Page 14 - Air and gas Drilling Field Guide 3rd Edition

4 CHAPTER 1 Introduction and Units

considered fundamental dimensions of the system and all others units, including
force, can be derived.
The reason for this distinction between gravitational and absolute is the laud-
able desire that the concept and magnitude of the mass of an object should
remain the same regardless of where it is with respect to other objects that would
influence it through gravitational attraction. In this manner, the SI would be in
accordance with Newton’s universal gravitation, which describes the universality
of gravity (Newton’s universal gravitation is an extension of Newton’s general
Law II given earlier). The average force of gravitational attraction is shown math-
ematically in Newton’s universal gravitation by
m 1 m 2
F gravity ¼ G ; (1-1)
d 2
where F gravity is the gravitational attraction force (lb, N), G is a constant of propor-
-8 2 2 -11 2 2
tionality (3.437 10 lb-ft /slug ,or 6.673 10 N-m /kg ), m 1 is mass 1 (slug,
kg), m 2 is mass 2 (slug, kg), and d is the distance between the masses (ft, m).
Newton’s Law II can be written as
F ¼ ma; (1-2)
where F is the force being applied to a mass near the Earth’s surface (lb, N), m is
any object mass (slug, kg), and a is the resultant acceleration of that mass as a
2
2
result of the applied force F (ft/sec , m/sec ).
If a mass is on or near the Earth’s surface, the force of attraction of the mass to
the Earth’s mass becomes the special force denoted as weight (assuming that no
other forces act on the mass). In this situation, the acceleration term a becomes
g, which is the gravitation acceleration of the mass falling freely toward the Earth’s
center. Substituting g into Equation (1-2) and letting the F terms in Equations (1-1)
and (1-2) equal each other, g becomes

Gm earth
g ¼ : (1-3)
d 2
Substituting the respective unit system values, Earth’s average mass at midlati-
tudes, and the distance between the center of the Earth and the object near the
Earth’s surface gives the acceleration term that is used in most practical engineer-
ing mechanics problems. Table 1-1 gives the values of g for both USCS and SI. The
high accuracy values are given with the commonly used engineering values.

Table 1-1. Acceleration of Gravity

g (precision) g (engineer)
2
USCS (ft/sec ) 32.1740 32.2
2
SI (m/sec ) 9.8067 9.81