For more information, please see full course syllabus of High School Physics

For more information, please see full course syllabus of High School Physics

### Newton's Third Law

- Forces always come in pairs: each force is equal in magnitude, but opposite in direction. Taken together, they would cancel each other out.
- This is true of
__all__forces. - If forces always come in pairs that can cancel each other out, why don't we normally see it come into play when we're working on problems? Two main reasons:
- The force in the problem is
__external__to the system. The force is guaranteed, and we don't care what happens to the thing causing the force. - The "equal and opposite" force is somehow translated into the Earth, where the planet's large mass makes it negligible.

- The force in the problem is

### Newton's Third Law

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

- Intro
- Newton's Third Law
- Everyday Examples
- Note
- Newton's Third Law Sometimes Doesn't Come Into Play When Solving Problems: Reason 1
- Newton's Third Law Sometimes Doesn't Come Into Play When Solving Problems: Reason 2
- Example 1: What Force Does the Moon Pull on Earth?
- Example 2: An Astronaut in Deep Space Throwing a Wrench
- Example 3: A Woman Sitting in a Bosun's Chair that is Hanging from a Rope that Runs Over a Frictionless Pulley

- Intro 0:00
- Newton's Third Law 0:50
- Newton's Third Law
- Everyday Examples 1:24
- Hammer Hitting a Nail
- Swimming
- Car Driving
- Walking
- Note 3:57
- Newton's Third Law Sometimes Doesn't Come Into Play When Solving Problems: Reason 1
- Newton's Third Law Sometimes Doesn't Come Into Play When Solving Problems: Reason 2
- Example 1: What Force Does the Moon Pull on Earth? 7:04
- Example 2: An Astronaut in Deep Space Throwing a Wrench 8:38
- Example 3: A Woman Sitting in a Bosun's Chair that is Hanging from a Rope that Runs Over a Frictionless Pulley 12:51

### High School Physics Online Course

### Transcription: 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

1 answer

Last reply by: Professor Selhorst-Jones

Sat Jan 11, 2014 11:17 AM

Post by Jack Wilshere on January 11, 2014

Hello, I do not understand how the third example obeys the law of conservation of energy. Let's say the guy has a weight of 800 N and the height of the entire system is 3 m. At the top, the gravitational potential energy he has is 2400 J (800*3), yet the energy he spends going up is only 1200N (since the force that he exerts is only 1200 N and the distance traveled is 3m). What's going on?

1 answer

Last reply by: Professor Selhorst-Jones

Sun Jul 28, 2013 9:05 PM

Post by enya zh on July 27, 2013

How come the moon doesn't drop into the Earth? What does it mean to have the moon in freefall?

Thanks!!!Ã¢ËœÂº

3 answers

Last reply by: Professor Selhorst-Jones

Fri May 24, 2013 2:08 PM

Post by Goutam Das on May 24, 2013

My questions may seem like unusual.Sorry about that.

1.I have no doubt about that the forces will be always equal, but the question is "why they are always equal"?

2.And What is the "source of that opposite force": Electromagnetic Force or something else?

3.Is there any "exception" of The 3rd Law?

1 answer

Last reply by: Professor Selhorst-Jones

Fri May 24, 2013 11:15 AM

Post by Goutam Das on May 24, 2013

Hi Professor,

In the third example, why does pulling upwards with a pulley yield twice the force?

6 answers

Last reply by: Professor Selhorst-Jones

Wed Nov 21, 2012 2:21 PM

Post by Tanveer Sehgal on November 20, 2012

Hey,

In the third example, there are two tensile forces acting in the positive direction and 1 in the negative direction. So why is it that we do not consider the force acting in the negative direction? The net force 2T-Fg. Why is not T-Fg?