High School Physics Newton's Third Law

Hi, welcome back to educator.com, today we are going to be talking about Newton's third law.0000

Put your hand, just as a quick experiment, on the edge of the table, or something hard that is fixed in place, and push for a while.0005

Just push for 10 seconds or so, and then take a look at what the bottom of your hand looks like.0014

If you look at it, you will notice that there is actually a mark on your hand, there will be some sort of line, or some sort of indentation.0020

So what happened?0030

You were pushing on the table, but what happened to your hand?0031

Your hand got pushed back on by the table.0034

Every force is going to have a force that resists it.0037

There is going to be an equal and opposite reactionary force.0040

If you push a certain amount of force into the table, the table is going to push a certain amount of force back into your hand.0042

You push on the table, it pushes back on you.0048

Newton's third law, one way to put it, (Newton put it in a slightly different way himself), but in modern language, 'Whenever an object a force on another object, the second object exerts a force of equal magnitude in the opposite direction, on the first object'.0052

If you put in a force of some amount of newtons, say, x N this way, the object is going to put a force of x N this way.0067

If you put it symbolically, the force of A on B = - the force of B on A, but negative, i.e. F_A-B = - F_B-A, so same magnitude, but opposite directions.0075

Just some basic everyday examples..0085

How about the hammer hitting a nail?0088

We have got a nail like this, and a hammer comes down on it, what happens?0090

The hammer hits the nail, and bounces back off, stops in place, the nail gets driven down into the wood, so there is definitely a force on the nail, but the hammer stops, for the hammer to stop, there has to be a force on the hammer.0099

The amount of that force is the amount of force that the hammer puts in to the nail, the same amount of force that the hammer gets from the nail.0112

They are going to be in opposite directions, but they are going to be equal, and that is what stops the hammer, and moves the nail, and then friction arrests the movement of the nail, we will talk about that later when we get to friction.0119

What if you are swimming?0129

If you are swimming, you are swimming along, you got yourself in the water, and you push on the water this way.0131

For example, if you do a breaststroke, and when you are swimming like this, your hands are cupping the water, they are catching the water, and they are pushing against the water.0140

So, you push against the water, and because you are pushing against the water, the water pushes back on you, which pushes you forward.0148

If you are driving along in a car, the car, it has wheels, (we have not talked about friction yet, we will very soon), the wheels, they push on the earth, they spin , and because of friction, them trying to rotate, pushes on the earth.0155

They are going to try to rotate this way, the wheels try to rotate this way, because of their friction, they have got friction, they stick to the earth, they are going to push the earth this way, the response of which is going to push the car this way.0178

Friction once again, combined with Newton's third law, is what gives our car motion.0189

When we walk on the earth, when you walk along, your foot pushes into the earth at a certain amount, which is going to cause you to be pushes in the opposite direction.0196

You push on the earth, if you want to jump, you bend your knees, and you push down really hard, and that is going to result in you getting pushed up, which is going to cause you to fly up into the air.0210

That is how you move, you move by pushing on something, and it responds because of Newton's third law, every force has an equal and opposite reaction force.0223

You push a certain amount , and that thing is going push back on you with that same amount in the opposite direction.0232

A careful thing to pay attention to is that, Newton's third law is always true, but often when we are working on our problems, it will not come into play.0239

It is still there, it is still happening, but this is because our problems are not normally going to have to include Newton's third law in the way we think about it.0247

It is still there if you want to think about it, but it will not have any effect on what we are doing in our work.0255

One reason why it often happens is that the force in the problem is external, it is guaranteed by the problem, we do not care what happens to the thing causing the force.0260

Very often we have talked about a block on a frictionless table or a block on a table.0269

We put some force into that block, what is putting that force in the block?0275

We do not know, it could be rockets on the back of the block, or it could be a person just standing there and pushing on the block, and so let us say it is a person standing there pushing on the block.0279

What happens to the person?0293

The person is going to wind up getting pushed back by the block by the amount that he push on the block.0294

But, we have been guaranteed by the problem, we have been told that a constant force is being applied, so we know that the person is somehow dealing with the force from the block, probably by putting it into the earth, by pushing against feet, and they are managing to handle the force that they are getting back from the block, and manage to keep up a constant force.0300

However the force is handled, we are guaranteed by the problem that there is a constant force, so with that point we can just deal with the constant force.0318

We do not have to worry about where the other part of it is going, because we have been given this external force that is guaranteed.0325

We do not have to care about where the forces are coming from, because it is given to us in the problem statement, it is given.0331

The other thing is, equal and opposite forces are often translated into the earth.0338

For example, with the person pushing on the block, which cause the person to be pushed back by a certain amount.0341

What does that person do?0354

The person then translates that force by pushing into the earth with his legs, which then cancels it out, so the amount that they get pushed by this becomes zero, because they get a net force of zero.0356

They put a push into the ground, (push by the person are in 'blue'), they push a blue up here, and a blue down here with their legs.0368

So the reactionary force is, from the person's point of view, they wind up experiencing the reaction forces, so the two cancel out, the person stands still, they can manage to keep up that constant force.0382

What happens to the force that gets us into the earth?0393

The equal and opposite force, if they get translated into the earth (or any planet), it is normally expected that the planet's mass is so large, so incredibly large compared to the force put into it, that it is going to experience this miniscule acceleration, we do not have even have to care about it, because the acceleration is so small, it is of little consequence.0396

Mass is giant for the earth, compared to these forces we are dealing with, they are comparatively puny, so there is no effect on the earth as far as we are concerned.0415

Let us start looking at some examples.0425

Let us say that the earth is sitting here, and up in the sky, we have got the moon.0427

If the earth exerts a pull of force of gravity F_g on the moon, how much does the moon pull on the earth?0436

