Engineering Fundamentals: An Introduction to Engineering, 4th ed.c

234 Chapter 9 Mass and Mass-Related Parameters

0.0685 slugs = 2.205 lbm and 1 slug = 32.2 lbm). In practice, the mass of an object is measured

indirectly by using how much something weighs. The weight of an object on earth is the force that

is exerted on the mass due to the gravitational pull of the earth. You are familiar with spring scales

that measure the weight of goods at a supermarket or bathroom scales at home. Force due to grav-

ity acting on the unknown mass will make the spring stretch or compress. By measuring the deflec-

tion of the spring, one can determine the weight and consequently the mass of the object that created

that deflection. Some weight scales use force transducers consisting of a metallic member that behaves

like a spring except the deflection of the metal member is measured electronically using strain gauges.

You should understand the difference between weight and mass, and be careful how you use them

in engineering analysis. We will discuss the concept of weight in more detail in Chapter 10.

9.3 Density, Specific Volume, and Specific Gravity

In engineering practice, to represent how light or how heavy materials are we often define prop-

erties that are based on a unit volume; in other words, how massive something is per unit vol-

ume. Given 1 cubic foot of wood and 1 cubic foot of steel, which one has more mass? The

steel of course! Thedensityof any substance is defined as the ratio of the mass to the volume

that it occupies, according to

(9.1)

Density provides a measure of how compact the material is for a given volume. Materials such

as mercury or gold with relatively high values of density have more mass per 1 ft

3

volume or 1 m

3

volume than those with lower density values, such as water. It is important to note that the

density of matter changes with temperature and could also change with pressure. The SI unit for

density is kg /m

3

, and in BG and U.S. Customary system the density is expressed in slugs /ft

3

,and

lbm/ft

3

, respectively.

Specific volume, which is the inverse of density, is defined by

(9.2)

Specific volume is commonly used in the study of thermodynamics. The SI unit for specific vol-

ume is m

3

/ kg. Another common way to represent the heaviness or lightness of some material

is by comparing its density to the density of water. This comparison is called thespecific grav-

ityof a material and is formally defined by

(9.3)

It is important to note that specific gravity is unitless because it is the ratio of the value of two

densities. Therefore, it does not matter which system of units is used to compute the specific

gravity of a substance, as long as consistent units are used.

specific gravity

density of a material

density of water@4°C

specific volume

volume

mass

density

mass

volume

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