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

This lesson's called Terminal Velocity and we'll be looking at falling objects and how they speed up until they eventually reach a maximum falling speed as they fall through a gas or a liquid.

By the end of this lesson, you're going to be able to describe the forces acting on an object as it falls and to be able to find the resultant force.

You're then gonna be able to use that resultant force in Newton's second law motion or F = m a to explain the motion of the object, why it gets faster.

These are the key words that will help you understand the lesson.

The first is the gravitational force, and that's a non-contact force that attracts masses towards each other, it pulls things downwards on earth.

Drag is the force as you're moving through a fluid that opposes its motion, it works against the movement.

The resultant force is the overall effect of forces acting on an object and the terminal velocity is the maximum velocity and object reaches as it falls through a fluid.

And that is because the resultant force becomes zero eventually.

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

This lesson has three parts and in the first part we're going to be describing the forces acting on an object as it falls through a fluid and to come up with the idea of terminal velocity.

And the second part, you're going to carry out an experiment to attempt to measure the terminal velocity of an object.

And then the third part, we're gonna again look at the forces and how they can be used to explain the motion of the object and why it's getting faster at certain points and eventually reaches that final speed terminal velocity.

So let's start by looking at the forces as you fall through a fluid.

When you first release an object or drop it, there's only a gravitational force acting on it and that gravitational force is gonna cause an acceleration.

So the acceleration is purely going to be due to that gravitational force acting and that acceleration doesn't depend on its mass.

So if I was on the moon for example and I had a feather and a rock and I dropped them both from a height of two metres and both reached the ground at the same time and I've actually worked that out.

On the moon the strength of gravity, the gravitational field strength is 1.

6 metres per second squared.

And if I drop them from two metres, it would take 1.

9 seconds for a feather to fall straight down and hit the moon's surface and it'd take exactly the same time for a rock to fall that distance.

However, on earth, the situation's a bit more complicated because the objects need to fall through an atmosphere.

On the moon, there is no atmosphere.

So the atmosphere is going to produce a drag force acting on the objects as they move through it.

So any object moving through a fluid will experience a drag force and that drag force is going to reduce the resultant force acting on the object as it falls.

So they're not actually going to accelerate at the same rate.

So if I tried the same experiment on earth where gravity's a bit stronger, 9.

8 metres per second squared, if I drop the feather, it does still take about 1.

8 seconds to reach the ground.

'Cause the drag force is reducing the acceleration on it and the stone, well that's going to fall through the air quicker, it's gonna accelerate more, it's gonna reach the ground in 0.

6 seconds so the objects don't fall at the same rate.

We can explain the difference in the way the objects move on earth by considering the forces acting on them.

So we're gonna look at the gravitational force first, and that doesn't depend on the speed the objects moving at.

If I've got a stone and I drop it and I initially released it it might have a weight of 50 newtons, so there's 50 Newtons pulling down.

And then as it's moving it speeds up and it gets to 10 metres per second, that weight hasn't changed, it's still 50 newtons.

And third faster still, still 50 newtons.

And even when it's moving at a very, very high speed, that weight's unchanged, it's 50 newtons all the time.

So the weight of something or the gravitational force pulling it down doesn't change.

However, the drag force actually changes as the object's moving through the atmosphere.

When I initially release the stone, there's no drag force on it because it's not moving and that instant I've released it, so I've just got the weight acting on it.

But as it speeds up, a drag force is going to be produced as it moves through the atmosphere.

I've got it here as four newtons.

So it's moving at 10 metres per second, there's a small drag force acting on it.

As it speeds up that drag force increases.

So at 20 metres per second, drag force is more than doubled.

I've got something at about 10 newtons now and you can see that's going to affect the overall resultant force.

And when the stone's moving at very high speed, the drag force is getting quite similar to the weight or the gravitational force acting on the object.

That drag force is increasing because the stone is having to push more air out the way as it falls every second.

