BI-WEEKLY COMMENTS ON SI Comment 6 KILOGRAM-FORCE AND POUND-FORCE 6.1 The kilogram-force (symbol kgf) Prior to the inception of the SI, scientists decided to establish a unit of force that was based upon the force of gravity acting on a mass of 1 kg. However, in order to establish such a unit of force, it was first necessary to define a specific value for the acceleration due to gravity. As we learned in Comment 5 (section 5.7), the standard of acceleration defined by the CGPM in 1901 was 9.80665 m/s2 . Using F = ma, the standardized force of gravity acting on a mass of 1 kg became F = 1 kg × 9.80665 m/s2 = 9.80665 kg·m/s2 This unit of force was given the special name kilogram- force, symbol kgf. It represents the standardized force of gravity acting on a mass of 1 kg. It is very close to the pull we feel when lifting a mass of 1 kg. We can therefore write 1 kgf = 9.80665 kg·m/s2 Recalling that 1 N = 1 kg·m/s2 It follows that 1 kgf = 9.80665 N (exactly) In Germany and Sweden, the kilogram- force was named kilopond. Both the kilogramforce and the kilopond are today of limited historical interest. By using the kilogram- force as a unit, it was possible to define the force of gravity for any other mass. For example, the standardized force of gravity acting on a mass of, say, 375.4 kg was automatically equal to 375.4 kgf. This numerical equivalence between mass and the force of gravity was found to be very convenient. But it had its pitfalls, as we shall see. 6.2 Force of gravity depends upon the location The actual force of gravity that pulls a mass of 1 kilogram downwards depends upon the http://www.wildi-theo.com Copyright © 2005 Sperika Enterprises Ltd All rights reserved SI Comment 6.doc location. For example, the acceleration due to gravity at the National Institute of Science and Technology (NIST) in Washington, D.C., is 9.800 821 m/s2 . Consequently, the actual force of gravity acting on this 1 kg mass is: FWashington = ma = 1 kg × 9.800 821 m/s2 = 9.800 821 kg·m/s2 However, since by definition 1 kgf = 9.80665 kg·m/s2 , it follows that FWashington = 9.800 821/9.80665 kgf = 0.999 406 kgf 6.2 The pound-force (symbol lbf) The unit named “pound-force” was established in a way similar to the kilogram- force. However, the pound (lb), foot (ft), and second (s) were used as base units. Also, the scientific authorities had established by definition that ft = 0.3048 m exactly. Consequently, the standard acceleration due to gravity in the foot, pound, second system became (9.80665/0.3048) ft/s2 = 32.17404... ft/s2 Again using F = ma, the standardized force of gravity (in foot, pound, second terms) acting on a mass of 1 lb became F = ma = 1 lb × 32.1740 ft/s2 = 32.1740 lb·ft/s2 This unit was given the special name pound-force, symbol lbf. Therefore 1 lbf = 32.1740... lb·ft/s2 By using the pound- force as a unit, it was possible to define the force of gravity for any other mass. For example, the standardized force of gravity acting on a mass of , say, 35.6 lb was automatically equal to 35.6 lbf. This numerical relationship between mass and the force of gravity was found to be very convenient. But it also had its pitfalls, as we shall see. 6.3 Confusion caused by kgf and lbf The unit of force kgf caused much confusion, because people tended to drop the term “force” appended to kilogram, and simply called the “kilogram- force” a “kilogram”. As a result, mass became confused with force, and many people thought the two meant the same thing. But, as we know, mass and force are entirely different physical quantities. http://www.wildi-theo.com Copyright © 2005 Sperika Enterprises Ltd All rights reserved SI Comment 6.doc The same confusion occurred with the pound- force, because people again dropped the word “force”, and simply said “pound” instead of “pound-force”. As a result, people again got the impression that mass and force were the same thing. Holy cow! What a mess ! Fortunately, the SI solved this vexing problem by naming the newton as the unit of force and the kilogram as the unit of mass. All units of force based upon the force of gravity were dropped with the advent of SI. However, the pervasive 9.80665 m/s2 lives on to this day, as regards the calculation of the nominal force of gravity acting on a body at the surface of the Earth. 6.4 The poundal (historical) Referring to the Wildi SI Chart on ⊗ FORCE, the poundal is a special name for another unit of force that was devised in earlier years. It is the force needed to accelerate a mass of 1 lb at a rate of 1 ft/s2 . The chart shows graphically that the poundal is considerably smaller than the newton. Today, the poundal is only of historical interest. 6.5 The dyne (historical) An earlier metric system that used the centimeter, gram and second as base units, defined a special unit of force, named the dyne. One dyne is the force needed to accelerate a mass of 1 gram at a rate of 1 cm/s2 . The dyne is only of historical interest. 6.6 The words weight and weigh The noun “weight” means force. Thus, at the surface of the Earth, a mass of 5.4 kilograms (5.4 kg) has a weight that is close to 5.4 × 9.80665 = 52.9 N. The term “weigh” usually implies mass; for example, this box weighs 250 kilograms. 6.6 Just for fun – try this SI quiz a) A force of 7 newtons is applied to a mass of 4 kg that is initially at rest. Calculate the resulting acceleration in m/s2 b) Referring to the appropriate Wildi SI Chart, and assuming 4- figure accuracy, express the following quantities in SI units: (i) 50 ft/s2 (ii) 50 ft/s http://www.wildi-theo.com SI Comment 6.doc (iii) 40 pounds (iv) 40 pound- force Copyright © 2005 Sperika Enterprises Ltd, All rights reserved The solutions to these questions are given below. But don’t look until you’ve tried to discover the answers by yourself. ⊗ SOLUTIONS THAT’S ALL FOR NOW FOLKS ! SEE YOU IN TWO WEEKS ! This large beam balance, more than 1.3 meter high is employed for comparing heavy masses. Two standard 500-lb masses are shown in the foreground. (Courtesy of U.S. Department of Commerce, National Bureau of Standards) http://www.wildi-theo.com Copyright © 2005 Sperika Enterprises Ltd All rights reserved SI Comment 6.doc