Gravity is an attractive force; the Earth is pulling on you towards it's center just as much as you're pulling the Earth towards your center, but because our planet is so much more massive than us, our pull on the Earth doesn't do much but the Earth's pull on us keeps us grounded.
So is the "Normal force" just electromagnetism or what? Because, to me, that sounds like what your talking about.
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Normal force is a contact force. Your weight pushes down on the ground, and by the third law, some force has to push back up . That some force is the normal force. I believe egr is right in saying normal force, at the microscopic level, has to do with electromagnetism. Contact forces are due to interactions between atoms at or near the surfaces of interaction.
Yup, any contact force is the sum of the electromagnetic interactions between the two bodies on the molecular level. The reason we call it weight, normal force, friction, etc, is because its fairly difficult to precisely calculate so many electric interactions. It is easier for us to make a very reliable approximation that is the contact force and call it good.
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