Okay, time for the first check of the lesson and what I'd like you to do is use the information in this diagram to calculate acceleration.

So the diagram shows the force is acting on a ball of mass, 9.

5 kilogrammes falling through the year, calculated acceleration using Newton's second law equation, F = m X a.

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

Welcome back, hopefully you selected 3.

4 metres per second.

I've got the resultant force by subtracting the drag from the gravitational force, though it's 1.

7 newtons, then I used it in this equation and it gives me 3.

4 metres per second squared.

Well done if you've got that.

You may have already noticed in the previous diagrams that the resultant force is going to change in an object as it falls.

So I'm gonna call the resultant force in our diagrams Fr from now on and it's gonna be acting on a falling object.

And it's going to decrease as the speed of the falling object increases.

So in this situation here I've got the object falling and I've got a resultant force of 40 newtons because there's a 15 Newtons gravitational force or weight put down and 10 newtons of drag up.

As the object moves faster, as the stone moves faster, my drag force has increased and that caused a decrease in my resultant force, it's now only 20 newtons.

And in my third situation I've got a drag force and a gravitational force that are equal to each other.

So eventually I'm going to have a situation where the resultant force is zero.

When there's no resultant force acting on an object, it stops accelerating, it doesn't stop moving, it stopped accelerating.

And what that means, it's going to be moving at a constant speed.

So I've got my diagram here and I can prove that it's not accelerating anymore.

I've got my equation to calculate the acceleration.

This is Newton's second law again.

If I substitute the values in there, I've got the zero newton's divided by whatever the mass of the stone is, it doesn't really matter 'cause if you divide zero by anything, you're still gonna get zero.

So that stone's no longer accelerating, it's reached a steady falling velocity and we call that falling velocity or falling speed a terminal velocity.

Okay, I'd like you to look at these four diagrams and look at the information provided on each and decide which of these objects has reached its terminal velocity as it's falling.

So pause the video, make your selection and restart.

Welcome back.

Hopefully you selected C.

As you can see in that one, the upwards force, the drag knot, putting on six newtons and the downs force, the gravitational force is not putting on six newtons.

This is zero resultant force, it's not going to accelerate.

In all the other situations, the forces are unequal.

So there is going to be a resultant force and therefore some acceleration.

Well done if you selected C.

Now we've reached the first task with the lesson and it's all about falling objects.

And what I'd like you to do is answer these three questions about the four identical balls that are falling.

So I've got all the information on the slide there.

I've got four balls all with the same mass, not put on 0.

25 kilogrammes.

And you can see there's different forces in each of those situations.

I'd like you to identify which ball is falling slowest and fastest and explain how you've reached that conclusion.

Discuss whether any of those balls has reached terminal velocity based on the information you can see.

And then calculate the acceleration of ball B for me, just that one.

So pause the video, answer those questions and restart.

Welcome back.

And here's the answer to the first two.

So ball D must be falling the slowest, if you look carefully at it, there's no drag force on it.

It's actually not moving downwards at all at this point, it's just been released.

So it's not moving.

The one that's falling fastest will be the one with the greatest drag force and that's ball C.

None of the balls have reached terminal velocity for question two.

And you can tell that because there's no situation where the forces are equal to each other and there's no resultant force.

Well done if you've got those two.

And finally, to calculate the acceleration of ball B, we find the resultant force on it and that's 0.

34 newton's.

And then we use Newton's second law equation to actually calculate the acceleration.

I get that as 1.

36 metres per second squared often rounded to two significant figures at 1.

4 metres per second squared.

Well done if you've got the answer.

We've reached the second part of the lesson now and what we're going to do is plan and carry out an investigation and then attempt to measure the terminal velocity of an object.

So let's start there.

The first thing I should explain is it's difficult to actually measure the terminal velocity of some objects when they're falling through in a laboratory.

And that because terminal velocities can be very high, it can be dozens of metres per second, perhaps even 50 metres per second.

