The pound-force or simply pound (abbreviations: lb, lbf, or lbf) is a unit of force.
Contents |
Definitions
The pound-force is approximately equal to the gravitational force exerted on a mass of one avoirdupois pound on the surface of Earth. Since the 18th century, the unit has been used in low-precision measurements, for which small changes in Earth's gravity (which varies from place to place by up to half a percent) can safely be neglected.[1]
The 20th century, however, brought the need for a more precise definition. A standardized value for acceleration due to gravity was therefore needed. Today, in accordance with the General Conference on Weights and Measures, standard gravity is usually taken to be 9.80665 m/s2 (approximately 32.17405 ft/s2)[2][3]
From the acceleration of the standard gravitational field and the international avoirdupois pound, we arrive at the following definition:[4]
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1 pound-force ≡ 1 pound times standard acceleration due to gravity ≡ 0.45359237 kg × 9.80665 m/s2 = 4.4482216152605 N = 32.17405 lbm·ft/s2
Sixteen avoirdupois ounces (as a unit of mass) are equal to one avoirdupois pound (as a unit of mass). Similarly one ounce-force is equal to a sixteenth of a pound-force.
Conversion to other units
| 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. | |||||
Foot-pound-second systems of units
In some contexts, 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 otherwise be ambiguity, the symbols "lbf" and "lbm" and the terms "pounds-force" and "pounds-mass" can be used to distinguish.
Three common, equally valid foot-pound-second (fps) systems of units for doing calculations with mass and force are summarized in the table below, which also includes the corresponding metric units.
| System | Gravitational | Engineering | Absolute | |||
|---|---|---|---|---|---|---|
| Force (F) | F = m·a | F = m·a/gc = w·a/g | F = m·a | |||
| Weight (w) | w = m·g | w = m·g/gc ≈ m | w = m·g | |||
| Units | English | Metric | English | Metric | English | Metric |
| Acceleration (a) | ft/s2 | m/s2 | ft/s2 | m/s2 | ft/s2 | m/s2 |
| Mass (m) | slug | hyl | pound-mass | kilogram | pound | kilogram |
| Force (F) | 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[5]—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.
See also
- Weight for a more complete discussion of customary units of force and mass
- Pounds per square inch, a unit of pressure
- Foot-pound (energy) and pound-foot (torque), units of work (energy), and torque, derived from the pound-force
- Mass versus weight for the difference between the two physical properties
- Pound-mass
Notes and references
- ^ Acceleration due to gravity varies over the surface of the Earth, generally increasing from about 9.78 m/s2 (32.1 ft/s2) at the equator to about 9.83 m/s2 (32.3 ft/s2) at the poles.
- ^ In 1901 the third CGPM declared (second resolution) that:
This value was the conventional reference for calculating the kilogram-force, a unit of force whose use has been deprecated since the introduction of SI.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.
- ^ Barry N. Taylor, Guide for the Use of the International System of Units (SI), 1995, NIST Special Publication 811, Appendix B note 24
- ^ The international avoirdupois pound is defined to be exactly 0.45359237 kg.
- ^ The acceleration unit is the distance unit divided by the time unit squared.
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