Page 47 - Shigley's Mechanical Engineering Design

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22 Mechanical Engineering Design
The International System of Units (SI) is an absolute system. The base units
are the meter, the kilogram (for mass), and the second. The unit of force is derived
by using Newton’s second law and is called the newton. The units constituting the
newton (N) are

ML (kilogram)(meter) 2
F = 2 = 2 = kg · m/s = N (1–9)
T (second)
The weight of an object is the force exerted upon it by gravity. Designating the weight
as W and the acceleration due to gravity as g, we have
W = mg (1–10)

2
In the fps system, standard gravity is g 32.1740 ft/s . For most cases this is rounded
off to 32.2. Thus the weight of a mass of 1 slug in the fps system is
2
W = mg = (1 slug)(32.2ft/s ) = 32.2 lbf
2
In the ips system, standard gravity is 386.088 or about 386 in/s . Thus, in this system,
a unit mass weighs

2
2
W = (1 lbf · s /in)(386 in/s ) = 386 lbf
With SI units, standard gravity is 9.806 or about 9.81 m/s. Thus, the weight of a 1-kg
mass is
2
W = (1 kg)(9.81 m/s ) = 9.81 N
A series of names and symbols to form multiples and submultiples of SI units has
been established to provide an alternative to the writing of powers of 10. Table A–1
includes these prefixes and symbols.
Numbers having four or more digits are placed in groups of three and separated by
a space instead of a comma. However, the space may be omitted for the special case of
numbers having four digits. A period is used as a decimal point. These recommenda-
tions avoid the confusion caused by certain European countries in which a comma
is used as a decimal point, and by the English use of a centered period. Examples of
correct and incorrect usage are as follows:

1924 or 1 924 but not 1,924
0.1924 or 0.192 4 but not 0.192,4
192 423.618 50 but not 192,423.61850
The decimal point should always be preceded by a zero for numbers less than unity.

1–15 Calculations and Significant Figures
The discussion in this section applies to real numbers, not integers. The accuracy of a real
number depends on the number of significant figures describing the number. Usually, but
not always, three or four significant figures are necessary for engineering accuracy. Unless
otherwise stated, no less than three significant figures should be used in your calculations.
The number of significant figures is usually inferred by the number of figures given
(except for leading zeros). For example, 706, 3.14, and 0.002 19 are assumed to be