Pound-force
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A pound-force (abbreviations: lbf or lbf) is a unit of force. One pound-force is the force equivalent to that exerted on a mass of one avoirdupois pound on the (idealized) 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, but other values have been used, including 32.16 ft/s² (approximately 9.80237 m/s²). 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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[edit] Equivalence to other units of force
A pound-force is the force a pound-mass exerts in the standard acceleration due to Earth's gravity of 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 approximately 4.448222 newtons (conversely, 1 newton is 0.22481 pounds-force).
| 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 |
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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).
[edit] Use of the pound as a unit of force
By convention, the "pound" is usually defined to refer to a unit of force. In some limited circumstances, however, a pound can refer to a unit of mass. Where there may be ambiguity, the symbol "lbf" or the term "pounds-force" can be used for the unit of force, and the term "pounds-mass" can be used for the unit of mass.
For example, in structural engineering applications the term "pound" is used almost exclusively to refer to a unit of force and not to refer to the unit of mass. In those applications, the preferred unit of mass is:
- the slug, i.e. lbf·s²/ft.
There are three practical 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). Those three ways are summarised in the table below, which also sets out the corresponding position under the International System of Units (SI).
| SI | fps | |||
|---|---|---|---|---|
| gravitational | engineering | absolute | ||
| unit of time | s | s | s | s |
| unit of distance | m | ft | ft | ft |
| unit of mass | kg | slug | pound-mass | pound-mass |
| unit of force | N | pound-force | pound-force | poundal |
| Newton’s second law | F = m·a | F = m·a | F = m·a/gc | F = m·a |
| weight of an object | W = m·g | W = m·g | W = m·g/gc | W = m·g |
The SI system and the absolute and gravitational fps systems are coherent systems of units. They have the advantage that force can be expressed as the product of mass and acceleration.
The engineering fps system requires the introduction of the factor gc into the relationship between force on the one hand and mass and acceleration on the other hand. The factor is a dimensionless constant equal to the value of the standard acceleration of Earth's gravity used to define a pound-force, when expressed in ft/s². This must be distinguished from the actual local value of the acceleration of gravity, g, which can vary from place to place. The factor is usually taken to be 32.17405 lb·ft/(lbf·s²).
No one of the three fps systems is more correct than the other two. Ordinary measurements are not made using these specialized subsets of mechanical units, which are used only in practical calculations.
[edit] Historical origins
Pounds-force had been used in low-precision measurements since the 18th century, but they were never well-defined units until the 20th century.
The second resolution of the third General Conference on Weights and Measures (CGPM) in 1901 declared that: 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. [1]
[edit] See also
- Weight for a more complete discussion of customary units of force and mass.
- Pound-force per square inch for a unit of pressure
- Foot-pound force, a unit of work, energy, or torque
