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# Normal forces (2013)

last edited by 6 years, 2 months ago

Prerequisites

According to our Newtonian theoretical framework for viewing motion, when we see an object that is not changing its velocity (for example, not moving) we have to infer that the influences of all the objects in the outside world acting on it (the forces it feels) has to balance.  The framework also suggests that there are half-a-dozen different kinds of forces we can consider that objects exert on each other: three forces that objects exert on each other when they touch (normal, tension, resistive), and three that they exert at a distance (gravity, electric, magnetic).  In this page we consider the implications of the framework for making sense of the normal force -- that part of touching when two objects are pressing on each other in a direction perpendicular to the surfaces that are in contact.

## The implications of the Newtonian framework

 Let's follow our usual physics approach and consider the simplest possible example: a block sitting on a table. We have modeled this by throwing away all consideration of the structure of the block or the table; we have simplified the situation by considering the situation of no motion.  Let's see what we can infer.   Since the block is not accelerating (not even moving) we can infer that the net force acting on it is 0.  Everything must balance.  But there are forces acting on it.  There is always the earth pulling an object towards the earth's center, its weight.  So there has to be another force on the box to cancel it.  It's not accelerating sideways so there is no unbalanced sideways force acting on it.  But there is only one object touching it -- the table.  It's the only object that might exert a sideways force (friction) but since there is no resultant sideways force, there must be no friction acting.  But what cancels the downward force of the block's weight?

 We only have one possibility.  We have no indication of any non-touching forces other than weight -- no electric charge or magnets visible.  So we must have a force from the only object touching it -- the table.  Since the force needed is upward, perpendicular to the surface of contact and directed into the box, there must be a normal force from the table onto the block.  Here's the final free-body diagram for the box.  (Why don't we include the force of the box on the table?  There must be one by Newton 3. The resulting FBD is shown at the right.   But it does seem a bit strange that the table is doing anything to the box at all.  Doesn't the table "just sit there"?   How does it know about the box?  If we put a heavier box -- or even pushed down on top of the box -- the table would have to "respond" by exerting a larger normal force on the box.  How can it know to do that?

## Reasoning with intuition vs reasoning with principles

One of the interesting things this situation is illustrating is the difference between working in the Newtonian theoretical framework and using your intuitions.  Here, the formal framework says "the table has to exert a force".  Our intuitions may not worry about whether such a force exists or not.  There are a couple of reasons to ignore the table's force, if there is one.

(1) Tables are inert objects and so we have a tendency to not think about their doing something that seems "active" -- like exerting a force.  But we have to remember that by "force" here, we don't mean common speech force which is often associated with will or intent.  We mean the technical term "physical force" that simply means "what objects do to each other when they interact that tends to change each other's velocities."  This doesn't require an active agent.

(2) When we put things on tables they typically stay there.  We have no need to think about what the table is doing.  It suffices to say that the table "is strong enough to keep the object from falling."  We focus on the blocking of the fall rather than the pushing back to cancel the gravitational pull of the earth.

These intuitions are not wrong and they are useful in everyday life.  But if we want to make a coherent framework that allows us to describe motion -- and lack of motion -- in terms of a few powerful principles, then we have to refine and reconcile our intuitions with the science we are learning.  What it means in Newtonian physics, is often learning to see "invisible forces" -- like normal forces and friction.

In the case of a normal force, once you realize you have to have one, you can sort of realize that it must be there.  If you push your hand down on a table you can feel the table pushing back.  But that still leaves the irritating question: How does the table know how much to push back?  How does it know how big a normal force to exert?  For that, we have to create a more complex model of solid matter.  See the follow-on text, A simple model of solid matter.

Follow-ons

Joe Redish 9/25/11

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