Well done for reaching the end of the lesson.

I'll see you in the next one.