Mass and Weight

THERMODYNAMIC PROPERTIES Thermodynamics According to Newton’s 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 earth’s 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 Newton’s 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 Newton’s second law by the gravitational constant (g_c). � � � � � � 32.17 lbm ft lbf sec² g_c Newton’s second law can be expressed by Equation 1-2. (1-2) F ma g_c Use of the gravitational constant, g_c, adapts Newton’s 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. NOTE: In Equation 1-2, acceleration "a" is often written as "g" because, in this case, the acceleration is the gravitational acceleration due to the earth’s gravitational field (g = 32.17 ft/sec²). Example: Using Equation 1-2, prove that 1 lbf = l lbm on earth. Solution: F mg g_c 1 lbf (1 lbm) (32.17 ft/sec²) 32.17 (lbm ft) (lbf sec²) 1 lbf 1 lbf (an equality) HT-01 Page 2 Rev. 0