At least two forces are acting on me right now while I am sitting in a
chair.  What are these forces?  On what is the equal and opposite
force to each of these acting? (Newton's Third Law)

The three laws and the law of gravity, taken together,

were a prescription for calculation the motion of planets

as described by Kepler laws:


http://home.cvc.org/science/kepler.htm

When people, teachers and popularisators, attempt to describe such

'recepies for calculation' aka algorithms

(see
http://www.answers.com/algorithm&r=67
)

 in common (non-mathematical)  language, they invariably generate 
 meanigless confusing verbiage.
 
Third law is a prime example of this phenomenon.

  There are only two ways which make sense:

1) Learn to calculate it (requires calculus)
2) just say 'there is some math, which allows [some] people to predict
the orbits of planets'

Anything else, including the posted comments, is waste of the bandwith.


Hedgie

The gravity exerts a force down upon you which pushes your butt into
the chair. In exchange, the chair exerts an equal and opposite force
upward onto your butt so there is no net acceleration.

For some examples see:
http://dosxx.colorado.edu/~bagenal/1010/SESSIONS/7.UniversalMotions.html

Note there is a subtlety here. You may ask, how can the chair exert a
force up? It doens't do anything?  Well this question raises to
points. First, the chair need not exert a force up. If it was made of
jello, your butt would fall straight through the floor. It is the
chair's rigidity, which on the microscopic scale is characterized by
electromagentic interactoins between atoms, that force  you up.
This lastly raises the question, how does the floor hold the chair up?
For there is an equal and opposite reaction there as well.  Well the
floor is rigid, as is the earth, and if you keep asking this question
you essentially enlarge your definition of the system you are asking
about. In the system that contains the entire earth and you as too
seperate bodies, the problem is described differently in terms of
Newton's law of gravitatoin. You are gravitationaly attracted to the
earth just as much as the earth is attracted to you. Thus they exert
equal and opposite forces See:
http://dosxx.colorado.edu/~bagenal/1010/SESSIONS/8.Gravity.html 

Enjoy!

Let's simplify this by eliminating the chair. It's really superfluous.
Picture just you standing firmly upon Earth's surface.

   Newtons laws say that given an interaction between two bodies, A &
B, the force by A upon B equals that by B upon A.

   The most obvious force between you & Earth is gravity. You &
Earth's centers of mass accelerate towards each other, tending to
converge. That's the first force. But, interestingly, as your feet
become pressed upon terre firma, the two mass centers stop actually
getting closer to each other at some finite distance. Something is
interfering with gravitation. The force of gravity is pulling you &
Earth together, but at some point there's another force, in the exact
opposite direction, pushing you both apart with an acceleration of
equal magnitude to that of gravity. This force must aquire its
strength over a very, very short distance, since your feet come
apparently into contact with Earth before bringing your gravitational
motion to a grinding halt.

   That force is the electrostatic force between negatively charged
electrons exposed at both Earth's surface and yours. But- it's
experimentally showable that the electrical force between charges is
trillions of times greater per unit of mass than is true for gravity.
So why then does the electrical repulsion only beome strong enough to
counter gravity just as your feet come into contact with the ground?

   It is because the electrons are only part of the electrical
composition of gross bodies of matter. Such a body is actually a very
large number of chemical atoms, each of which has both negatively
charged electrons and, usually, an equal number of positively charged
protons. An atom is extremely small, and so the distance between the
electrons & protons is also small. At any distance much larger than
the radius of an atom, the acceleration induced by the electrons is
very nearly balanced by that of the protons. For objects as extremely
large as you and Earth, the electrical forces between you is
effectively zero.

   But as your feet approach Earth, the surface atoms get close, and
at some very close range, the outer electrons finally are
significantly closer to each other than they are to the protons within
the electrons' orbital shells. At this point the electronic repulsion
accumulates very rapidly with decreasing distance and the
accelerations equal that by gravity, balancing you upon a
gravitational/electric cushion.

I think that the two comments originally stated under this question
delve into too much physics to answer this question. Lets go as basic
as we can get.

