Normal Force

Every object is pulled down by the Earth's gravity. However, in everyday life, you'll notice that despite being pulled down by the Earth, you're not just plummeting through the ground on a day-to-day basis. So, clearly there's some force from the ground keeping you up such that you won't just fall through the ground.

This force is known as the normal force, and it acts on the object perpendicular to the surface the object is in contact with.

As you can see, the bag on the top of the table is exerting its weight on the table. The table exerts a normal force back upwards that is perpendicular to the surface of contact. Since the bag isn't moving up or down, it has 0 net force acting on it. Thus, the normal force from the table equals the bag's weight.

Notice how the table "sags" a little bit when the bag is placed on it. This actually happens with any surface assuming there isn't too much weight on the surface such that the surface breaks. Even placing a paper on a table will cause the table to sag. However, the sag is so unnoticeable in most tables that you can still assume the table is level. However, if you have used a cardboard table before, placing weight on it will cause it to sag noticeably.

Most rigid objects, including springs which are discussed later, deform(change shape) when load(weight) is placed on them. Whenever rigid objects deform, they exert what is known as a restoring force on the object causing them to deform. Thus, the greater the sag on a surface, the greater the deformation of the surface and the greater the restoring force. Thus, the more you deform/sag a surface(assuming it doesn't break), the greater the normal force it exerts back.

This notion has a very subtle and often unnoticed implication. If the sag is greater, the normal force is greater. This means that unlike the example diagram above, the normal force isn't solely based on weight. If another force is acting upwards on an object, then less normal force needs to be exerted by the surface to make the object stay in equilibrium. For example, if an object has a downwards weight of 25 N and a tension is pulling it up by 10 N, the upward normal force required to keep the net force 0 would be 15 N. However, if the tension isn't there, the normal force required would be 25 N, too. The same applies for if forces act downwards, in which case the normal force would be greater because there's more force being applied downwards on the surface.