Basic Thermodynamics ~ J. Pohl ©

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3.0 Work and Energy: BODY

We have studied events (including permanence or no event) for selections of physical reality (systems) with that matter approximate as a BODY. Two characteristics of a BODY are its position in space and velocity. Both characteristics are vectors; velocity requires calculus for its definition. Newton's Laws of Motion included the construct, force, as the cause of change of motion of a BODY.

(1) The "property" of the Newton's 2'nd Law is the principle idea. Momentum of the BODY (a vector) exists in the horizontal space, 0XY.

(2) The 2'nd Law time displacement is a new, and powerful, physical perspective. Momentum becomes energy-rate; force becomes work-rate.

Newton's Second Law has two aspects: reality and theoretically. The real part of the laws it is physics and First, the Law is mathematical, being a first-order vector differential equation with momentum of the BODY as the dependent variable, time as its independent variable, and the sum of forces (often called the "forcing function") as a non homogeneous term. The equation is general but made specific in application once a BODY is selected, a time domain is chosen, coordinates are ascribed, and an initial condition and the forcing function are prescribed. Second, while Newton's 2'nd Law is expressed with the elegance of mathematics, it is more than mathematics; it is physical. Its solutions (adjusted by way of experimentation) provide valuable approximations of actual events of physical reality. Equation solutions of the 2'nd Law actually predict the outcomes of motion.

Extension of Newton's Second Law:   A fact of mathematics is that when an equation is multiplied by a constant, or a variable or some operator acts, that equation is unchanged. Put otherwise, the information of the equation after the operation is no more that it was previously. However, when Newton's 2'nd Law is multiplied by an arbitrary vector differential displacement the resulting scalar equation is altogether different from the original. How can that be?

The reason is Newton's 2nd Law is not merely mathematical. The mathematical operation, multiplication of the 2nd Law by a differential displacement represents physical change. The original physical entities, the terms of the 2nd Law, become new independent physical entities: differential kinetic energy (differential potential energy ~ about this later) and differential work.

Mathematics is the tool for equation development. When Newton's 2nd Law ( differential in form) is scalar vector multiplied by an arbitrary displacement three ideas (each potentially related to the other two) emerge. Two ideas are energy forms which are kinetic energy, potential energy and work. A general development, being a bit complex, is done later. First we consider some special cases.

Work is the Measure of Energy   This ultimate idea is seen the easiest. The ultimate idea from the transformation of Newton's 2nd Law is that matter has energy and that work is the measure of energy. This is to say that work can be made quantitative and by that fact so also can energy of a BODY.

Work with Vertical Motion:  To move a BODY vertically and uniformly, In its general occurance, work of a BODY results in changes of both kinetic energy and potential energy. For the special occurance wherein work occurs to a BODY that moves in a plane horizontal to Earth, no change of potential energy occurs. Some call this work, acceleration work.

• intro the Momentum Equation
• Extend the Momentum equation BODY to include the energy transfer mechanism, work. This will need three parts.

• We will do Work horizontally to identify KE and "acceleration" work.
• Do work vertically to identify gravity work PE.
• Put these together

• Many examples ~ BODY
• Examples will ruin the idea BODY
• One Example will point need of Internal Energy.