When you stand outside and pick up a rock and let it fall, you move it
from a state of having no velocity, to having velocity. In doing this
you accelerate the rock (changing the velocity or direction of a
moving object is definted as acceleration).  Now, anything that rises
must fall, and so a still object lifted above the ground is at
velocity 0.  When it starts falling it is accelerated towards the
earth (it's velocity increases) and it hits the ground.

The First Force
On Earth, any object is being accelerated no matter whether it is
moving, or sitting on the ground. The Earth's gravity is always trying
to accelerate us towards the center of the earth. This, is the first
force that is acting on you. Gravity is holding your feet to the
ground. Now any object on the Earth will be accelerated towards the
center of the Earth, at 9.8m/s^2
Governed by the law F=ma,
If an object has mass, and is being accelerated, there is a force
acting on it. That force (as stated above) is gravity.

The Second Force
In order to move an object from rest, a force needs to be applied to
it. If a force is being applied to an object, that mass must be
accelerating. (F=ma). As stated above, gravity is a force that is
pulling is down towards the center of the Earth, but i'm not
accelerating into the Earth?
The second force is what is sometimes referred to as the Normal force.
But, in effect, this force is what keeps you from accelerating into
the earth. This "Normal" force is what keeps us standing on the
ground. It is caused by the surface of which you are standing (or
sitting) on.  Both of these forces balance out (unless the chair
you're sitting on happens to break under the force of gravity!) to
keep you sitting still in your chair.

Newton's Third Law
A force is a push or a pull upon an object which results from its
interaction with another object. Forces result from interactions! some
forces result from contact interactions (normal, frictional,
tensional, and applied forces are examples of contact forces) and
other forces are the result of action-at-a-distance interactions
(gravitational, electrical, and magnetic forces). According to Newton,
whenever objects A and B interact with each other, they exert forces
upon each other. When you sit in your chair, your body exerts a
downward force on the chair and the chair exerts an upward force on
your body. There are two forces resulting from this interaction - a
force on the chair and a force on your body. These two forces are
called action and reaction forces and are the subject of Newton's
third law of motion. Formally stated, Newton's third law is:

"For every action, there is an equal and opposite reaction."
The statement means that in every interaction, there is a pair of
forces acting on the two interacting objects. The size of the forces
on the first object equals the size of the force on the second object.
The direction of the force on the first object is opposite to the
direction of the force on the second object. Forces always come in
pairs - equal and opposite action-reaction force pairs.

A variety of action-reaction force pairs are evident in nature.
Consider the propulsion of a fish through the water. A fish uses its
fins to push water backwards. But a push on the water will only serve
to accelerate the water. In turn, the water reacts by pushing the fish
forwards, propelling the fish through the water. The size of the force
on the water equals the size of the force on the fish; the direction
of the force on the water (backwards) is opposite the direction of the
force on the fish (forwards). For every action, there is an equal (in
size) and opposite (in direction) reaction force. Action-reaction
force pairs make it possible for fish to swim.

Consider the flying motion of birds. A bird flies by use of its wings.
The wings of a bird push air downwards. In turn, the air reacts by
pushing the bird upwards. The size of the force on the air equals the
size of the force on the bird; the direction of the force on the air
(downwards) is opposite the direction of the force on the bird
(upwards). For every action, there is an equal (in size) and opposite
(in direction) reaction. Action-reaction force pairs make it possible
for birds to fly.
 I hope you understand this as you would want!
  Sarge

I recommend this book: "The New Science of Strong Materials or Why You
Don't Fall Through the Floor" by J E Gordon (Pelican Books, Second
Edition 1976).

Gordon says:
"If I weigh 200 pounds and stand on the floor, then the soles of my
feet push downwards with a push or thrust of 200 pounds (or 900
Newtons, if you must); that is the business of feet.  At the same time
the floor must push upwards on my feet with a thrust of 200 pounds (or
900 Newtons; that is the business of floors."

He goes on:
"All this is merely a statement of Newton's third law of motion which
says, roughly speaking, that if the status quo is to be maintained
then all the forces on an object must cancel each other out.  This law
does not say anything about how these forces are generated."

And again:
"There is no such thing as a truly rigid material.  Everything 'gives'
to some extent. . . . It is probably obvious by this time that these
deflections, be they large or small, generate the forces of resistance
which make a solid hard and stiff and resistant to external loads.  In
other words, a solid deflects exactly far enough to build up forces
which just counter the external load applied to it."

