A pound or pound-force (abbreviations: lb, lbf, or lbf) is a unit of force. Pound is also the name of a unit of mass. One pound-force is approximately equal to the gravitational force exerted on a mass of one avoirdupois pound on the surface of Earth. The standard acceleration due to Earth's gravity is usually taken to be 9.80665 m/s² (approximately 32.174 05 ft/s²) today,[1] but other values have been used, including 32.16 ft/s² (approximately 9.80237 m/s²).[2] The actual acceleration due to Earth's gravity varies from place to place, in general increasing from the equator (9.78 m/s²) to the poles (9.83 m/s²).
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Relationship to other units of force
A pound-force is the amount of force exerted by gravity on a pound-mass in the standard gravitational field at Earth's surface, which causes free falling bodies to accelerate at exactly 9.80665 m/s² (32.1742 ft/s²). An international avoirdupois pound is exactly 453.59237 grams or 0.45359237 kg. This means that 1 pound-force is equal to (0.45359237 × 9.80665) newtons, or exactly 4.4482216152605 newtons.
| newton (SI unit) | dyne | kilogram-force, kilopond | pound-force | poundal | |
|---|---|---|---|---|---|
| 1 N | ≡ 1 kg·m/s² | = 105 dyn | ≈ 0.10197 kp | ≈ 0.22481 lbf | ≈ 7.2330 pdl |
| 1 dyn | = 10−5 N | ≡ 1 g·cm/s² | ≈ 1.0197×10−6 kp | ≈ 2.2481×10−6 lbf | ≈ 7.2330×10−5 pdl |
| 1 kp | = 9.80665 N | = 980665 dyn | ≡ gn·(1 kg) | ≈ 2.2046 lbf | ≈ 70.932 pdl |
| 1 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/s² |
The value of gn as used in the official definition of the kilogram-force is used here for all gravitational units.
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The pound-force has the same relationship to the 'ounce' used as a unit of force as the pound (unit of mass) has to the ounce (unit of mass).
Use of pound as a unit of force
In some contexts, such as structural engineering applications, the term "pound" is used almost exclusively to refer to the unit of force and not the unit of mass. In those applications, the preferred unit of mass is the slug, i.e. lbf·s²/ft. In other contexts, the unit "pound" refers to a unit of mass. In circumstances where there may be ambiguity otherwise, the symbols "lbf" and "lbm" and the terms "pounds-force" and "pounds-mass" can be used to distinguish. There are three common, equally valid ways of doing calculations with mass and force in the foot-pound-second (fps) systems (and other systems such as inch-pound-second systems not discussed here). These three ways are summarized in the table below, which also includes the corresponding metric units.
| Systems | Gravitational | Engineering | Absolute | |||
|---|---|---|---|---|---|---|
| Newton’s second law | F = m·a | F = m·a/gc = w·a/g | F = m·a | |||
| Weight of an object | w = m·g | w = m·g/gc | w = m·g | |||
| Units | English | Metric | English | Metric | English | Metric |
| Time | second | second | second | second | second | second |
| Distance | foot | meter | foot | meter | foot | meter |
| Mass | slug | hyl | pound-mass | kilogram | pound | kilogram |
| Force | pound | kilopond | pound-force | kilopond | poundal | newton |
In the "engineering" fps system, the weight of the mass unit (pound-mass) on Earth's surface is approximately equal to the force unit (pound-force). The price for this convenience is that the force unit is not equal to the mass unit multiplied by the acceleration unit[3]—the use of Newton's Second Law, F = ma, requires another factor, gc, usually taken to be 32.17405 lb·ft/(lbf·s²). The "gravitational" fps system is a coherent system of units: by using the slug as the unit of mass, it avoids the need for such a constant. The "absolute" system is similarly coherent; the SI units are those of the "absolute" metric system.
Historical origins
The pound has been used in low-precision measurements since the 18th century, but it was not a precisely defined unit until the 20th century. The second resolution of the third General Conference on Weights and Measures (CGPM) in 1901 declared that:[4] The value adopted in the International Service of Weights and Measures for the standard acceleration due to Earth's gravity is 980.665 cm/s², value already stated in the laws of some countries. This value was the conventional reference for calculating the kilogram-force, a unit of force whose use has been deprecated since the introduction of the SI.[5]
See also
- Weight for a more complete discussion of customary units of force and mass
- Pounds per square inch, a unit of pressure
- Foot-pounds, a unit of work (energy), or torque
- Mass versus weight for the difference between the two physics properties
- Pound-mass
Notes and references
- ^ Barry N. Taylor, Guide for the Use of the International System of Units (SI), 1995, NIST Special Publication 811, Appendix B note 24[1]
- ^ J. Edmond Shrader, Physics for Students of Applied Science, McGraw Hill, 1st ed., 1937, p. 24.
- ^ The acceleration unit is the distance unit divided by the time unit squared.
- ^ Resolution of the 3rd CGPM
- ^ Bureau International des Poids et Mesures
