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# 2.01 Mass, Volume and Density

The subject of Newtons First and Second Laws is
physical reality modeled as a BODY.

In 1687 Newton published two axiomatic statements, three Laws of Motion and much else. His first axiom stated the existence of measurable mass as quantity of matter.

Axiom I: The quantity of matter is the measure of the same, arising from its density and bulk (volume) conjointly.

Newton related measurable mass to its volume and density. A simple equation is used:

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It will be the style of this writing to inspect every equation - as we go. Looking as this equation we realized every system (every amount of mass) has a measurable mass (a number for "m") and similarly has a number for its volume ("V"). Hence for every system there is a number, ρ = m/V, which represents the system density. In some cases the measurement is a density, a thermodynamic property. In other cases the number represents a pseudo of effective" density.

Density:  Density as the quotient of system mass divided by its volume is a property for homogeneous systems. A body of water for example has the same "m/V" taken as a whole or taken as a small mass of that whole.

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Effective Density:  Sometimes a text problem will ask for the density of the water in a swimming pool with an automobile in it, there is a number "Σm/ΣV" but that number is not a density; it is an "effective density."

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Newton's System: the BODY  At this point it is convenient to state that Newton's system (the perspective of matter he used for his laws of motion) had mass but did not involve density or volume. The system model is called a BODY (some call this a "point mass" "or particle.") To model system matter as a BODY is to assume its entire mass to reside "at a point" in space. A BODY (point mass or particle) is assumed to have no "extent."

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