The pound of force or pound-force (symbol: lbf,IEEE Standard Letter Symbols for Units of Measurement (SI Units, Customary Inch-Pound Units, and Certain Other Units), IEEE Std 260.1™-2004 (Revision of IEEE Std 260.1-1993) sometimes lbf,) is a unit of force used in some systems of measurement, including English Engineering units and the foot–pound–second system.
Pound-force should not be confused with pound-mass (lb), often simply called pound, which is a unit of mass, nor should these be confused with foot-pound (ft⋅lbf), a unit of energy, or pound-foot (lbf⋅ft), a unit of torque.
The 20th century, however, brought the need for a more precise definition, requiring a standardized value for acceleration due to gravity.
The value adopted in the International Service of Weights and Measures for the standard acceleration due to Earth's gravity is , 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 SI.Barry N. Taylor, Guide for the Use of the International System of Units (SI), 1995, NIST Special Publication 811, Appendix B note 24
The standard values of acceleration of the standard gravitational field ( gn) and the international avoirdupois pound (lb) result in a pound-force equal to .
1\,\text{lbf} &= 1\,\text{lb} \times g_\text{n} \\ &= 1\,\text{lb} \times 9.80665\,\tfrac{\text{m}}{\text{s}^2} / 0.3048\,\tfrac{\text{m}}{\text{ft}}\\ &\approx 1\,\text{lb} \times 32.174049\,\mathrm{\tfrac{ft}{s^2}}\\ &\approx 32.174049\,\mathrm{\tfrac{ft {\cdot} lb}{s^2}} \\ 1\,\text{lbf} &= 1\,\text{lb} \times 0.45359237\,\tfrac{\text{kg}}{\text{lb}} \times g_\text{n} \\ &= 0.45359237\,\text{kg} \times 9.80665\,\tfrac{\text{m}}{\text{s}^2}\\ &= 4.4482216152605\,\text{N}\end{align}
This definition can be rephrased in terms of the slug. A slug has a mass of 32.174049 lb. A pound-force is the amount of force required to accelerate a slug at a rate of , so:
1\,\text{lbf} &= 1\,\text{slug} \times 1\,\tfrac{\text{ft}}{\text{s}^2} \\ &= 1\,\tfrac{\text{slug} \cdot \text{ft}}{\text{s}^2}\end{align}
In the "engineering" systems (middle column), the weight of the mass unit (pound-mass) on Earth's surface is approximately equal to the force unit (pound-force). This is convenient because one pound mass exerts one pound force due to gravity. Note, however, unlike the other systems the force unit is not equal to the mass unit multiplied by the acceleration unitThe acceleration unit is the distance unit divided by the time unit squared.—the use of Newton's second law, , requires another factor, gc, usually taken to be 32.174049 (lb⋅ft)/(lbf⋅s2). "Absolute" systems are coherent systems of units: by using the slug as the unit of mass, the "gravitational" FPS system (left column) avoids the need for such a constant. The SI is an "absolute" metric system with kilogram and meter as base units.
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