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Newton (unit)
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newton
Visualization of one newton of force
General information
Unit systemSI
Unit offorce
SymbolN
Named afterSir Isaac Newton
Conversions
1 N in ...... is equal to ...
   SI base units   1 kg⋅m⋅s−2
   CGS units   105 dyn
   Imperial units   0.224809 lbf

The newton (symbol: N) is the unit of force in the International System of Units (SI). Expressed in terms of SI base units, it is 1 kg⋅m/s2, 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.

Definition

[edit]

A newton is defined as 1 kg⋅m/s2 (it is a named derived unit defined in terms of the SI base units).[1]: 137  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 measuring a rate of change in velocity per unit of time, i.e. an increase in velocity by one metre per second every second.[2]

In 1946, the General Conference on Weights and Measures (CGPM) Resolution 2 standardized 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.[3] The MKS system then became the blueprint for today's SI system of units.[4] The newton thus became the standard unit of force in the Système international d'unités (SI), or International System of Units.[3]

The newton is named after Isaac Newton. As with every SI unit named after 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 the force exerted on an object is directly proportional to the acceleration hence acquired by that object, thus:[5] where represents the mass of the object undergoing an acceleration . When using the SI unit of mass, the kilogram (kg), and SI units for distance metre (m), and time, second (s) we arrive at the SI definition of the newton: 1 kg⋅m/s2.

Examples

[edit]

At average gravity on Earth (conventionally, = 9.80665 m/s2), a kilogram mass exerts a force of about 9.81 N.

  • An average-sized apple with mass 200 g exerts about two newtons of force at Earth's surface, which we measure as the apple's weight on Earth.
(where 62 kg is the world average adult mass).[6]

Kilonewtons

[edit]
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.

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 the thrust of an F100 jet engine are both around 130 kN.[citation needed]

Climbing ropes are tested by assuming a human can withstand a fall that creates 12 kN of force. The ropes must not break when tested against 5 such falls.[7]: 11 

Conversion factors

[edit]
Units of force
newton dyne kilogram-force,
kilopond 		pound-force poundal
1 N ≡ 1 kg⋅m/s2 = 105 dyn ≈ 0.10197 kgf ≈ 0.22481 lbF ≈ 7.2330 pdl
1 dyn = 10−5 N ≡ 1 g⋅cm/s2 ≈ 1.0197×10−6 kgf ≈ 2.2481×10−6 lbF ≈ 7.2330×10−5 pdl
1 kgf = 9.80665 N = 980665 dyn ≡ gn × 1 kg ≈ 2.2046 lbF ≈ 70.932 pdl
1 lbF ≈ 4.448222 N ≈ 444822 dyn ≈ 0.45359 kgf ≡ gn × 1 lb ≈ 32.174 pdl
1 pdl ≈ 0.138255 N ≈ 13825 dyn ≈ 0.014098 kgf ≈ 0.031081 lbF ≡ 1 lb⋅ft/s2
The value of gn (9.80665 m/s2) 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[8][9]
Base 		Force Weight Mass
2nd law of motion m = ⁠F/a⁠ F = ⁠W ⋅ a/g⁠ F = m ⋅ a
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
SI multiples of newton (N)
Submultiples Multiples
Value SI symbol Name Value SI symbol Name
10−1 N dN decinewton 101 N daN decanewton
10−2 N cN centinewton 102 N hN hectonewton
10−3 N mN millinewton 103 N kN kilonewton
10−6 N μN micronewton 106 N MN meganewton
10−9 N nN nanonewton 109 N GN giganewton
10−12 N pN piconewton 1012 N TN teranewton
10−15 N fN femtonewton 1015 N PN petanewton
10−18 N aN attonewton 1018 N EN exanewton
10−21 N zN zeptonewton 1021 N ZN zettanewton
10−24 N yN yoctonewton 1024 N YN yottanewton
10−27 N rN rontonewton 1027 N RN ronnanewton
10−30 N qN quectonewton 1030 N QN quettanewton

See also

[edit]

References

[edit]
Revisions and contributorsEdit on WikipediaRead on Wikipedia

Newton (unit)