And that's difficult velocity to actually measure.

And inside indoors we're gonna have very small distances.

So it's very difficult to measure the time it takes for the objects to move at the small distance when it's travelling at a very high velocity.

What we need to do to actually have measurable results is to increase the drag forces acting on the object and that's going to reduce the terminal velocities and make our measurements simpler.

So for example, if I was trying to measure the terminal velocity of something like a golf ball, well that's actually got a terminal velocity of 40 metres per second and that'd be very difficult to measure in a laboratory.

If I make it move through water, I reduce the terminal velocity to only seven metres per second because it's moving through a thicker fluid, a more dense fluid.

So I might be able to measure that if it had a large enough apparatus because it's slower.

So what I'm gonna do in the experiment is use a different fluid like water to reduce the terminal velocity of the moving object.

When an object's moving through a liquid, it's going to experience a much larger drag force than when it's moving through air.

So to investigate the terminal velocity of a small object as we're going to do, we're going to make the object fall through a column of water.

So something like this, I've got a large measuring cylinder here and I'm gonna fill it with water and drop objects into that measuring cylinder and hopefully as they fall through that water, they're going to reach their terminal velocity and I can measure it.

So it's a tall measuring cylinder, it is the simplest thing, I fill it with water and then I'm gonna drop a small object into that measuring cylinder from just above the surface of the water.

And I wanna drop an object that's going to sink in the water, but it's not really dense so I'm not gonna use a metal ball.

I'm probably going to use something like a plastic bead which will sink, but it won't sink particularly quickly and hopefully it will reach its terminal velocity before it reaches the bottom of the cylinder.

As the bead moves through the water, there's going to be two main forces acting on it.

First of all, there's going to be a constant downward force as we saw with any other object dropped falling through a fluid.

The gravitational force of the weight of the object acting downwards is going to be constant.

And there's also going to be a changing drag force, which is gonna increase as the object speeds up.

So I've got those two forces acting on it.

As the speed increases on the object, that drag force is gradually going to increase and that means the resultant force acting is gradually going to decrease as the object gets faster until eventually those two forces will equal each other and the resultant force will be zero and will be at terminal velocity.

Okay, to see if you understand the basics of the experiment, I've got five measuring cylinders here.

I'm showing the forces acting on a plastic bead, they're all identical plastic beads.

I'd like you to work out on which point in the motion A, B, C, D, or E is the acceleration of the bead smallest.

So pause the video, work up when the acceleration is smallest and restart please.

Welcome back, hopefully you selected D.

It's smallest there because the resultant force will be smallest.

If you look carefully, the drag force is almost the same as the weight of the gravitational force on the bead and so the smallest resultant force will be there and that means the smallest acceleration.

Well done if you've got that.

To measure the speed of the bead, you're going to need to know what depth it is beneath the surface of the liquid.

And there's a fairly simple way of doing that.

We can mount a ruler alongside the measuring the cylinder and that will allow us to see how deep the beads got in the water at particular times.

We can observe the position of the bottom of the bead.

Now you'll notice I've lined the rule up very carefully with the surface of the water, making sure the zero is in line with it and that will allow me to get the depth of the bottom of the bead.

And I can just read across from any image it can take, we're going to be recording the movement and the depth though is not at one five metres or 15 centimetres.

If you can't measure it with a ruler, you can actually use these side markings if you work out exactly what the spacing there are on the markings on the measuring cylinder, they can be used as a sort of ruler as well.

As I just mentioned, we are going to be filming the bead falling through the water because even though it's falling fairly slowly, it's still quite difficult to work out it's speed if you're just trying to observe things and use manual timing.

So we are going to position a camera so that we've got some footage of the bead falling and then put a stop clock along the side or use the timing of the video itself to actually get images where the bead is 0.

1 seconds apart or something like this.

And then we can look at the depth at the first 0.

1 seconds and the depth 0.

1 seconds later or 0.

