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# Newton (unit)

newton
Visualization of one newton of force
General information
Unit systemSI derived unit
Unit ofForce
SymbolN
Named afterSir Isaac Newton
Conversions
1 N in ...... is equal to ...
SI base units   1 kgms−2
CGS units   105 dyn
Imperial units   0.224809 lbf

The newton (symbol: N) is the International System of Units (SI) derived unit of force. It is defined as 1 kg⋅m/s2, the force which gives a mass of 1 kilogram an acceleration of 1 metre per second per second. It is named after Isaac Newton in recognition of his work on classical mechanics, specifically Newton's second law of motion.

## Definition

A newton is defined as 1 kg⋅m/s2 (it is a derived unit which is defined in terms of the SI base units).[1] 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.[2] The units "metre per second squared" can be understood as a change in velocity per time, i.e. an increase of velocity by 1 metre per second every second.

In 1946, Conférence Générale des Poids et Mesures (CGPM) Resolution 2 standardized the unit of force in the MKS system of units to be the amount needed to accelerate 1 kilogram of mass at the rate of 1 metre per second squared. In 1948, the 9th CGPM Resolution 7 adopted the name newton for this force.[3] 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 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.

In more formal terms, Newton's second law of motion states that the force exerted on an object is directly proportional to the acceleration hence acquired by that object, namely:[4]

${\displaystyle F=ma,}$

where ${\displaystyle m}$ represents the mass of the object undergoing an acceleration ${\displaystyle a}$. As a result, the newton may be defined in terms of kilograms (${\displaystyle {\text{kg}}}$), metres (${\displaystyle {\text{m}}}$), and seconds (${\displaystyle {\text{s}}}$) as

${\displaystyle 1\ {\text{N}}=1\ {\frac {{\text{kg}}\cdot {\text{m}}}{{\text{s}}^{2}}}.}$

## Examples

At average gravity on Earth (conventionally, g = 9.80665 m/s2), a kilogram mass exerts a force of about 9.8 newtons. An average-sized apple exerts about one newton of force at Earth's surface, which we measure as the apple's weight on Earth.[5]

1 N = 0.10197 kg × 9.80665 m/s2    (0.10197 kg = 101.97 g).

The weight of an average adult exerts a force of about 608 N.

608 N = 62 kg × 9.80665 m/s2 (where 62 kg is the world average adult mass).[6]

## Kilonewtons

A carabiner used in rock climbing, with a safety rating of 26 kN when loaded along the spine with the gate closed, 8 kN when loaded perpendicular to the spine, and 10 kN when loaded along the spine with the gate open.

It is common to see forces expressed in kilonewtons (kN), where 1 kN = 1000 N. For example, the tractive effort of a Class Y steam train locomotive and the thrust of an F100 jet engine are both around 130 kN.

One kilonewton, 1 kN, is equivalent to 102.0 kgf, or about 100 kg of load under Earth gravity.

1 kN = 102 kg × 9.81 m/s2.

So for example, a platform that shows it is rated at 321 kilonewtons (72,000 lbf) will safely support a 32,100-kilogram (70,800 lb) load.

Specifications in kilonewtons are common in safety specifications for:

## Conversion factors

Units of 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
The value of gn as used in the official definition of the kilogram-force is used here for all gravitational units.
Three approaches to units of mass and force or weight[7][8]
Base Force Weight Mass
2nd law of motion m = F/a F = Wa/g F = ma
System BG GM EE M AE CGS MTS SI
Acceleration (a) ft/s2 m/s2 ft/s2 m/s2 ft/s2 Gal m/s2 m/s2
Mass (m) slug hyl pound-mass kilogram pound gram tonne kilogram
Force (F),
weight (W)
pound kilopond pound-force kilopond poundal dyne sthène newton
Pressure (p) pound per square inch technical atmosphere pound-force per square inch standard atmosphere poundal per square foot barye pieze pascal
Standard prefixes for the metric units of measure (multiples)
Prefix name N/A deca- hecto- kilo- mega- giga- tera- peta- exa- zetta- yotta-
Prefix symbol da- h- k- M- G- T- P- E- Z- Y-
Factor 100 101 102 103 106 109 1012 1015 1018 1021 1024
Standard prefixes for the metric units of measure (submultiples)
Prefix name N/A deci- centi- milli- micro- nano- pico- femto- atto- zepto- yocto-
Prefix symbol d- c- m- μ- n- p- f- a- z- y-
Factor 100 10–1 10–2 10–3 10–6 10–9 10–12 10–15 10–18 10–21 10–24

## References

1. ^ The International System of Units – 9th edition – Text in English (9 ed.). Bureau International des Poids et Mesures (BIPM). 2019. p. 137.
2. ^ "Newton | unit of measurement". Encyclopedia Britannica. Archived from the original on 2019-09-27. Retrieved 2019-09-27.
3. ^ International Bureau of Weights and Measures (1977), The International System of Units (3rd ed.), U.S. Dept. of Commerce, National Bureau of Standards, p. 17, ISBN 0745649742, archived from the original on 2016-05-11, retrieved 2015-11-15.
4. ^ "Table 3. Coherent derived units in the SI with special names and symbols". The International System of Units (SI). International Bureau of Weights and Measures. 2006. Archived from the original on 2007-06-18.
5. ^ Whitbread BSc (Hons) MSc DipION, Daisy. "How much is 100 grams?". Archived from the original on 24 October 2017. Retrieved 22 September 2020.
6. ^ Walpole, Sarah Catherine; Prieto-Merino, David; Edwards, Phillip; Cleland, John; Stevens, Gretchen; Roberts, Ian (2012). "The weight of nations: an estimation of adult human biomass". BMC Public Health. 12 (12): 439. doi:10.1186/1471-2458-12-439. PMC 3408371. PMID 22709383.
7. ^ Comings, E. W. (1940). "English Engineering Units and Their Dimensions". Industrial & Engineering Chemistry. 32 (7): 984–987. doi:10.1021/ie50367a028.
8. ^ Klinkenberg, Adrian (1969). "The American Engineering System of Units and Its Dimensional Constant gc". Industrial & Engineering Chemistry. 61 (4): 53–59. doi:10.1021/ie50712a010.