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# 1.26  Newton's Analytic Method

Today HS physics teaches Newton's understandings of physical reality principally via his "Laws of Motion" with the most used law being his 2nd Law. Mor subtly included with his laws are his manners of application which we call his Methods. Today HS physics teaches Newton's understandings of physical reality principally via his "Laws of Motion" with the most used law being his 2nd Law. More subtly included with his laws are his manners of application which we call his Methods.

Physical Reality  Newton and his contemporaries sought understanding, explanations of behaviors of matter of physical reality. Simple events were studied to discover perspectives of analysis.

BODY  The properties of Newtonian systems were mass, its position, its velocity and velocity changes. The perspectives or points of focus of Newton were systems modeled as a Body. To this day we continue to use Newtonian Mechanics as the basis for study of events of physical matter, of physical systems.

The idea, system, an accomplishment of Newton, is used today in the understanding of all events of matter. The focal point of the method is a selected amount and identity of matter called the SYSTEM. Force is a construct of the Newtonian method. The general steps of application of the method proceeds as follows:

Physical Scenario:  Initially, at thew very conception of a study or analysis, there is a physical scenario. It consists of matter in space and some event (or non-event) which is happening, expected to happen or imagined but desired not-to-happen. An engineer might want to improve a machine, a worker might seek reduced physical stress (or more speed) with some task. In many cases the physical scenario includes some manner of event initiation. The physical scenario is a vision. It resembles a photograph or painting. But it is not a system - yet.

System, Boundary and Surroundings:  There is nothing to analyze until the physical scenario is divided into a system with surroundings. The system is matter specifically selected as being relevant to some event. Selection of the system matter separates all of space, called the Universe, into two parts which are the system and the surroundings. A surface of zero thickness is imagined to envelope the system, to be between the system which is finite and surroundings which are infinite. This surface is called the system boundary. Upon initial selection, the system resides within and as part of the physical scenario. As the system is defined it is as though an imaginary, snug-fitting bag or envelope is passed over matter. The matter inside the bag is the system, that outside is matter of the surroundings.

Isolation  The thought, line of thinking applied next is to imagine the system to be removed from the scenario, separated from it in one's mind. The system is set apart, represented alone still inside its snug boundary. As the system is removed from the physical scenario, one might imagine a vacant hole being created in the scenario. And the system sketch, about its boundary, there seems to be complete independent of the surroundings. Obviously this is a contradiction because the surroundings indeed might influence any system event. Newton knew to include these possibilities. He invented "constructs," which are special perspectives to include influences of the surroundings on system events. The first construct, that of Newton's Laws of Motion was force. Force was the "cause" of change of momentum.

Force, Work and Heat:   For mechanical systems, Newton invented the idea or construct, force. The possibility of forces acting on the system was incorporated in terms of body forces and surface forces. Mechanical equilibrium exists for mechanical systems when the sum of forces equals zero. The specification of a thermodynamic system proceeds much the same. The constructs needed are work and heat. Today the first step of Newton's method, the selection and "isolation" of matter, we call "definition of a mechanical system." The vision of part of physical reality as "isolated," is called (by engineering educators) a "free-body diagram."

Types of Force:   Development of the concepts work and energy raised reason for the division of force effects of the surroundings to be classed as body forces (sometimes called "forces at a distance") or surface forces. Body forces act over all of the matter of the system while surface forces act only upon system material at the system surface. All forces consist of distributions of force over volume or over surface area.  Commonly, distributed forces are represented by a single "arrow" the length being proportional the force magnitude and aligned and located properly.

Body Forces:  There are three sources of body force: gravitational attraction of masses, called gravitation, electrostatic attraction or repulsion of static charges (Coulomb's Law) and the added effects associated with moving electric charges (Ampere's Law or the Biot-Savart Law).

Gravity:   The principal gravity source is the earth. The force is associated with Newton's Law of Gravitation.

Electrostatic:   These forces are responsible, in part, for operation of electronic equipment. They are associated with Coulomb's Law of Electric Charges.

Electromagnetic:  Moving charges have special forces. The Biot-Savart Law or Ampere's Law describe these forces.

Surface Forces:  Systems selected with boundaries at the interface of separate materials are said to experience "surface forces." There are many specializations of surface force:

External:  In the event of throwing a baseball the force of the pitcher's hand is labeled, external.

Friction Forces:  For a surface to slide upon a contacting surface will require a force to oppose friction.

Contact Forces:  When one object contacts another a contact force might exist.

Compressive Force:  When a system is submerged in a liquid or high pressure gas.

Normal Force:  A force that acts perpendicular to the tangent of the surface.

Internal Forces:  Sometimes a system boundary is selected with part of the boundary cutting through a homogeneous material. Over that matter separating part of the system surface ascribed forces are called internal forces though they are not "internal." Since internal forces are distributed over area it is common to state them "normed" on area as "component stresses" or combined as a complicated mathematical property, a "stress tensor."

Stress:  Stress is sometimes a simple property and other times a complex force per unit area.

Tensile Force or Stress:  The normal component of stress. The force passed through a rope amounts to tension or a tensile force.

Shear Force or Stress:  The stress component parallel to the internal surface. Cutting devices apply shear forces.

SPRING FORCE:  Steel or other metals are specially fabricated into a wide variety of springs.

DRAG FORCE:  Friction forces act on objects that move through liquids or gases are classed as one of three types:

SKIN DRAG:  Drag associated with the surface of the system. Barnacles on a ship, contribute to skin drag.

Form Drag:  Systems are stream-lined to reduce form drag. Airplanes use swept back wings to reduce form drag.

Wave Drag:  Wakes that propagate from ships are frictional costs to the ship's propulsion system. The greater the surface wave generated by a moving ship, the greater the cost of operating it.

Pressure Acting Over an Area:  Systems bounded by solids such as gases in tanks, the hulls of ships and submarines and hot air balloons all have the pressure of the surrounding fluids acting over their surface areas. The effect of this is determined by integration of the pressure distribution over the contact area.

Buoyancy:  The sum of the integral of pressure over surface area.

Thrust:  One consequence of momentum change of flowing gas or liquid streams are termed thrust.

Pseudo Forces:  By Newtons understanding, kinematic properties are related to forces. One perspective used by some is to treat the kinematic properties as though they were forces. In this manner, parts of the kinematics of motion can be attributed to be forces. Some believe this approach makes analysis easier. When an observer fixed in an accelerating coordinate reference observes an event, the system dynamics (for example, the position, velocity and acceleration of a particle in time) appear not to obey the laws of Newtonian Mechanics. This is expected since the frame of reference is "non-inertial." Two "remedies" for this are:

Recast the problem with the position vector initiating at the origin of a "sufficiently" non-accelerating coordinate reference.

Postulate a "pseudo force" the effect of which "corrects" for the non-inertial part of the dynamics.

Examples of Pseudo Forces are:

Inertial Force:  This topic to be developed later.

Centripetal Force:  This topic to be developed later.

Coriolis Force:  This topic to be developed later.

## 1.25 Newton's Analytic Method

To write a summary of Newton's approach and to include the extensions of his work made to this day is a lofty goal of writing. Stated otherwise, "What Newton said and where we are as a consequence" is not a light topic. But we give it a try.

Premise presently unwritted!