So, F_g has been pulled by the earth.0448

We can turn these into vectors if we want, so, F_g is pulled by the earth on the moon, how much does the moon pull back on earth?0452

It is just going to be the equal and opposite force.0461

Gravity is a two way street, and so, - F_g is the exact amount that the moon is going to pull on earth, because it is going to pull with the exact same magnitude, but in the opposite the direction, they are pulling towards one another.0463

Why is the moon not falling to the earth?0481

We will talk about that later, when we talk about how gravitation works, the fact that moon is basically in continuous free fall, and the pull is what keeps it in that free fall as opposed to just slinging off into space, but we will talk about that in a future section.0483

For now, we have to understand the gravity is equal between the two things.0495

Same if you are sitting wherever you are, standing wherever you are, the earth is pulling on you, but you are also pulling on the earth by a certain amount.0500

From the earth's point of view, it is hardly going to notice you because your mass is so slow compared to the earth's mass.0508

But, you are still exerting a force on the earth, and it is equal to your own weight.0514

Second example: Say there is an astronaut in deep space, and he has got no external forces acting on him.0519

The astronaut has a wrench.0531

Now, what happens if the astronaut throws that wrench, the astronaut has a mass of 100 kg, and over here, we have got, mass of wrench = 2 kg .0536

The astronaut throws the wrench by applying a force of 50 N on the wrench.0552

He applies it for time = 0.2s.0562

What is the wrench's velocity?, what is the astronaut's velocity?0568

Normally when we would have talked about this being on earth, the person would have translated the force from the throw through their legs, and made it so that they had no force.0572

But this person is currently in deep space.0580

He has no where he can translate this force, so the throw is going to affect him equally.0581

So what is the force on the person?0586

From Newton's law, we know that they have to be equal and opposite, so the astronaut is going to also experience a 50 N force.0589

It is going to be going in the opposite direction.0595

So, what is the wrench's velocity?0598

We just use F = ma , 50 N = (2 kg) × a , a = 25 m/s/s, is the acceleration of the wrench.0600

What is the acceleration of the astronaut?0619

F_{on the astronaut} = ma_{on the astronaut} , - 50 = 100 × a (negative because it is in the opposite direction, and since we took the other as the positive direction), a = (1/2) m/s/s .0622

Once again, keep attention to where your units are, although we have been dropping them for ease.(it will save you from making a really simple foolish mistake.)0659

Now, if we want to know what the velocity is, well, how long do they experience the acceleration?0680

They experience the acceleration for 0.2 s, so velocity = a × t .0685

So, for the wrench, velocity_wrench = 20 × 0.2 = 5.0 m/s.0694

What about for the astronaut?0710

Velocity_astronaut = (-1/2)m/s/s × 0.2 s = -0.1 m/s.0713

So they are going to wind up experiencing very different velocities because of their very different masses, just like the experience between you and the earth, you notice the pull off the earth, but the earth hardly notices the pull of you, because of your very different masses.0732

It is the same thing with the astronaut and the wrench.0745

He will throw the wrench, and the wrench will move away from him 50 times faster than him moving in the opposite direction, because his mass is 50 times more. He currently weighs nothing, because he is in deep space.0747

But the inertia is going to be 50 times more.0760

So we have go the answer here, we know that it is going to move at 5 m/s, and the astronaut is going to move in the opposite direction at 0.1 m/s.0763

Third example: For this one, we have got a woman sitting in a bosun's chair, (bosun's chair is designed to help to make it easier for you to lift yourself up, used in sailing, used in window washing things like this).0772

It is hanging from a mass-less that runs over a mass-less frictionless pulley.0786

The chair and the woman have a combined mass of 75 kg.0789

With what force does she need to pull on the rope to have a constant velocity?0797

What force does she need to pull for it to have an acceleration of 1 m/s/s?0803

Let us think about what happens when she pulls.0808

She pulls down with some force, and that is going to be the force that becomes the tension.0810

So she pulls down with some T, now this force is translated into the rope, so we have got this pull coming along, and it is going to pull up here, with a force of T.0814

But, we have not paid attention to Newton's third law.0828

If you try to yank on something, if you are climbing, if you are pulling a rope, you put a tension into it, which cause you to rise, because the amount of tension that you put into the rope is the amount of force resultant o you, going in the opposite direction.0831

The resultant force from her pull is going to be T.0845

So, what is the total force that the woman is going to experience from the pull?0849

She is going to experience 2T going up.0852

What other forces are on her?0855

Her weight = Mg, and she has got a 2T going.0857

So, if she wants to have a constant velocity, we need the sum of the forces = mass × acceleration, if we want constant velocity, that is going to be equal to zero.0865

So (making up the positive direction), 2T - Mg = 0 (no acceleration).0874

So, 2T = Mg, T = 75 × 9.8 / 2 , T = 367.5 N, is the tension that she needs to put into the rope.0890

What if she wants to have an acceleration of 1 m/s/s?0911

Very similar, 2T - Mg = M × 1, T = (Mg + M)/2 , T = ((75 × 9.8) + 75) / 2 , T = 405 N .0916

Notice, she is able to do this at a very different rate, she is able to put way less force into pulling herself up using the bosun's chair because she is taking advantage of the Newton's third law.0952

She knows that by putting a tension into the rope, she is going to get lifted by that tension doubly, by the resultant force from pulling, the tension put into the rope will wind up pulling her up, but so will the resultant force.0960

She is making Newton's third law work for her, it is helping her out in this case.0980

So she is able to pull with considerably less than what her weight is.0984

She is going at a constant velocity, she only has to pull at half her weight.0987

So that is a really clever way to be able to use less effort on our part, to be able to go up.0991

We are able to take advantage of the way Physics works.0996

That is the end for Newton's third law.0999

Hope this made sense.1001