According to Newtons Second Law of Motion, force (F) = ma, where a is acceleration. For
example, on earth an object has a certain mass and a certain weight. When the same object is
placed in outer space, away from the earths gravitational field, its mass is the same, but it is
now in a "weightless" condition (that is, gravitational acceleration and, thus, force equal zero).
The English system uses the pound-force (lbf) as the unit of weight. Knowing that acceleration
has the units of ft/sec2 and using Newtons second law, we can determine that the units of mass
are lbf-sec2/ft. For simplification, 1 lbf-sec2/ft is called a slug. The basic unit of mass in the
English system is the slug. However, the slug is an almost meaningless unit for the average
individual. The unit of mass generally used is the pound-mass (lbm). In order to allow lbm to
be used as a unit of mass, we must divide Newtons second law by the gravitational constant (gc).
Newtons second law can be expressed by Equation 1-2.
Use of the gravitational constant, gc, adapts Newtons second law such that 1 lbf = 1 lbm at the
surface of the earth. It is important to note that this relationship is only true at the surface of the
earth, where the acceleration due to gravity is 32.17 ft/sec2. However, because all of our
discussions will be based upon experiences and observations on earth, we will use the lbm as the
unit of mass.
In Equation 1-2, acceleration "a" is often written as "g" because, in this case, the
acceleration is the gravitational acceleration due to the earths gravitational field
(g = 32.17 ft/sec2).
Using Equation 1-2, prove that 1 lbf = l lbm on earth.
(1 lbm) (32.17 ft/sec2)
1 lbf (an equality)