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46-587: Collectively, the variants of the FPS system were the most common system in technical publications in English until the middle of the 20th century. Errors can be avoided and translation between the systems facilitated by labelling all physical quantities consistently with their units. Especially in the context of the FPS system this is sometimes known as the Stroud system after William Stroud , who popularized it. When

92-435: A coherent system the units of force , energy and power be chosen so that the equations hold without the introduction of constant factors. Once a set of coherent units have been defined, other relationships in physics that use those units will automatically be true— Einstein 's mass–energy equation , E  =  mc , does not require extraneous constants when expressed in coherent units. Isaac Asimov wrote, "In

138-414: A constant that depends on the units used. Suppose that the metre (m) and the second (s) are base units; then the kilometer (km) and the hour (h) are non-coherent derived units. The metre per second (mps) is defined as the velocity of an object that travels one metre in one second, and the kilometer per hour (kmph) is defined as the velocity of an object that travels one kilometre in one hour. Substituting from

184-408: A definition. It does not imply that a unit of velocity is being defined, and if that fact is added, it does not determine the magnitude of the unit, since that depends on the system of units. In order for it to become a proper definition both the quantity and the defining equation, including the value of any constant factor, must be specified. After a unit has been defined in this manner, however, it has

230-430: A magnitude that is independent of any system of units. This list catalogues coherent relationships in various systems of units. The following is a list of quantities with corresponding coherent SI units: The following is a list of coherent centimetre–gram–second (CGS) system of units: The following is a list of coherent foot–pound–second (FPS) system of units: Newton (unit) The newton (symbol: N )

276-410: Is a derived unit that, for a given system of quantities and for a chosen set of base units , is a product of powers of base units, with the proportionality factor being one. If a system of quantities has equations that relate quantities and the associated system of units has corresponding base units, with only one unit for each base quantity, then it is coherent if and only if every derived unit of

322-486: Is a coherent variant of the FPS system that is most common among engineers in the United States. It takes the pound-force as a fundamental unit of force instead of the pound as a fundamental unit of mass. In this sub-system, the unit of mass is a derived unit known as the slug . In the context of the gravitational FPS system, the pound-force (lbf) is sometimes referred to as the pound (lb). Another variant of

368-428: Is a statement that determines the ratio of any instance of the quantity to the unit. This ratio is the numerical value of the quantity or the number of units contained in the quantity. The definition of the metre per second above satisfies this requirement since it, together with the definition of velocity, implies that v /mps = ( d /m)/( t /s); thus if the ratios of distance and time to their units are determined, then so

414-447: Is a system of units of measurement used to express physical quantities that are defined in such a way that the equations relating the numerical values expressed in the units of the system have exactly the same form, including numerical factors, as the corresponding equations directly relating the quantities. It is a system in which every quantity has a unique unit, or one that does not use conversion factors . A coherent derived unit

460-425: Is indistinguishable from the four-unit system, since what is a proportionality constant in the latter is a conversion factor in the former. The relation among the numerical values of the quantities in the force law is { F } = 0.031081 { m } { a }, where the braces denote the numerical values of the enclosed quantities. Unlike in this system, in a coherent system, the relations among the numerical values of quantities are

506-412: Is named after Isaac Newton . As with every SI unit named for a person, its symbol starts with an upper case letter (N), but when written in full, it follows the rules for capitalisation of a common noun ; i.e., newton becomes capitalised at the beginning of a sentence and in titles but is otherwise in lower case. The connection to Newton comes from Newton's second law of motion , which states that

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552-527: Is the pure number one. Asimov's conclusion is not the only possible one. In a system that uses the units foot (ft) for length, second (s) for time, pound (lb) for mass, and pound-force (lbf) for force, the law relating force ( F ), mass ( m ), and acceleration ( a ) is F = 0.031081 ma . Since the proportionality constant here is dimensionless and the units in any equation must balance without any numerical factor other than one, it follows that 1 lbf = 1 lb⋅ft/s . This conclusion appears paradoxical from