I can see serious misunderstandings in many of the postings here. Even
the official Answer is rather unhelpful and shows little understanding
of physics, I'm afraid to say. Rather than point out their many
mistakes, let me give a straightforward answer to a straightforward
question.

(a) "At least two forces are acting on me right now while I am sitting in a
chair.  What are these forces?"  

The two forces acting on me are (i) the force of gravity that the
Earth exerts on me (otherwise known as my weight), which acts
downwards (ii) the contact force that the chair exerts on me, which
acts upwards (this force is ultimately electromagnetic in origin).

(b) "On what is the equal and opposite force to each of these acting?
(Newton's Third Law)"

Newton's third law states that if body A exerts a force on body B,
then body B also exerts a force on body A which is equal in magnitude
but opposite in direction.

Notes: (i) the action-reaction pair of forces act on DIFFERENT objects
(ii) hence, there is no question of them causing equilibrium of any
particular object.

Going back to the question and applying this law tells us that (i) the
reaction force to my weight is the gravitational force I exert on the
Earth, which is exactly equal to my weight but directed upwards, and
acting ON THE EARTH (ii) the reaction force to the contact force that
the chair exerts on me is the contact force that I exert on the chair,
which is of the same magnitude but directed downwards.

I hope this makes things clear.

Nicely put, physdoc.

Number of comments to such a simple question shows that quite a few
people left high school, puzzled by this mysterious statment - the 3rd law.

    Researchers are not paid to argue with the comments, and I have no intention
to enter a dispute. Neverthless, considering the number of comments,
and level of general confusion, I will add this one clarification:

Firstly, what quite a few comments say:

  " That force is the electrostatic force between negatively charged
electrons exposed at both Earth's surface and yours..."

is probably true, but irrelevant to the question. That explanation 
is an answer to a question:
'what is a molecular basis of elasticity?' and has nothing to do with
meaning of the third law.

What phys-doc asserts :

-----------------\\
From: physdoc-ga on 23 Sep 2005 12:01 PDT 	  	

"I can see serious misunderstandings in many of the postings here. Even
the official Answer is rather unhelpful and shows little understanding
of physics, I'm afraid to say..."  
---------------//
is worse then irrelevant - it is misleading.

The modern formulation of the 3rd law is:

Sum of all forces acting on a body is zero. 

That includes static forces, which depend on position vector R 
and dynamic forces, friction which depends on velocity V= d/dt  R
and inertia which is M * A where A, the acceleration is change
of velocity A= d/dt V.

When only static forces are considered, then 'sum of forces =zero'
means equilibrium was reached. When dynamic forces are included, that
statement
represents Equation of Motion. It is a differential equation, which when
'solved', provides trajectory of that body.
That what Newton did in Principia. He included inertia and force of gravity
R * M1 * M2 / |R| ^3. He solved that equation and obtained Kepler's Laws.

This is the use and meaning of the third law, which I described in my 'official'
answer.

There is another use, practiced in some high schools, which do not
have qualified science teachers. That use, sometimes called 'solerian
physics', is
to confuse students by having them to memorise meanigless dogma and so
convince them that physics and science in general is complex and hard
to understand.

The physdoc and apparently racecar may  prefer that branch of explanation.
Some people in that branch get further confused by this 'zero sum' of the
forces (equal and opposite) and ask: of total of forces is zero, how come it
is moving?  The right answer, or at least the answer given in Principia, is:
The included dynamical force is describing how it is moving.
The solerian answer is: These forces are acting on different bodies.

I did not included solerian explanation since  this was a $2 question
and that pseudo explanation is of minor interest. More complete description
of solerian physics, it's history and possible usefulness, would require at
least $50 question focused on this specific science folklor. 
 
Hedgie

Hmmm....

