3.1  ENERGY AND WORK OF A BODY

Although the system model, Body, is of limited use, study of that system shows the pathway of thought from mechanics to thermodynamics. The fundamental properties of a body are its mass and velocity. Momentum of a body was defined by Newton as a "quantity of mothion." been investigated. Next we address energy of the body which changes with work. The problems we cover are of value - they are the first, simplest shots at prediction. Thus we will bare with the body for a while longer.

Everyone understands the meaning of "speed kills" and why it can be "bad luck" to walk under a ladder. When a mass moves at high speed or resides at a high elevation, we are wary that an event might cause personal injury. These objects have something we call energy or which is a potential for change or an event. Energy of a body associated with its motion relative to Earth is called kinetic energy with the symbol, KE_body. Mass that resides at an elevation higher than some Earth-datum is said to have potential energy, noted as PE

With scientific study and development quite a bit of ternminology and nomenclature arises. Words of description assist learning but also impede it. In this section we introduce and study the simplest forms of energy and work. Work is one mechanism of change of energy. It is logical to call the equation we discuss here, the equation that relates energy change and work - the "energy equation." But no sooner than we are familiar with the equation, we will begin to change it to a new equation more encompassing of energy, with new manners of work and a new idea - heat. We will want to call the next, new and improved equation the "energy equation." But what then do we call the previous "energy equation?" The rule is that successive understandings represented in an equation include all terms of the previous understandings. The simplest energy consideration for an event is obtained from the last, super energy equation by reduction, by casting out inapplicable terms.

Beginning level understandings of energy and work use the system model - body (or extended body with its center of mass). The introductory cases, events studied are called mechanics. Kinetic and potential energy are identified by some as mechanical energy forms. and events are studied are

PROPERTIES OF A BODY

Everyone has studied physics; none of the ideas discussed here is new. However, to put the ideas into an equation is not always done in physics. In this introduction to energy and work. Our considerations are restricted to physical reality modelled as either of the system types: body or extended body. These simplest systems will suffice for development of the concepts: work, kinetic energy, and potential energy. A list of properties of a body (or extended body), includes:

• Mass:   If the system exists, it is matter and matter has mass. The terms, body and point mass, state that selected matter will be modelled as being a body with its mass residing "at a point." If the model "works," good. If not, a more complicted model is used.
  
  
• Position and Velocity:   Definition of these physical vectors require an inertial (non-rotating, constant velocity) coordinate reference and a vector basis. The position of a body is a vector that extends from the origin (of the vector space) to the body (or the center of mass of the extended body). Often system position is time depependent. Velocity, a concept of calculus, is the limit of changes in position ove time. Not much calculus (only the sweetest part ) is needed.
  
  
• Momentum:   System mass times its velocity is the vector property, momentum which is the principal property of Newton's Laws of Motion. A coordinate space and vector basis are required to specify momentum of a body.
  
  
• Kinetic Energy and Potential Energy:  To begin this historical path of ideas is the ancient idea, mass (m ~ scalar). Newton sought to specify movement of matter in space. He define the position then using calculus, he defined velocity - V (also a vector). By his logic arrived his "quantity of motion" which we call momentum (mV~vector). For momentum of a body, mass is constant. Momentum changes continuously.

  Newton studied momentum differentially (very slow-motion camera), that is, at the limit of its "very least" change. No friction - that slow!

  Momentum, expressed at is basis, is , displacement, work, then kinetic and potential energy. To follow this path is to encounter momentum (a vector property) then displacement (also vectoral), then effect the multipicationly.

  Kinetic energy, the initial energy form of matter, is a composite property. The answer to "why does kinetic energy equal the mass times one half its speed squared.?" is work. Work is the measure of energy; it prescribes the form of kinetic energy and others. Potential energy is a grand convenience that arises when Earth is included as part of the system. A thorough derivation of these energy forms requires serious vector mathematics.

WORK

Work is a construct.

Work is not a property; it does not belong to a system.

Work is mechanism, a where-with-all, or event, whereby energy of a body might changed. As importantly, work is the means whereby energy of a body is made quantitive.

When work occurs, force (Newton's construct - a vector) acts at the system boundary and is displaced.

The body displaces (a vector entity) either in the direction of the vector force, in the opposite direction or any other direction. Work, being part force, part displacement (both vectors) is defined as the integral of their vector product. 

ENERGY EQUATION - Mechanical Form

A principal extension of Newton's Laws of Motion involved the scalar multiplication of the Laws of Motion by displacement of the system (body). The concept, the relation of system momentum with system energy was made (left of equality, immediately being kinetic energy. Right of

Specification of the system (and its essential aspects) occupies much of problem statements and solutions because every discussion of kinetic energy, potential energy, work, momentum... relates to a system. Below is presented the most elementary energy equation. The equation is a beginning; it will be expanded to serve more difficult physics, as we go.

Sufficient familiarity with kinetic and potential energy is assumed such that simple, ground-work considerations of energy analysis can be revisited. Once simple techniques of application are "refreshed," a derivation be provided. Till then, elementary calculations regarding energy changes and work of simple systems will be addressed in a unified way by the beginning level energy equation in its increment form. This form is suited to events that are incremental in time, that is, have that aspects, "start" and "stop."

The above equation is implicit. It relates energy change with the sum of works of an event. Summation signs remind us, "... include all instances," thereof. The equation is written energy-explicit as:

We will carry the subscript, c.m., meaning "in regard to the center of mass." Also the applicable velocities and elevations are those of the center of mass. The work W of the equation is all-inclusive and there are occasion when more than one work effect occur simultaneously. An umambiguous way to write work as it appears in energy equations is to precede it woth the simple math symbol that means "summation of." We will use the notation: ΣW.

Thermodynamics is not literature. Early goals of school are to mimic, to solve problems in the taught style to obtain the predicted number. The numbers of this writing are tainted by assumption and approximation. The problems are false and academic, admittedly. But their solutions serve as branches the only branches we have. once you understand the branches here, once you can climb to their ends, ... then you are as likely as anyone to see something new and understand it.

The next pages show calculations you might have seen in physics. But here there is a system approach. Refresh your understandings about mass, force, gravity, velocity, momentum and the energies, kinetic and potential.