598-409: Is the ratio of velocity to its unit. The definition, by itself, is inadequate since it only determines the ratio in one specific case; it may be thought of as exhibiting a specimen of the unit. A new coherent unit cannot be defined merely by expressing it algebraically in terms of already defined units. Thus the statement, "the metre per second equals one metre divided by one second", is not, by itself,

644-505: Is the unit of force in the International System of Units (SI) . Expressed in terms of SI base units , it is 1 kg⋅m/s , the force that accelerates a mass of one kilogram at one metre per second squared. The unit is named after Isaac Newton in recognition of his work on classical mechanics , specifically his second law of motion . A newton is defined as 1 kg⋅m/s (it is a named derived unit defined in terms of

690-533: The Akkadian emperor Naram-Sin rationalized the Babylonian system of measure, adjusting the ratios of many units of measure to multiples of 2, 3 or 5, for example there were 6 she ( barleycorns ) in a shu-si ( finger ) and 30 shu-si in a kush ( cubit ). Non- commensurable quantities have different physical dimensions , which means that adding or subtracting them is not meaningful. For instance, adding

736-779: The Middle East (10000 BC – 8000 BC). Archaeologists have been able to reconstruct the units of measure in use in Mesopotamia , India , the Jewish culture and many others. Archaeological and other evidence shows that in many civilizations, the ratios between different units for the same quantity of measure were adjusted so that they were integer numbers. In many early cultures such as Ancient Egypt , multiples of 2, 3 and 5 were not always used—the Egyptian royal cubit being 28 fingers or 7 hands . In 2150 BC,

782-591: The SI base units ). One newton is, therefore, the force needed to accelerate one kilogram of mass at the rate of one metre per second squared in the direction of the applied force. The units "metre per second squared" can be understood as measuring a rate of change in velocity per unit of time, i.e. an increase in velocity by one metre per second every second. In 1946, the General Conference on Weights and Measures (CGPM) Resolution 2 standardized

828-416: The cgs system, m/s is not a coherent derived unit. The numerical factor of 100 cm/m is needed to express m/s in the cgs system. The earliest units of measure devised by humanity bore no relationship to each other. As both humanity's understanding of philosophical concepts and the organisation of society developed, so units of measurement were standardized—first particular units of measure had

874-524: The foot-candle were the first defined units of light, defined in the Metropolitan Gas Act (1860). The foot-candle is the intensity of light at one foot from a standard candle . The units were internationally recognized in 1881, and adopted into the metric system. Together with the fact that the term "weight" is used for the gravitational force in some technical contexts (physics, engineering) and for mass in others (commerce, law), and that

920-438: The mass of an object to its volume has no physical meaning. However, new quantities (and, as such, units) can be derived via multiplication and exponentiation of other units. As an example, the SI unit for force is the newton , which is defined as kg⋅m⋅s . Since a coherent derived unit is one which is defined by means of multiplication and exponentiation of other units but not multiplied by any scaling factor other than 1,

966-443: The pascal is a coherent unit of pressure (defined as kg⋅m ⋅s ), but the bar (defined as 100 000  kg⋅m ⋅s ) is not. Note that coherence of a given unit depends on the definition of the base units. Should the standard unit of length change such that it is shorter by a factor of 100 000 , then the bar would be a coherent derived unit. However, a coherent unit remains coherent (and a non-coherent unit remains non-coherent) if

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1012-467: The poundal . The international standard symbol for the pound as unit of mass rather than force is lb. Everett (1861) proposed the metric dyne and erg as the units of force and energy in the FPS system. Latimer Clark's (1891) "Dictionary of Measures" contains celo (acceleration), vel or velo (velocity) and pulse (momentum) as proposed names for FPS absolute units. The technical or gravitational FPS system or British gravitational system

1058-566: The FPS system uses both the pound-mass and the pound-force, but neither the slug nor the poundal. The resulting system is sometimes also known as the English engineering system . Despite its name, the system is based on United States customary units of measure; it is not used in England. The unit of substance in the FPS system is the pound-mole (lb-mol) = 273.16 × 10 . Until the SI decided to adopt

