What exactly is the Normal Force?

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ghart
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I know that every action has a reaction, and I understand that applying a force on a surface yields a "force" from that surface to hold it up, and that it's magnitude and direction are equal and opposite, respectively. But conceptually, what is happening? Defining a force in terms of another force is not really doing it for me. What are the exact forces that are allowing this to happen? Intermolecular? Intramolecular? Or deeper?
 
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Welcome to PF;
The fundamental interaction in a contact force such as the "normal force" to a surface is electromagnetic. The electrons of the block (in the block-on-ramp examples in HS physics classes) repel the electrons of the surface, but are also bound to their various structures (details depending on what the block and surface is made of).

Force is never defined in terms of another force but in terms of the rate of change of an object's momentum. If the momentum is unchanged in some direction then there must be no net force in that direction... so the normal force is not defined in terms of the weight (or whatever it is equal and opposite to) but it is can be deduced (and computed) by considering the other forces we know more about.