Forces

=Forces=

Newton's Law's of Motion
Newton first defined forces as the impetus that governs motion in his 3 Laws of Motions.
 * 1) "Every body continues in its state of rest, or of uniform motion in a line, unless it is compelled to change that state by forces impressed upon it."
 * 2) "The acceleration produced on a body by a force is proportional to the magnitude of the force and inversly proportional to the mass of the object."
 * 3) "For every action there is an equal and opposite reaction."

The first law suggests that a //force// causes an object to accelerate or change direction. The second law creates the F=ma equation based on three measurable quantities: force, mass and acceleration. The third law implies that all forces are coupled and precisely balanced.

Newton's Universal Law's of Gravitation
An attractive force exists between two masses. Four measurable quantities are defined in Newton's equation F = G * (m_1 * m_2)/r^2. This law demonstrates the inverse square relationship between gravitational force and distance. This equation also illustrates an important constant (G), which was measured experimentally be Cavendish and used to calculate the mass of the earth.

Principle of Least Action
Of all possible paths between two points, the path of least time minimizes the time integral or difference between kinetic and potential energy, i.e. the integral of the Lagrangian = 0. This is a proof of Hamilton's principle.

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Types of Forces
Classical descriptions of forces as defined by Newton have been presented. However, the gravitational force is relatively weak, generally experienced between massive objects, and is easily overcome by other types of forces at smaller length scales. These stronger forces also greatly influence all of the natural processes observed in the universal. There are 4 types of forces: Gravitational forces, Electrostatic forces, Strong forces, Weak forces Boson ||~ Relative Strength ||~ Law ||~ Range || overcome repulsion of protons || gluon || ~1 || Unknown || 10^-15 || The strong and weak forces are mainly due to the bosonic interactions. In particular, the **gauge bosons** are responsible for the **electromagnetic force** (from photons), the **weak force**(due to W and Z bosons) and the **strong force** (due to gluons).
 * ~ Type ||~ Coupling ||~ Particle/
 * Electromagnetic || Photon to charged particles || photon || ~10^-2 || Known || infinite ||
 * Gravitation || Gravity to all energy || graviton || ~10^-40 || Known || infinite ||
 * Weak nuclear || Weak beta/gamma decays || W+, W-, Z || ~10^-5 || Partly Known || 10^-17 ||
 * Strong nuclear || Mesons to baryons;

Unit of Force
According to Newton's Second Law of Motion, F=ma. The unit of force is kg * m/s^2 = 1 Newton (N). 1 N is equivalent to lifting a chicken egg, or three fig newtons. 1 N/m^2 is small. 100000 (10^5) N/m^2 is equivalent to 1 atm. Therefore, a common convention is the megapascal (10^6), where 0.1 MPa = 1 atm.

Nuclear Forces
Enormous forces hold nuclei together. The energy released is on the order of an atomic bomb, in contrast to a TNT explosion, which involves the interaction of electrons. Yukawa suggested that a force existed between protons and neutrons that when jiggled, behaved like a particle. The particles have a mass some 200-300 times lighter than electrons called //muons// (mu-meson), which are indeed found in cosmic rays. Later, the pion (pi-meson) was discovered

About 30 diffferent particles have been found in the cosmic rays, but there connections are limited by their mathematical complexities. A Mendelev-type chart has been produced to group similar particles by their "strangeness," known as baryons, mesons and leptons. A fundamental unit for mass was developed such that 1 Mev = 1.782 x 10^-30 kg. (Note: 1 amu = 1.6605 x 10^-27 kg). Particles of the same type can have multiplets of different charge states. Some particles have zero-mass such as neurtinos, photons and theortical gravitons.

Electrostatic Forces
Electrostatic forces include a variety of types:
 * 1) Columbic
 * 2) Van der Waals: all charges in two atoms exert forces on each other causing electrons to reposition. The VDW interactions account significantly for intramolecular bonding of neutral molecules

Van der Waals Attractive Forces
In 1873, Van der Waal modified the ideal gas to consider molecules with finite volume (V-b) and the attractive forces between them (a/V^2).

From PV=nRT to (p + a/V^2)(V-b) = RT

VDW forces encompasses a number of point-like interaction between two small objects: For further discussion on surface-type forces, refer to Israelachvili
 * Keesom interactions: dipole-dipole
 * Debye interactions: dipole-induced dipole
 * London interactions:instantaneous dipole-induced dipole

Van der Waals Calculations
VDW forces are calculated by
 * Pairwise Additivity: this approach attempts to sum individual interactions between pairs of objects. This leads to an term for the total intermolecular interactions, however, the mulitbody interactions are missing.
 * Lifshitz Theory: considers continuum dielectric properties of the bodies.

Van der Waals Repulsive Forces
Repulsive VDW forces are possible if the Hamaker constant becomes negative. A negative Hamaker can be due to destructive inference in between electric fields of two different materials across a medium. Perterubations in electric fields in this case are due to fluctuating dipoles.

Hydrogen Bonding Directional bonds between hydrogen and oxygen, nitrogen or flourine.

Friction
Friction is characterized by the coeffiient of friction between sliding surfaces and varies for different materials. The coefficient of friction is proportional to tan (theata). There are thus tables of coefficients of friction, but they do not reflect reality because true surfaces are imperfect with oxides, grease, etc. Then again, if two perfectly clean surfaces of the same material contacted each other, the objects would stick together; this spontaneous bridging is called cold fusion.

Molecular Forces
Molecular forces are the source of friction. Molecule forces attract at large distances and repel at short distances -Lennard Jones potential [\graph, attraction, repulsion] -The force of nonpolar moecues is related by F=k/r^7 -Hooke's Law: a elastic response as a function of a small displacement. Thus the force is proportional to the displacement F=kx

Fields
Fundamental forces, i.e. electrical force. F = (const) q1q2/r2. The electric field is a construct used to keep track of all the charges. Therefore, the electric is the sum of all the static charges. The magnetic force is related to the change in the electric field. Thus a magnetic field is produced by a changing electric field.

Nuclear Forces
The laws for nuclear forces are unknown. They are strong but die off almost exponentially with distance. No one has calculated the force between two nuclei.

Pseudo Forces
Pseudo forces are related to forces that feel like gravity when an object is accelerated.