1104-410: The SI definition of the newton: 1 kg⋅m/s . At average gravity on Earth (conventionally, g n {\displaystyle g_{\text{n}}} = 9.806 65  m/s ), a kilogram mass exerts a force of about 9.81 N. Large forces may be expressed in kilonewtons (kN), where 1 kN = 1000 N . For example, the tractive effort of a Class Y steam train locomotive and

1150-465: The absolute and gravitational FPS systems one needs to fix the standard acceleration g which relates the pound to the pound-force. While g strictly depends on one's location on the Earth surface, since 1901 in most contexts it is fixed conventionally at precisely g 0 =  9.806 65  m/s ≈  32.174 05  ft/s . Coherence (units of measurement) A coherent system of units

1196-423: The base units are redefined in terms of other units with the numerical factor always being unity. The concept of coherence was only introduced into the metric system in the third quarter of the nineteenth century; in its original form the metric system was non-coherent – in particular the litre was 0.001 m and the are (from which we get the hectare ) was 100 m . A precursor to the concept of coherence

1242-443: The cgs system, a unit force is described as one that will produce an acceleration of 1 cm/sec on a mass of 1 gm. A unit force is therefore 1 cm/sec multiplied by 1 gm." These are independent statements. The first is a definition; the second is not. The first implies that the constant of proportionality in the force law has a magnitude of one; the second implies that it is dimensionless. Asimov uses them both together to prove that it

1288-412: The definitions of the units into the defining equation of velocity we obtain, 1 mps = k m/s and 1 kmph = k km/h = 1/3.6 k m/s = 1/3.6 mps. Now choose k = 1; then the metre per second is a coherent derived unit, and the kilometre per hour is a non-coherent derived unit. Suppose that we choose to use the kilometre per hour as the unit of velocity in the system. Then the system becomes non-coherent, and

1334-416: The distinction often does not matter in practice, the coexistence of variants of the FPS system causes confusion over the nature of the unit "pound". Its relation to international metric units is expressed in kilograms, not newtons, though, and in earlier times it was defined by means of a mass prototype to be compared with a two-pan balance which is agnostic of local gravitational differences. In July 1959,

1380-427: The effect of identifying the pound-force with the pound. The pound is then both a base unit of mass and a coherent derived unit of force. One may apply any unit one pleases to the proportionality constant. If one applies the unit s /lb to it, then the foot becomes a unit of force. In a four-unit system ( English engineering units ), the pound and the pound-force are distinct base units, and the proportionality constant has

1426-472: The foot–pound–second and foot–slug–second systems. In practice, these are most associated with the centimetre–gram–second system. The 1929 "International Critical Tables" gives in the symbols and systems fpse = FPS electrostatic system and fpsm = FPS electromagnetic system. Under the conversions for charge, the following are given. The CRC Handbook of Chemistry and Physics 1979 (Edition 60), also lists fpse and fpsm as standard abbreviations. The candle and

Foot–pound–second system of units - Misplaced Pages Continue

1472-471: The force exerted on an object is directly proportional to the acceleration hence acquired by that object, thus: F = m a , {\displaystyle F=ma,} where m {\displaystyle m} represents the mass of the object undergoing an acceleration a {\displaystyle a} . When using the SI unit of mass, the kilogram (kg), and SI units for distance metre (m), and time, second (s) we arrive at

1518-445: The gram-mole, the mole was directly derived from the mass unit as (mass unit)/(atomic mass unit). The unit (lbf⋅s/ft)-mol also appears in a former definition of the atmosphere. The electrostatic and electromagnetic systems are derived from units of length and force, mainly. As such, these are ready extensions of any system of containing length, mass, time. Stephen Dresner gives the derived electrostatic and electromagnetic units in both

1564-417: The g⋅cm /s ) could bear a coherent relationship to the base units. By contrast, coherence was a design aim of the SI, resulting in only one unit of energy being defined – the joule . Each variant of the metric system has a degree of coherence—the various derived units being directly related to the base units without the need of intermediate conversion factors. An additional criterion is that, for example, in

