# Newton’s third law and the relationship between weight and normal forces

The weight force and the normal force are not an action-reaction pair, as they act on the same body, and are therefore at odds with Newton’s third law.

One of the most well-known and cited names in physics is certainly that of Isaac Newton. This great physicist made important contributions, such as the publication of the book Mathematical principles of natural philosophy , where Newton’s famous three laws are stated, he also formulated the law of universal gravitation and published important works in the fields of optics and mathematics.

Newton’s three laws ( Inertia , Fundamental Principle of Dynamics and Law of Action and Reaction ) are perhaps the most famous contributions of this important physicist, because they have simple statements, but some details can go unnoticed and generate serious conceptual errors.

Here we will address the issue of the force of weight and normal reaction not forming an action-reaction pair.

The weight force is the result of the gravitational attraction established between the planet and any body and always has a vertical direction and feeling downwards. When this body is supported on a surface, it is necessary that the surface exerts a force contrary to the weight in order to support the body. That’s where the confusion comes from!

Newton ‘s third law says that for every action of a force there is an equal but opposite reaction. As the normal force is contrary to the weight and, in most cases, of equal value, the surface being horizontal, we are led to think that the normal force is the reaction of the weight. But that thought is wrong.

Something that is implied in Newton’s third law is that action and reaction act on different bodies , for example: if you slap a wall you are using this law. The action was done on the wall and the reaction on your hand, so logically you will feel pain! But realize that the action was on the wall and the reaction was on your hand.

Of the forces shown, we have the weight force (mg) vertically downwards, as a result of the gravitational attraction between the Earth and the block, and the normal force upwards, resulting from the surface resistance to support the block. Note that both weight and normal act on the same body and therefore cannot be considered as an action and reaction pair.

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