Newton´s Third Law

The  english physicist, mathematician and astronomer Sir Isaac Newton (1642-1727), basen on the studies of Galileo and Descartes, published in 1684 the first great work in Physics: Philosophiæ Naturalis Principia Mathematica, also known as Principia. In the first of the three parts in which the work is divided, he exposes in three laws of motion the relations between forces and their dynamic effects: the laws of motion.

• Newton´s first law or inertia principle
• Newton´s second law or law of force and acceleration
• Newton´s third law or law of action and reaction

Newton´s third Law or action and reaction principle establishes that for every action force, there is an equal and opposite reaction force. We will go in deph through the following three points:

• Concept
• Definition
• Application examples

Shall we start?

Concept

Imagine several marbles, all of them with the same mass. When you throw a marble against another, probably the first one will stop and the second one will get a very similar velocity than the first marble had.

From this simple example, you can verify that, for both marbles to modify their velocity have had to go through to forces. Since we can suppose marbles are isolated (they don´t interact with any other element), forces have only appeared during the blow. It seems a force over the hit marble has appeared during this action, which makes it set in motion. Therefore, it seems clearly that, since the "hitting" marble stops, it must experiment a reaction with a similar force but opposite direction.

We can now give a definition for Newton´s third law.

Definition

Some important observations are that:

• Action and reaction forces have an equal and opposite direction so... why don´t they cancel each other?

• These forces don´t cancel each other because they are applied on different bodies.

  

  Action and reaction forces.

  When you push a box, the force which is applied acts on the box (in blue), This force is the responsible for the box to be moved. At the same time , the box exerts a reaction force on yourself (in red) which is the responsible for you to feel, on your hand, a resistance against the box´s movement.

• An exception to the previous point is the case we find when we study the two bodies as one (the particles making a  rigid body, for example). In this situation they would cancel each other, indeed.
• The principle is applicable not only to contact interactions, but to distance forces also. For instance, the Sun, due to its mass, exert an attraction force on Earth, but that also applies an attraction force on the Sun of equal (in size) and opposite direction. Then... why does the Earth orbit around the Sun and not the other way around? The truth is that actually, both orbit around a common point: the center of mass of the two of them. Because the mass of the Sun is bigger than the Earth´s mass, this point in inside the Sun, and the only perceptible orbit is our orbit turning around the Sun.
• The previous example also emphasizes that equal forces don´t imply equal effects. So, the effect of the force on Earth is much clearer than on the Sun.
• The principle assumes that forces occur simultaneously and are spread instantly. This is not easy to refut in the contact interactions. In the case of electromagnetic interaction, or even gravitatory, Einstein´s general relativity theory marks the maximum speed the interactions can be transmitted. This opened up a new horizon in the study of the dynamic that took to redifine some of the concepts we have introduced... but this is a long story that, for the moment, is far from the range of this level.

Applications

Your day to day is full of examples where you use the action-reaction principle to get on well in your environment. In the subject Newton´s law applications we will study many of these examples, we start here with some of them, though:

Standing up

When you are standing up, the Earth applies an attraction over you, but... why don´t you sink? Due to the reaction of the ground. It has equal value and opposite direction. As it is reflected on the following figure, we can distinguish:

• ${\overrightarrow{F}}_{\text{Earth-you}}$: The attraction force exerted by the Earth and acts on you. We call it weight and it´s an action-at-a-distance force.
• ${\overrightarrow{F}}_{\text{you-Earth}}$: As a reaction, you also attract the Earth. This force is also a distance force acting on Earth. Of course, the Earth will barely notice this force but it exists...
• ${\overrightarrow{F}}_{\text{you-ground}}$: It is the force you apply by contact on ground, just for being standing up. Its value and direction is equal to ${\overrightarrow{F}}_{\text{Earth-you}}$, but it acts on the ground.
• ${\overrightarrow{F}}_{\text{ground-you}}$: It is the reaction to the previous force. It acts on you and it´s call normal force. Observe the normal force is not the reaction to the weight-force but the force you exert on ground and acts on ground. Bear in mind that action-reaction forces acts on different bodies. Otherwise, motion would not be possible.

Walk

When you walk, and thanks to the frictional force, you "propel the Earth backwards". The reaction of the Earth on your feet is to propel them forward.

Run

In the starting line the athletes use the track to propel themselves. They do it by exerting a force against the track, so the reaction of it gives them the drive desired.

Swim

On the same way, when you swim you move the water backwards, because of this, the water pushes you forward. When you get to the end of the pool and you want to turn around, you will probably propel yourself hard with your feet against the wall. The reaction of the wall on your feet is what let you to "gather momentum".

To kick a ball

When you play football and kick the ball, it´s the force on the ball the one that makes the ball to be shot off. This, at the same time, exert a reaction force on your foot that it will make the foot to go backwads from the impact spot.