1610-421: The numerical value equation for velocity becomes { v } = 3.6 { d }/{ t }. Coherence may be restored, without changing the units, by choosing k = 3.6; then the kilometre per hour is a coherent derived unit, with 1 kmph = 1 m/s, and the metre per second is a non-coherent derived unit, with 1 mps = 3.6 m/s. A definition of a physical quantity is a statement that determines the ratio of any two instances of

1656-424: The point of view of competing systems, according to which F = ma and 1 lbf = 32.174 lb⋅ft/s . Although the pound-force is a coherent derived unit in this system according to the official definition, the system itself is not considered to be coherent because of the presence of the proportionality constant in the force law. A variant of this system applies the unit s /ft to the proportionality constant. This has

1702-492: The pound is used as a unit of mass, the core of the coherent system is similar and functionally equivalent to the corresponding subsets of the International System of Units (SI), using metre, kilogram and second (MKS), and the earlier centimetre–gram–second system of units (CGS). This system is often called the Absolute English System . In this sub-system, the unit of force is a derived unit known as

1748-446: The principle of coherence. In the SI system, the derived unit m/s is a coherent derived unit for speed or velocity but km / h is not a coherent derived unit. Speed or velocity is defined by the change in distance divided by a change in time. The derived unit m/s uses the base units of the SI system. The derived unit km/h requires numerical factors to relate to the SI base units: 1000 m/km and 3600 s/h . In

1794-418: The quantity. The specification of the value of any constant factor is not a part of the definition since it does not affect the ratio. The definition of velocity above satisfies this requirement since it implies that v 1 / v 2 = ( d 1 / d 2 )/( t 1 / t 2 ); thus if the ratios of distances and times are determined, then so is the ratio of velocities. A definition of a unit of a physical quantity

1840-399: The same as the relations among the quantities themselves. The following example concerns definitions of quantities and units. The (average) velocity ( v ) of an object is defined as the quantitative physical property of the object that is directly proportional to the distance ( d ) traveled by the object and inversely proportional to the time ( t ) of travel, i.e., v = kd / t , where k is

1886-481: The same value across a community , then different units of the same quantity (for example feet and inches) were given a fixed relationship. Apart from Ancient China where the units of capacity and of mass were linked to red millet seed , there is little evidence of the linking of different quantities until the Enlightenment . The history of the measurement of length dates back to the early civilization of

Foot–pound–second system of units - Misplaced Pages Continue

1932-490: The system is coherent. The concept of coherence was developed in the mid-nineteenth century by, amongst others, Kelvin and James Clerk Maxwell and promoted by the British Science Association . The concept was initially applied to the centimetre–gram–second (CGS) in 1873 and the foot–pound–second systems (FPS) of units in 1875. The International System of Units (SI) was designed in 1960 around

1978-449: The unit lbf⋅s /(lb⋅ft). All these systems are coherent. One that is not is a three-unit system (also called English engineering units) in which F = ma that uses the pound and the pound-force, one of which is a base unit and the other, a non-coherent derived unit. In place of an explicit proportionality constant, this system uses conversion factors derived from the relation 1 lbf = 32.174 lb⋅ft/s . In numerical calculations, it

2024-556: The unit of force in the MKS system of units to be the amount needed to accelerate one kilogram of mass at the rate of one metre per second squared. In 1948, the 9th CGPM Resolution 7 adopted the name newton for this force. The MKS system then became the blueprint for today's SI system of units. The newton thus became the standard unit of force in the Système international d'unités (SI), or International System of Units . The newton

2070-406: The various national foot and avoirdupois pound standards were replaced by the international foot of precisely 0.3048 m and the international pound of precisely 0.453 592 37  kg , making conversion between the systems a matter of simple arithmetic. The conversion for the poundal is given by 1 pdl = 1 lb·ft/s = 0.138 254 954 376   N (precisely). To convert between

2116-416: Was however present in that the units of mass and length were related to each other through the physical properties of water, the gram having been designed as being the mass of one cubic centimetre of water at its freezing point. The CGS system had two units of energy, the erg that was related to mechanics and the calorie that was related to thermal energy , so only one of them (the erg, equivalent to

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