# Newton‘s 3rd Law: Example

by Jared Rovny

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00:01 Finally let's get to an example of Newton's third law.

00:04 That actually is equal and opposite with reaction.

00:07 Here's an example problem that if you have a force acting from the left on two objects which are in contact with each other, m1 and m2 and we know the masses of this object and we know the total force pushing both objects, we can ask what are the forces specifically on just the first object or specifically just the second object.

00:27 So let's see if we can find those forces using Newton's third law and I would recommend again that you try this on your own so pause and go through and see if you can find what the different individual forces are acting on these two objects if you know that the total force pushing the whole thing to the side is as given here.

00:44 So if you've done this problem you can see a way to think about it here which might be helpful.

00:51 First of all, when we were considering Newton's second law, what we should always keep in mind is that we're considering the forces acting on an entire system, a given system that we can choose.

01:02 So for example in this problem, I have two boxes, I could consider the force just on the first mass and go through all of Newton's second law for that object.

01:10 I could also do all of Newton's second law for just the second mass and do everything with that object.

01:16 Or I could consider my system to be both objects together and consider all the forces acting on my system.

01:22 So that's what I am doing in this first one, is I'm considering the total system.

01:25 So in this total system, I have force equals mass times acceleration of my total system.

01:30 The mass of the system is the sum of the two individual masses.

01:35 That is the total mass of my system.

01:37 I also know that the only external force acting on this as a system is 15 Newtons.

01:43 You might ask about the force between the two boxes, and those are forces in this problem but they are what we would call internal forces, they're just acting between the boxes.

01:52 They're not actually pushing on the whole thing as a system, there is working together.

01:55 So again considering the whole thing as a system, the only force is this external force from the side and it's acting on our entire system together.

02:03 The acceleration of the system you can solve just by dividing both sides by the total mass, which I've done here.

02:09 Now again, on the force acting on each object, we can then change what system we're looking at.

02:15 So for example we can look at just m1 or just m2 and each one of this object, each system that we can choose will have Newton's second law be valid for that object.

02:25 So for example for mass 1, we have all the forces on mass 1, will be equal to its mass times its acceleration and the same thing for mass 2.

02:33 If we write all the forces acting on mass 1, we do not only have the force acting from the left but we also have whatever reaction force the second small box is pushing back with from the right.

02:44 So writing up both of those forces on the left hand side of this equation for m1.

02:49 We have the total force acting from the left, but we also have the force of object 2, on object 1.

02:56 acting from the right, towards the left.

02:57 Writing up all of these force and keeping in mind the direction, the sign of these forces, we can see that we can solve for the force of object 2, just acting on object 1.

03:08 Simply by rearranging the equation as written, and we can solve finding that the force that object 2 is exerting on object 1 will simply be 5 Newtons.

03:17 The minus sign there is telling us that the force of object 2, on object 1 is in a negative direction.

03:22 Finally, we can look at object two and say its force is its mass times its acceleration and the key thing in this problem is that these two objects are staying in contact as they move and so they both have the same acceleration and that's very important to understand that any system that's staying together, without parts moving on their own, like this system is just moving altogether.

03:43 Every object in that system has the same acceleration and so in this equation for F2, we have the same acceleration for the object mass 2 as we have for mass 1.

03:54 So writing up the rest of this equation, we have the total force of object 1, on object 2, will be equal to its mass times its acceleration because this is the only force that object 2 feels.

04:06 It is important to notice that in the left hand side of the equation for mass 2, I did not write the total force, I did not write 15 Newtons.

04:13 And the reason for that is that this 15 Newton force is not actually acting directly on mass 2.

04:18 The only thing actually touching and actually pushing on mass 2 is mass 1 and so the only forces on mass 2 as a system, and you have to sort of zoom into that system and just think of yourself as being mass 2, is just getting pushed from the side by mass 1 and so that's the only force that we will write in Newton's second law for that mass.

04:36 Writing them up we have the mass and we know the acceleration, so putting these together, we have that the force of object 1, on object 2 is 5 Newtons and to our relief we find that just by doing this separately, we found Newton's third law all on our own.

04:50 We saw that the force of object 2 on object 1 is equal and opposite to the force of object 1, on object 2.

04:56 They're both 5 Newtons but they're just in different directions and that's the reason for the minus sign.

05:00 And that is the summary of our lecture on forces, so now that we have an idea of not only how things move in one and two dimensions, but how they act when you apply forces on them in both one and two dimensions.

05:13 You should be able to solve basic problems for forces and Newton's second law as well as Newton's third law in one and two dimensions.

05:21 Thanks for listening.

The lecture Newton‘s 3rd Law: Example by Jared Rovny is from the course Force.

### Included Quiz Questions

1. 3 N
2. 15 N
3. 10 N
4. 5 N
5. 2 N
1. The striking foot pushes back against the ground. The ground friction provides an opposite and equal force forward.
2. There is no acceleration. As a runner, I have a fixed velocity.
3. The foot not touching the ground propels the entire body as it swings forwards.
4. The upper body of the runner quickly leans forwards, which causes the entire body to begin accelerating forward.
5. As one leg moves backward, it provides an opposite and equal force for the other foot to move forward.
1. Newton’s third Law
2. Newton’s first Law
3. Newton’s second Law
4. Law of gravity
5. Newton’s second law and Newton’s third law
1. The horse's feet push back on the ground. By Newton’s third law, the ground exerts a force on the horse forward, which causes the horse and carrier to go forward.
2. The horse's feet push back on the ground. By Newton’s first law, the ground exerts a force on the horse forward, which causes the horse and carrier to go forward.
3. The horse's feet push back on the ground. By Newton’s second law, the ground exerts a force on the horse forward, which causes the horse and carrier to go forward.
4. The carrier is pushing back on the horse, by Newton's thirds law there is a force from the horse applied on the carrier which causes the carrier and the horse to go forward.
5. The law of gravitation and Newton’s third law
1. 4 N
2. 10 N
3. 2 N
4. 7 N
5. 5 N

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