2 seconds there.

And that will give us a way of working out the change in depth for that 0.

1 seconds.

So we've got a distance that each travels and we've got a time and we can use that to actually calculate its velocity.

So what I'd like you to do is to follow this method and try and find the terminal velocity of that bead or optic as it falls through water.

I've got all the instructions laid out there alongside a diagram.

One of the critical things is to make sure when you're recording this that you can see the bead and the time at the same time and the ruler so that you can actually measure the speeds.

We'll have a quick look at a video recording to show you the basic process.

Okay, hopefully that's given you the right idea.

<v ->What you're going to do is, as I've said,</v> is follow these instructions.

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

You don't need to record the velocities yet, we are going to be calculating those in the next part of the lesson.

So I'd like you to carry out the instructions, you can return to that previous slide and then restart the video once you've done.

Welcome back, hopefully your results, follow a pattern or something like this.

I've got some depths, some changes in depths and as I said I've not worked out of the velocities yet.

So if you collected that data, well done, let's move on to the next part.

And now we're onto the final part of the lesson and we're going to find the terminal velocity of the object and discuss the forces acting on objects as they fall again.

We can find the terminal velocity of the bead falling through the water based upon the distance it travels and time it takes to travel at distance for very small sections of the movement.

So we're going to use the speed equation or the velocity equation where velocity is distance divided by time.

In this case velocity is the change in depth 'cause that's the distance divided by the time taken and it is written in symbols there as v = d divided by t.

So I've got some example data from the table here and you can see I've got times depth and most importantly the change in depth and that change in depth is the change in depth for each 0.

1 second.

And I can calculate the velocity for each of those time periods.

So for the first one, after the first 0.

1 seconds, you can see I can write the equation and the change in depth is 0.

41 metres, I've taken that from the row of the table and the time it took to change that amount of depth was 0.

1 seconds.

And that gives me a velocity of 0.

41 metres per second, which I fill in the table.

For the next row of the table.

Again, I'm looking between 0.

1 and 0.

2 seconds.

The change in depth there was 0.

07 metres, but the time period, the amount of time that passed as it changed, that amount of depth was again 0.

01 seconds.

So I can calculate the velocity during that 0.

1 second period and it's 0.

72 metres per second and I fill it in there.

Okay, it's time for you to have a go.

I'd like you to use this data table which has got different data in it and calculate the velocity of the bead at time = 0.

2 seconds for that row of that table.

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

Welcome back, hopefully you selected 0.

73 metres per second.

I've got my calculation here.

The change in depth was 0.

73 metres and remember each time period was 0.

10 seconds, so that gives me 0.

73 metres per second.

Well done if you've got that.

Once we've calculated all the velocities, we can quite easily find the terminal velocity.

So I've got a data table here and I'm looking for a situation where the velocity has stopped increasing.

So if I look at the first, sorry, after the first 9.

10 seconds, you can see the velocity has increased to 9.

41 metres per second.

And then it's increased again.

The number's gone up, it increases again, it increases again and then it increases one more time.

After this point, once I've reached 1.

05 metres per second, you can see the velocity's not changing anymore.

So I've reached the terminal of velocity, which must be 1.

05 metres per second.

Okay, what I'd like you to do here is to identify the terminal velocity for this falling object from that data table.

So pause the video, work out what the terminal of velocity must be and restart please.

Welcome back.

Well hopefully you selected 1.

22 metres per second.

As you can see, once we've reached 1.

22 metres per second, there's no further increase in velocity.

So that must be the terminal velocity.

Well done if you've got that.

When we've reached terminal velocity, the drag force and the gravitational force must be the same as each other because there's no resultant force.

And what that allows me to do is to calculate the maximum drag that would happen on a falling object.

So if I calculate the gravitational force using this expression you may have seen before, the gravitational force is the mass times the gravitational field strength and we use the symbol W for the gravitational force or sometimes call it the weight.

