ENGINEERING MECHANICS STATICS AND DYNAMICS Chapter 1. General Principles Part - 2

 

ENGINEERING MECHANICS 

STATICS AND DYNAMICS

Part - 2

Chapter 1. General Principles

Author:- Jakkir Hussain. 

1.3 Units of Measurement

The four basic quantities-length, time, mass, and force are not all independent from one another, in fact, they are related by Newton's second law of motion, F = ma Because of this, the units used to measure these quantities cannot all be selected arbitrarily. The equality F = ma is maintained only if three of the four units, called base units, are defined and the fourth unit is then derived from the equation.

SI Units :

The International System of units, abbreviated SI after the French "Système International d'Unités," is a modern version of the metric system which has received worldwide recognition. As shown in Table 1-1, the SI system defines length in meters (m), time in seconds (s), and mass in kilograms (kg). The unit of force, called a newton (N) is derived from F = ma Thus, I newton is equal to a force required to give 1 kilogram of mass an acceleration of m / (s ^ 2) * (N = kgm / (s ^ 2)) .

If the weight of a body located at the "standard location" is to be determined in newtons, then Eq * 0.1 - 3 must be applied. Here measurements give g = 9.806 * 65m / (s ^ 2) however, for calculations, the value : e = 9.8 m/s² will be used. Thus,

W = mg(g = 9.81m / (s ^ 2)) ---------(1-4)

Therefore, a body of mass 1 kg has a weight of 9.81 N, a 2-kg body weighs 19.62 N, and so on, Fig. 1-2a.

U.S. Customary :

In the U.S. Customary system of units (FPS) length is measured in feet (ft), time in seconds (s), and force in pounds (lb). Table 1-1. The unit of mass, called a slug, is derived from F=ma. Hence, 1 slug is equal to the amount of matter accelerated at 1 ft t / (s ^ 2) when acted upon by a force of 1 lb (slug= lb * s ^ 2 / f * t ) .

Therefore, if the measurements are made at the "standard location," whereg g = 32.2ft / (s ^ 2) then from Eq. 1-3,

m = W/g * (g = 32.2ft / (s ^ 2)) (1-5)

And so a body weighing 32.2 lb has a mass of 1 slug, a 64.4-lb body has a mass of 2 slugs, and so on, Fig. 1-2b.

Conversion of Units. Table 1-2 provides a set of direct conversion

factors between FPS and SI units for the basic quantities. Also, in the FPS system, recall that 1 ft = 12in (inches), 5280 ft = 1 mi (mile) . 1000 Ib = 1kip (kilo-pound), and 2000lb = 1ton

1.4 The International System of Units

The SI system of units is used extensively in this book since it is intended to become the worldwide standard for measurement. Therefore, we will now present some of the rules for its use and some of its terminology relevant to engineering mechanics.

Prefixes. When a numerical quantity is either very large or very

small, the units used to define its size may be modified by using a prefix. Some of the prefixes used in the SI system are shown in Table 1-3. Each represents a multiple or submultiple of a unit which, if applied successively, moves the decimal point of a numerical quantity to every third place. For example, 4 000 000 N = 4 000 kN (kilo-newton) = 4 MN (mega-newton), or 0.005 m = 5 mm (milli-meter). Notice that the SI system does not include the multiple deca (10) or the submultiple centi (0.01), which form part of the metric system. Except for some volume and area measurements, the use of these prefixes is to be avoided in science and engineering.

Rules for Use : 

Here are a few of the important rules that describe the proper use of the various SI symbols:

◆ Quantities defined by several units which are multiples of one another are separated by a dot to avoid confusion with prefix notation, as indicated by Nkg.m/s²kg·ms. Also, mes (meter-second), whereas ms (milli-second).

◆ The exponential power on a unit having a prefix refers to both the unit and its prefix. For example, mu N^ 2 = overline (mu*N) ^ 2 = mu*N*mu*N Likewise, mm² represents (mm) ^ 2 = mmmm

◆ With the exception of the base unit the kilogram, in general avoid the use of a prefix in the denominator of composite units. For example, do not write N/mm, but rather kN/m; also, m/mg should be written as Mm/kg.

◆ When performing calculations, represent the numbers in terms of their base or derived units by converting all prefixes to powers of 10. The final result should then be expressed using a single prefix. Also, after calculation, it is best to keep numerical values between 0.1 and 1000; otherwise, a suitable prefix should be chosen. For example, (50 kN)(60 nm) = [50(10 ^ 3) * N][60(10 ^ - 9) * m]

= 3000(10 ^ - 6) * Nm = 3(10 ^ - 3) * Nm = 3mNm