# How can normal force and weight be similar in a body at rest?

How can normal force and weight be similar for a body at rest? I understand that these are not an example of Newton's 3rd law, and that if $$f=ma$$ by newtons 2nd law and body is at rest, the net forces must be zero because the aceleration is zero. However, its strange to think about this. For example, if a man of 80kg is at rest on the floor, then the normal force equals his weight, and if a man of 140kg is at rest on the floor, then the normal forces equal is weight again. Is there any specific reason or mechanism behind this or is it simply a consequence of newtons 2nd law ?

• The problem is with the correct definition of weight in physics. Dec 30, 2020 at 14:39

This is a consequence of equilibrium.

To see why we must first understand where the normal force comes from. The floor is made up of atoms and molecules and when no one is touching the floor all these atoms are in a 'happy' arrangement. With happy I mean that if you were to move one of these atoms by a small amount it would want to return to its original position. If a man now walks on top of these atoms they all get compressed a little. They are uncomfortable because they are too close to their neighbouring atoms. So they produce a force to try and restore the balance. The more they are compressed the larger the force they produce.

So imagine you hover an 80 kilo man above the floor attached to ropes. He is just touching the floor but is still applying zero weight. Before you cut the ropes the floor is producing zero force; the atoms aren't compressed so they are producing no force. As soon as you cut the rope the man starts falling because of gravity and starts compressing the atoms in the floor. The normal force starts increasing until it matches the weight of the man. At that point the net force is zero and the man is stationary.

Actually the normal force will not match the weight immediately. The man will have also picked up some downwards velocity which needs to be cancelled before he reaches equilibrium. But the end result is clear: in the end the man is stationary so the weight must match the normal force.

Before equilibrium is reached the normal force can actually be bigger than the weight. The reason that a ball bounces upwards after you throw it on the floor is because the normal force exceeded the weight of the ball for some time resulting in upwards acceleration.

• thanks this answer was great and gave me a really good intuition behind this process! Dec 30, 2020 at 14:26
• @JoãoCosta Great :) Dec 30, 2020 at 14:27

It is a consequence of the 3rd law. The man pushes down on the floor, with his weight, and the floor pushes back with an equal and opposite normal force.

• Wrong! . These two are different types of fundamental forces . Normal = electromagnetic force and gravitational force is gravitational force. Hence they don't form action reaction pair. Dec 30, 2020 at 14:17
• @Bhavay Why do you think 2 different types of forces cannot interact for a net result? Dec 30, 2020 at 16:05
• @AdrianHoward They can certainly can act for a net result , but it is wrong/misleading to say it is a "consequence of the Newton's 3rd law" as two forces in Newton's third law are of the same type. Dec 30, 2020 at 16:28
• Newton's 3rd law does not qualify the nature of the forces. Dec 30, 2020 at 16:42

@AccidentalTaylorExpansion gave the accurate answer and the proper reasoning that the normal force depends on the intermolecular distances.

You can visualise it actually in a ground with mud.

When you try to walk, your foot goes into it and after a certain depth you may stop sinking. This shows that when you came in contact with the surface of mud , your weight was not equal to the normal contact force but when you pressed the mud the atoms came closer and after a certain distance it equalised your weight and this is the point where you came to rest and ready to take the second step.

Hope it helps 🙂.

• Yes I understand it now, really interesting! thank you all for the excelent explanation Dec 30, 2020 at 14:30
• @john if you liked either of the answers you can upvote it. :) Dec 30, 2020 at 14:32
• unfortunately the site doenst allow me yet I think Dec 30, 2020 at 14:32
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The normal force is the perpendicular component of the force that the supporting surface exerts on the resting object. Friction, if there is any is the tangential component. It is a compressive contact force, and is analogous to pushing on a very stiff spring. The harder you (or gravity) pushes on the spring the harder it pushes back. Just like a spring there is also displacement, very small, but non-zero. Unless the surface breaks, it will keep balancing the mg force, so that ma=0.

When you stand still on the floor, are you accelerating toward the center of the Earth?

If your acceleration is zero, that must mean that the net forces acting on your body are zero. That must mean, that the contact force pushing up against your feet must be equal and opposite to the force of gravity pulling you down.

Weight is defined as the force with which the body is acting on its support or the suspension, whereas the normal force is the force with which the support acts on the body. (Note that this is different from what is understood by weight in everyday life - the measure of gravitational mass.)

Depending on a situation these may or may not form a 3rd law couple:

• If a block rests on a horizontal surface, the weight and the normal force form the third law couple
• On an inclined surface, the weight is composed of the force counteracting the normal force and the friction force
• Adding a supsension to either of the above two cases may further complicate the situation.