English units require re-scaling of either force or mass to eliminate a numerical proportionality constant in the equation F = ma.[citation needed] The poundal represents one choice, which is to rescale units of force. Since a pound of force (pound force) accelerates a pound of mass (pound mass) at 32.174 049 ft/s2 (9.80665 m/s2; the acceleration of gravity, g), we can scale down the unit of force to compensate, giving us one that accelerates 1 pound mass at 1 ft/s2 rather than at 32.174 049 ft/s2; and that is the poundal, which is approximately 1⁄32 pound force.
Three approaches to units of mass and force or weight[2][3]
For example, a force of 1200 poundals is required to accelerate a person of 150 pounds mass at 8 feet per second squared:
The poundal-as-force, pound-as-mass system is contrasted with an alternative system in which pounds are used as force (pounds-force), and instead, the mass unit is rescaled by a factor of roughly 32. That is, one pound-force will accelerate one pound-mass at 32 feet per second squared; we can scale up the unit of mass to compensate, which will be accelerated by 1 ft/s2 (rather than 32 ft/s2) given the application of one pound force; this gives us a unit of mass called the slug, which is about 32 pounds mass. Using this system (slugs and pounds-force), the above expression could be expressed as:
Note: Slugs (32.174049 lb) and poundals (1/32.174049lbF) are never used in the same system, since they are opposite solutions of the same problem.
Rather than changing either force or mass units, one may choose to express acceleration in units of the acceleration due to Earth's gravity (called g). In this case, we can keep both pounds-mass and pounds-force, such that applying one pound force to one pound mass accelerates it at one unit of acceleration (g):
Expressions derived using poundals for force and lb for mass (or lbf for force and slugs for mass) have the advantage of not being tied to conditions on the surface of the earth. Specifically, computing F = ma on the moon or in deep space as poundals, lb⋅ft/s2 or lbf = slug⋅ft/s2, avoids the constant tied to acceleration of gravity on earth.
Obert, Edward F., “Thermodynamics”, McGraw-Hill Book Company Inc., New York 1948; Chapter I, Survey of Dimensions and Units, pages 1–24.
^Cardarelli, François (2003), "The Foot–Pound–Second (FPS) System", Encyclopaedia of Scientific Units, Weights and Measures: Their SI Equivalences and Origins, Springer, pp. 51–55, ISBN978-1-85233-682-0.
^Comings, E. W. (1940). "English Engineering Units and Their Dimensions". Industrial & Engineering Chemistry. 32 (7): 984–987. doi:10.1021/ie50367a028.
^Klinkenberg, Adrian (1969). "The American Engineering System of Units and Its Dimensional Constant gc". Industrial & Engineering Chemistry. 61 (4): 53–59. doi:10.1021/ie50712a010.
April 10, 2024
poundal, poundal, symbol, unit, force, introduced, 1877, that, part, absolute, english, system, units, which, itself, coherent, subsystem, foot, pound, second, system, poundalunit, systemabsolute, english, systemunit, offorcesymbolpdlconversions1, equal, base,. The poundal symbol pdl is a unit of force introduced in 1877 that is part of the Absolute English system of units which itself is a coherent subsystem of the foot pound second system poundalUnit systemAbsolute English SystemUnit ofForceSymbolpdlConversions1 pdl in is equal to AE base units 1 lb ft s2 SI units 0 1382550 N CGS units 13 825 50 dyn British Gravitational System 0 03108095 lbf 1pdl 1lb ft s2 displaystyle 1 text pdl 1 text lb cdot text ft text s 2 The poundal is defined as the force necessary to accelerate 1 pound mass at 1 foot per second squared 1 54 1 pdl 0 138254 954 376 N exactly Contents 1 Background 2 Conversion 3 See also 4 ReferencesBackground editEnglish units require re scaling of either force or mass to eliminate a numerical proportionality constant in the equation F ma citation needed The