POUND-FORCE

A 'pound' or 'pound-force' (abbreviations: 'lb', 'lbf', or 'lb_f') 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, 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).

Contents

Equivalence to other units of force

Use of the pound as a unit of force

Historical origins

See also

References

Equivalence to other units of force

A pound-force is the gravitational force exerted 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) (see relationships table). 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).
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 the pound as a unit of force

In some contexts, the unit "pound" refers to a unit of mass (see Use in Commerce under Pound (mass)). However, in other contexts, by convention, the "pound" refers to a unit of force. In circumstances where there may be ambiguity otherwise, the symbol "lb_f" or the term "pounds-force" can be used for the unit of force and the term "pounds-mass" ("lb_m") 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 summarized in the table below, which also sets out the corresponding position under the International System of Units (SI).

Force-mass relationships

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

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 a gravitational constant, ''g_c'', into the relationship between force on the one hand and mass and acceleration on the other hand. In this system, the weight of the mass unit (pound [mass]) on Earth's surface is equal to the force unit (pound-force). The price for this convenience is that the force unit is no longer equal to the mass unit multiplied by the distance unit divided by the time unit squared (the use of Newton's Second Law, F=MA, requires another factor, ''g_c''). This gravitational constant is usually taken to be 32.17405 lb·ft/(lbf·s²). The required introduction of the constant ''g_c'' is a reason why many, including people in engineering fields, prefer to the simpler "gravitational" fps system, and use the slug as the unit of mass.
No one of the three fps systems is more correct than the other two.

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]

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

References

★ Resolution of the 3rd CGPM