I can calculate the weight of the object and that must be the same as the maximum drag.

So I'm gonna calculate the weight of this 5.

9 kilogramme stone that I've dropped.

On earth, the gravitational field strength 9.

8 N/kg so I can calculate the weight or gravitational force of this stone like this.

And that gives me a way of 49 newtons.

At maximum speed at terminal velocity, the drag force must be equal to that weight.

So the drag force here at maximum or at terminal velocity is 49 newtons as well.

Let's see if you can do something similar.

I've got a tennis ball here.

Tennis ball is a mass, 50 grammes.

What's the maximum drag force? So what's the drag force acting when the ball reaches terminal velocity? So I've got four options though on the left.

Pause the video, make your selection and restart.

Welcome back, hopefully you picked 0.

49 newtons.

The drag force is going to be equal to the gravitational force at terminal velocity.

So I'm gonna calculate that gravitational force like this that gives me 0.

49 newtons.

So the drag force is also 0.

49 Newtons.

Well done if you've got that.

A graph showing the velocity against time for a falling object will have this shape as it falls through a fluid.

At first there's going to be a steep gradient and that indicates a very high acceleration.

So the object's going to accelerate a great deal at first.

A little bit later on the gradients going to be more shallow.

So we've got a lower gradient there and that shows there's a lower acceleration.

And finally, when the object reaches its terminal velocity, we're going to have a gradient of zero and that indicates that there's no acceleration at all.

Okay, let's see if you can interpret the graph.

I've got four fourth diagrams of a skydiver.

It's the same skydiver in each one and I've got a velocity time graph.

And I'd like you to match each of the marked positions on the graphs and the four diagrams of the skydivers together please.

So pause the video, do that and restart.

Welcome back.

Well for position A, that's when I first started and there's no drag force I've got the maximum acceleration.

So that was figure two.

For position B, that's figure one where I've got a small drag force.

For position C, I've got a larger drag force now, so a smaller acceleration.

And finally a D, the forces are equal to each other and in opposite direction, so there's no resulting force there.

Well done if you've got those four.

And now for the final task of the lesson and Alex has accidentally dropped a sandbag, which has a massive four kilogrammes from a hot air balloon, it's gonna fall directly downwards and before it reaches the ground, it reaches its terminal velocity.

What I'd like you to do is to explain in terms of the force that's acting on it, why the sandbag speeds up in the first few seconds, but then why it reaches a maximum falling speed.

And then once you've done that, I've got a diagram of the sandbag.

During the fall at one particular point I'd like you to calculate the gravitational force acting on it, and then the acceleration of the sandbag at that particular time please.

So pause the video, work out your answers to those and restart.

Welcome back.

And here's the explanations.

So for the first part why is it speeding up? Well, a gravitational force X downwards and a drag force X upward, the drag is smaller than the gravitational force.

So there is a result in force downwards and we can have acceleration.

The second part, why does it reach a maximum speed? Well eventually that drag force is going to be equal to the gravitational force.

So there's no resultant force, no rule acceleration, and we've got a terminal velocity.

Well done if you've got answers like that.

And here are the calculation parts.

Calculate the gravitational force.

Well I've used the W = m x g calculation and got it as 39.

2 newtons.

And then I'm gonna calculate the acceleration.

So I work out the resultant force there.

I take one force away from the other and the resultant force is 20 newtons and I can use that in Newton's second law equation F = ma and that gives me an acceleration of 5.

0 metres per second squared.

Well done if you've got that.

We've reached the end of the lesson.

So here's a summary of all the information.

An object falling through a fluid will experience two forces, constant gravitational force which acts downwards, and a drag force which increases as the velocity or speed of the object increases.

The resultant force causes the object to accelerate.

But when the drag force and the gravitational forces are equal there is no result in force, the object doesn't accelerate and it's reached its terminal velocity.

Well done for reaching the end of the lesson.

I'll see you in the next one.