poundal represents one choice which is to rescale units of force Since a pound of force pound force accelerates a pound of mass pound mass at 32 174 049 ft s2 9 80665 m s2 the acceleration of gravity g we can scale down the unit of force to compensate giving us one that accelerates 1 pound mass at 1 ft s2 rather than at 32 174 049 ft s2 and that is the poundal which is approximately 1 32 pound force Three approaches to units of mass and force or weight 2 3 vte Base Force Weight Mass2nd law of motion m F a F W a g F m aSystem BG GM EE M AE CGS MTS SIAcceleration a ft s2 m s2 ft s2 m s2 ft s2 Gal m s2 m s2Mass m slug hyl pound mass kilogram pound gram tonne kilogramForce F weight W pound kilopond pound force kilopond poundal dyne sthene newtonPressure p pound per square inch technical atmosphere pound force per square inch standard atmosphere poundal per square foot barye pieze pascalFor example a force of 1200 poundals is required to accelerate a person of 150 pounds mass at 8 feet per second squared 150 lb 8 fts2 1200 pdl displaystyle mathrm 150 lb times 8 frac ft s 2 1200 pdl nbsp The poundal as force pound as mass system is contrasted with an alternative system in which pounds are used as force pounds force and instead the mass unit is rescaled by a factor of roughly 32 That is one pound force will accelerate one pound mass at 32 feet per second squared we can scale up the unit of mass to compensate which will be accelerated by 1 ft s2 rather than 32 ft s2 given the application of one pound force this gives us a unit of mass called the slug which is about 32 pounds mass Using this system slugs and pounds force the above expression could be expressed as 4 66 slug 8 fts2 37 3 lbf displaystyle mathrm 4 66 slug times 8 frac ft s 2 37 3 lbf nbsp Note Slugs 32 174049 lb and poundals 1 32 174049 lbF are never used in the same system since they are opposite solutions of the same problem Rather than changing either force or mass units one may choose to express acceleration in units of the acceleration due to Earth s gravity called g In this case we can keep both pounds mass and pounds force such that applying one pound force to one pound mass accelerates it at one unit of acceleration g 150 lb 0 249g 37 3 lbf displaystyle 150 mathrm lb cdot 0 249g 37 3 mathrm lbf nbsp Expressions derived using poundals for force and lb for mass or lbf for force and slugs for mass have the advantage of not being tied to conditions on the surface of the earth Specifically computing F ma on the moon or in deep space as poundals lb ft s2 or lbf slug ft s2 avoids the constant tied to acceleration of gravity on earth Conversion editUnits of force vte newton dyne kilogram force kilopond pound force poundal1 N 1 kg m s2 105 dyn 0 10197 kp 0 22481 lbf 7 2330 pdl1 dyn 10 5 N 1 g cm s2 1 0197 10 6 kp 2 2481 10 6 lbf 7 2330 10 5 pdl1 kp 9 80665 N 980665 dyn gn 1 kg 2 2046 lbf 70 932 pdl1 lbf 4 448222 N 444822 dyn 0 45359 kp gn 1 lb 32 174 pdl 1 pdl 0 138255 N 13825 dyn 0 014098 kp 0 031081 lbf 1 lb ft s2The value of gn as used in the official definition of the kilogram force 9 80665 m s2 is used here for all gravitational units See also editSlug unit References editObert Edward F Thermodynamics McGraw Hill Book Company Inc New York 1948 Chapter I Survey of Dimensions and Units pages 1 24 Cardarelli Francois 2003 The Foot Pound Second FPS System Encyclopaedia of Scientific Units Weights and Measures Their SI Equivalences and Origins Springer pp 51 55 ISBN 978 1 85233 682 0 Comings E W 1940 English Engineering Units and Their Dimensions Industrial amp Engineering Chemistry 32 7 984 987 doi 10 1021 ie50367a028 Klinkenberg Adrian 1969 The American Engineering System of Units and Its Dimensional Constant gc Industrial amp Engineering Chemistry 61 4 53 59 doi 10 1021 ie50712a010 Retrieved from https en wikipedia org w index php title Poundal amp oldid 1214771255, wikipedia, wiki, book, books, library,