I do not see anything pseudoscientific about Newton's third law, in
the form of: to every action there is an equal and opposite reaction. 
If you are anywhere on the surface of the earth, there is a
gravitational force between you and the earth.  The earth pulls on
you, and (equal and opposite) you pull on the earth.  If you are
sitting in a chair, your butt exerts a force on the seat, and (equal
and opposite) the seat exerts a force on your butt.  True, this alone
does not allow you to calculate how things move, but it is not
meaningless either.  It is not impossible to imagine that forces could
be 'one-way'.  In fact, many people don't realize that they exert on
the earth a gravitational force equal to their weight, and that in
priciple if they jump up in the air, until they land the earth
accelerates (very slightly) upward under the influence of that force.

One of the ways in which the third law can be useful is in drawing
force diagrams for multi-body systems.  A common type high school
mechanics problem involves pulling a block along a table top with a
constant force while a second block rests on top of the first block,
with friction.  The third law tells you that the forward frictional
force the bottom block exerts on the top one (the force that causes
the top block to accelerate) implies a backward frictional force of
equal magnitude exerted by the top block on the bottom one.

It is true that without F=ma (2nd Law), the 3rd Law is not very
powerful.  But to my mind that does not make it meaningless, and I
don't think that teaching the 3rd Law makes physics complex or hard to
understand.

I disagree with the statement:

      The modern formulation of the 3rd law is:

      Sum of all forces acting on a body is zero.

I understand that the idea behind this claim is to regard inertia as a
force.  However, I think that makes 'sum of all forces = 0' more of an
incomplete statement of the 2nd Law than anything to do with the 3rd
Law. In fact, that definition invalidates the 3rd Law, because the
'force' of inertia is not applied by an external agent, and so it has
no equal and opposite counterpart. In any case, my personal opinion is
that whatever name you give to the statement above, it's a confusing
way to put things.  It seems more intuitive to me to say that when the
sum of the forces is zero, there is no acceleration, and when the sum
of the forces is NOT zero, there is acceleration.

I suppose in the end this is all more a question of philosophy than
physics, and for that reason there is no definitive correct answer. 
On the other hand, I think the answer given by physdoc is pretty
clearly the one jgrow-ga was after.

Responding to my earlier posting, Hedgie makes a series of statements
which only show how confused he is about basic Newtonian mechanics. It
is not my intention to enter into disputes either. However, he is
making assertions that are completely wrong. Racecar has already
answered some of these and I don't have time to dwell on this. So let
me just add some quick remarks.

(1) Hedgie asserts that "The modern formulation of the 3rd law is: Sum
of all forces acting on a body is zero." This is wrong. No physicist
will agree with this. Firstly, it is not a statement of Newton's third
law (NIII). Secondly, it is does not even make physical sense. Why
should the sum of all forces on a body necessarily be zero?

(2) To support his assertion in (1) Hedgie includes "inertia", which
he equates to M*A, as a force. This is a misuse of Newton's second law
(NII). NII states that the *resultant* force F acting on a body
produces acceleration A according to F=M*A. This does not mean that
there is a separate force M*A. It is merely the vector sum of the
forces acting on the body. As racecar has already pointed out, the
fallacy here is a wrong interpretation of NII. Moreover racecar
correctly observes that this misinterpretation contradicts NIII.

(3) The rest of Hedgie's assertions are too obscure to make any sense,
and it quickly becomes apparent  that he has run out of arguments. He
makes reference to the Principia but doesn't give any supporting
quotes, which is a pity.

In summary, he has got it all terribly wrong.

Quite a bit was written about concept of force
in Principia and in modern physics.

Interested person can find more in:

http://www.amazon.com/exec/obidos/tg/detail/-/019852675X/qid=1128696849/sr=8-3/ref=pd_bbs_3/102-2693043-5675335?v=glance&s=books&n=507846


Max Jammer in particular:
http://www.amazon.com/gp/reader/048640689X/ref=sib_dp_pt/102-2693043-5675335#reader-link
and
http://www.amazon.com/exec/obidos/tg/detail/-/048640689X/ref=pd_sim_b_5/102-2693043-5675335?%5Fencoding=UTF8&v=glance

is excellent historian of science.

 .. and they all agree   M*A , force of inertia is a force.

Hedgie writes:

"Quite a bit was written about concept of force
in Principia and in modern physics.
.. and they all agree   M*A , force of inertia is a force.""

I don't have these books to hand. Could you give us some quotes from
these sources in support of the statements you make?

Thanks.