Mass and Weight

The mass (m) of a body is the measure of the quantity of material present in that body. The weight (wt) of a body is the force applied by that body whenever its mass is accelerated in a gravitational field. The Mass and weight are associated as shown in equation below.

Here:

Wt = weight (lbf)

 M = mass (lbm)

 g = acceleration of gravity = 32.17 ft/sec²

 g_c = gravitational constant = 32.17 lbm-ft/lbf-sec²

Please note that g_c has similar numerical value as the acceleration of gravity at sea level, though is not the acceleration of gravity. Instead, it is a dimensional constant used to facilitate the use of Newton's Second Law of Motion with the English system of units.

The weight of a body is a force generated whenever the mass of the body is accelerated by a gravitational acceleration. The mass of a certain body will stay constant even when the gravitational acceleration acting upon that body modifies.

According to the Newton's Second Law of Motion, force (F) = ma, here a is acceleration. For illustration, on earth an object has some mass and a certain weight. Whenever similar object is located in outer space, away from earth's gravitational field, its mass is similar, though it is now in a "weightless" condition (that is gravitational acceleration and, therefore, force is equivalent to zero).

The English system employs the pound-force (lbf) as the unit of weight. Knowing that the acceleration has a unit of ft/sec² and by using Newton's second law, we can establish that the units of mass are lbf-sec²/ft. For generalization, 1 lbf-sec²/ft is termed as a slug. The fundamental unit of mass in the English system is the slug. Though, the slug is nearly meaningless unit for the average individual. The unit of mass normally used is the pound-mass (lbm). In order to permit lbm to be used as a unit of mass, we should divide Newton's second law by the gravitational constant (g_c).

Newton's second law can be stated by the Equation as,

By using of the gravitational constant, g_c, accept Newton's second law such that 1 lbf = 1 lbm at the surface of earth. It is significant to note that this association is only true at the surface of earth; here the acceleration due to gravity is 32.17 ft/sec². Though, since all of our debate will depend upon experiences and observations on earth, we will utilize the lbm as the unit of mass.