Is There Any Difference between Reaction Force and Normal Force?

Date: 01/26/2008 at 12:22:26
From: Mike
Subject: Is there any difference between reaction force and normal fo

Do reaction force and normal force mean the same kind of force... 
followed from Newton's third law?

Must the normal force always be perpendicular to the surface acted 
upon?  What about reaction force?  If a force of, say, 10 N acts on 
a surface at a 45 degree angle, what are the degrees of normal force 
and reaction force?  Should the normal force always be 90 degrees, 
regardless of the angle of the original force?

Date: 01/26/2008 at 17:32:23
From: Doctor Rick
Subject: Re: Is there any difference between reaction force and normal fo

Hi, Mike.

Normal force and reaction force are different.

In order to talk coherently about reaction force, we need to consider
*two* free body diagrams, for two different bodies:

            +---+         +---+
  R <-------| A |         | B |-------> F
            +---+         +---+

Body A exerts some force F on body B.  (The way I have drawn it, A is 
pushing on B.)  Newton's third law tells us that body B therefore 
exerts a force R (the reaction force) on body A; R is of equal 
magnitude and opposite in direction to force F.

When we talk about normal force, generally we aren't interested at 
all in a free body diagram for body B; it is essentially the earth. 
Its mass can be well approximated as infinite relative to A, and 
therefore its acceleration is well approximated as zero.  We don't 
care, or need, to add up all the forces acting on the earth!

You refer to "a force of, say, 10 N act[ing] on a surface ...".  This 
is not a clear way to talk about it: generally we have a body A, 
sitting on some surface, and the force F acts on body A, *not* on 
the surface.

                  N
                  ^
                  |
                  |
                +---+
       F <------| A |
        f       +---+
  --------------------\-------------
                        \
                  B       \
                           _|
                             F

To reiterate, F is *not* the force with which A acts on "body B", 
the object whose surface is shown.  We do not draw that force, since 
we are showing the free body diagram for body A only.  We *do* show 
the reaction force that body B exerts on body A, but we resolve that 
reaction force into two components: the normal force N 
(perpendicular to the surface), and the friction force F_f (parallel 
to the surface).

If the surface is assumed frictionless, then F_f = 0 and the 
"reaction force" is equal to N, strictly normal (perpendicular) 
to the surface.  In that case, it could be said that the reaction 
force and the normal force are the same force.

However, this can lead to confusion; it's best not to think of a
"reaction force" in this problem at all.  That's because if you 
call it a reaction force, you'll be tempted to think that Newton's 
third law is being invoked somewhere here--but it isn't, because we 
are only considering one free body diagram.  If you aren't careful, 
you might fall into the trap of thinking that N (or N + F_f) is equal 
and opposite to F.  KEEP THIS STRAIGHT: F is an external force acting 
on A, NOT a force with which A acts on B.

- Doctor Rick, The Math Forum
  http://mathforum.org/dr.math/