I.  INTRODUCTION-OVERVIEW

A force is generally defined by its effects.  A force causes or modifies a motion.  To understand fully this definition of forces one needs a clear definition of a motion.
An object is in motion when its position in space changes in time.  When the position of an object does not change in time, the object is said to be at rest (or in static equilibrium).  It is important to note here that a motion with a constant velocity, i.e., one with fixed speed and direction, is basically equivalent to a state of rest.

Each of the myriads of forces currently known is either one of the three (3) fundamental forces or a combination of some of the four (4) fundamental forces.  These three (3) fundamental forces are not totally separate from one another as explained farther below.  Many believe that the three (3) fundamental forces are different manifestations, in different circumstances, of a single force.  The search for the nature of this unique force is the subject of intense research in Physics (unification and grand-unification... theories).  The fundamental forces of nature are listed in the diagram below, along with some of their roles or application in explaining the physical universe.

Forces are defined by their actions.  A force causes or modifies a motion.  There are many  forms of physical forces. Physicists are looking for a single kind of force that leads to the known different forms or kinds.

The currently known forms or kinds of forces include the following:  gravity or gravitational force, electro-weak force (electromagnetic force and "weak" force) and the "strong" forces.

Caution :   "Weak forces" in physics has a special meaning different from "a force which is not very big or strong."

Key:  All currently known forces are one of the above three (3) kinds or a combination of the above kinds of force.
 

Gravity Forces

Isaac Newton discovered the Law of gravity.

Law of gravity:     Any two masses m1 and m2 attract each other with a gravity (or gravitational force)

   , where G= 6.67 x 10 -11 N*m^2/kg^2

Electric Forces

A well known fact of electricity is that two positive electric charges repel each other.  Two negatively charged objects also repel each other.  A positive charge and a negative electric charge always attract each other.

Question :  Positive (+) and positive (+) or negative (-) and negative (-) repel each other with a force of what magnitude or strength?

Answer :  Law of Electric Forces:   Any two charges, q1 and  q2, attract or repel each  other  with the force.

  , where K = 9 x 10^9  in SI units, and r is the distance between the centers of the charges.  Fel  < 0 means the two charges attract; Fel  > 0 means they repel.

Note that q (1 or 2) is negative if the charge is negative, and positive if  the charge is positive.

Magnetic Forces

Magnetic forces exist between magnets.  Like poles repel and unlike poles attract.  The strength of this interaction is given in college physics books.

Weak Forces

They come into play in explaining radioactivity,

i.e., the process by which a nucleus ejects some "particles" from within itself.

They are very strong!  They hold protons that are positively charged on top of each other in the nucleus of an atom!  They act only at very short distances!
 
 

III. The Search for a unified (or unique) force.

Electric and magnetic forces were first thought to be two different kinds or forms of forces.  It was proven in the 19th century that electric and magnetic forces are two manifestations of the same kind of force called electromagnetic force.  James Clark Maxwell is an architect of this unification of electric and magnetic forces.

Before the second half of the 20thcentury, electromagnetic forces were not believed to be related to the weak forces.  Weinberg and Salaam proved that electromagnetic and weak forces are two manifestations of the same kind of force called electro-weak force.

What is next?  We are waiting for some of you to figure it out.  The two examples of unification given above are a part of the reason that physicists (and some mathematicians) are feverishly looking for a single force whose different manifestations are called Strong, Electro-weak, and Gravity forces.
 
 

IV.  Explaining the Material Universe

The material universe, as we currently understand it, is shaped by the fundamental forces discussed above.  Objects around us, substances (organic and inorganic) are made of molecules that are associations of atoms.  There exist different states matter, solid, liquid, gas, and plasma, depending on the strength of inter-atomic or inter-molecular forces (that are of electromagnetic nature). (The Bose-Einstein condensate is a state of matter that has been recently confirmed, experimentally, by physicists).

Atoms

An atom comprises a nucleus (a dense mixture of protons and neutrons) and electrons that are swirling in elliptic orbits around the nucleus.

Atom:  Z=number of protons, Z=number of electrons in a neutral atom 

Clearly, for the atom, the following forces play key roles:
(1)  Strong forces hold the nucleus together (protons on top of each other.)
(2)  Electro-weak forces hold the whole atom together.  In particular, electromagnetic forces hold the negatively charged electrons turning around the positively charged nucleus.

Question:  If negative (electrons) and positive (protons) attract each other, why are the electrons not "falling" on the nucleus?

Answer:   Electrons do not fall on the nucleus because they are turning very fast around  it.  When a moving object takes a turn, a force known as centrifugal (fleeing away from the center) force acts on it.  If the path (trajectory) followed  is a perfect circle, the centrifugal force is easily given by

Note very well that Fcf  goes like v^2; when  m=1, r=1, and v goes from 1 to 10,  Fcf goes from 1 to 100!  Only the untrained will take a turn at a high speed.  The sharper the turn (r small), the larger the centrifugal force.  In the atom, the attractive force between the nucleus and the swirling electron is "balanced" by the centrifugal force.  Oh, yes it is the centrifugal force you feel when you are in a car that is taking a turn --

Molecules

Atoms form molecules - big and small.
 
 

When atoms 1 and 2 get very close, then the electron around nucleus 1 will also be attracted by nucleus 2, and that around 2 will be attracted by 1.

 

When the 2 atoms get close enough, they literally share their electrons:  the region of dots around and between the 2 nuclei is where the 2 shared electrons "reside."

 

Key  The electromagnetic forces are responsible for the formation, stability, and properties of molecules.  Molecules of water (H2O), Oxygen gas (O2 ), Methane (CH4), and of DNA are all the results of electromagnetic forces.

The states of matter are directly determined by the forces noted above. In particular,  the strong and  electromagnetic forces clearly  explain the structure of the atoms. And, given atoms of various elements, the electromagnetic forces determine the formation and properties of (a) molecules  (b) matter or substance in the solid, liquid, gas, plasma, and Bose-Einstein Condensate states. Please think about it, using the hints below.

In a gas, the electromagnetic forces between molecules are small; they cannot hold the molecules in place. The molecules fly and bounce around.
 

In a liquid, the electromagnetic forces between molecules are large enough to keep molecules close to each other but not strong enough to pin them down in fixed positions with respect to each other.

In a solid, the electromagnetic forces between atoms, ions, or molecules are strong enough to pin-down the atoms, ions, or molecules at fixed positions with respect to each other.

In a plasma, there generally is a  balanced mixture of positively and negatively charged ions.

In a Bose-Einstein condensate, generally at very low temperatures, atoms or molecules overlap each others in such a way they appear as one entity as opposed to a collection of separate ones!