View on Grokipedia
from Grokipedia
The newton (symbol: N) is the derived unit of force in the International System of Units (SI). It is defined as exactly the force that gives an acceleration of one metre per second squared (1 m/s²) when applied to a mass of one kilogram (1 kg). In terms of SI base units, one newton is equal to one kilogram metre per second squared (kg⋅m⋅s⁻²). This unit is coherent within the SI system, meaning it can be expressed directly from the base units of mass, length, and time without additional numerical factors. The newton was formally adopted as the name for the SI unit of force by the 9th General Conference on Weights and Measures (CGPM) in 1948, replacing the earlier term "MKS unit of force" established by the International Committee for Weights and Measures (CIPM) in 1946. It is named in honour of Sir Isaac Newton (1642–1727), the English and mathematician whose laws of motion form the foundation of , where force is central to describing interactions between bodies. Prior to its adoption, force was measured in units such as the (in the CGS system) or pound-force (in imperial systems), but the newton provides a standardized metric for scientific and engineering applications worldwide. In everyday contexts, one newton approximates the gravitational force exerted by on an object with a of about 102 grams (such as a small apple), since this equals the product of the and the standard acceleration due to gravity (approximately 9.81 m/s²). The unit is fundamental in fields like , , and physics, where forces range from micro-newtons in to meganewtons in ; common multiples include the kilonewton (kN = 10³ N) for larger forces, such as those in or . For non-SI conversions, one newton equals approximately 0.2248 pound-force.

Definition and Derivation

Formal Definition

The newton (symbol: N) is the SI derived unit of force. It is defined as the force that gives to a mass of one kilogram an acceleration of one metre per second squared when applied in the direction of the acceleration. This corresponds exactly to the expression 1 N=1 kg⋅m⋅s−21 \, \mathrm{N} = 1 \, \mathrm{kg \cdot m \cdot s^{-2}}, where the kilogram (kg) is the SI base unit of mass, the metre (m) is the base unit of length, and the second (s) is the base unit of time. The definition arises directly from Newton's second law of motion, which states that F\mathbf{F} equals mm times a\mathbf{a}, or F=ma\mathbf{F} = m \mathbf{a}; thus, when m=1 kgm = 1 \, \mathrm{kg} and a=1 m⋅s−2a = 1 \, \mathrm{m \cdot s^{-2}}, the resulting is 1 N. Following the 2019 revision of the SI by the 26th General Conference on Weights and Measures, the is now defined in terms of the fixed numerical value of the h=6.626 070 15×10−34 J⋅sh = 6.626 \, 070 \, 15 \times 10^{-34} \, \mathrm{J \cdot s}, rendering the newton indirectly fixed through this fundamental constant while preserving its exact value and relation to the base units.

Physical Interpretation

The newton (N) is the SI derived unit of , defined as the amount of force necessary to accelerate a of one by one meter per second squared in the direction of the applied force. This interpretation stems from Newton's second law of motion, where force equals times , providing a direct measure of the interaction that causes linear acceleration in an object. Expressed in terms of SI base units, one newton equals one meter per second squared, or kg⋅m⋅s⁻². This can be broken down dimensionally as the product of (kg, dimension [M]) and (m, dimension [L]) divided by the square of time (s², dimension [T]²), yielding the fundamental dimensions of : [M][L][T]⁻². These dimensions link the unit to the core physical quantities of , , and time, ensuring consistency across SI measurements of mechanical interactions. Although is fundamentally a vector —with both magnitude (measured in newtons) and direction—the newton itself specifies only the scalar magnitude, as the unit applies uniformly regardless of orientation. Unlike , which often refers specifically to the gravitational force on an object (and is thus also measured in newtons), the newton quantifies any type of , including non-gravitational ones such as electromagnetic or frictional forces acting on a body. This broad applicability underscores the unit's role in describing diverse physical phenomena beyond mere attraction to .

Historical Background

Origins in Physics

The conceptual foundations of the newton trace back to Isaac Newton's , published in 1687, where the second law of motion established that the change in motion of a body is proportional to the impressed and occurs in the direction of that . This principle, initially framed in terms of change rather than , laid the groundwork for quantifying in . The modern algebraic form F=maF = ma, relating directly to and , was first explicitly formulated by Leonhard Euler in 1750, building on Newton's ideas to enable precise analytical treatments in physics. In the early 19th century, as physics experiments demanded consistent units for , two prominent systems emerged outside the nascent metric framework. The foot-pound-second (FPS) system, widely used in British and American contexts, defined the poundal as the coherent unit of —the amount required to accelerate a one-pound by one foot per second squared. Concurrently, the centimeter-gram-second (CGS) system, proposed by the British Association for the Advancement of Science in 1874, introduced the as its force unit, defined as the accelerating a one-gram by one centimeter per second squared, which proved particularly useful for microscopic-scale measurements in early and experiments. The transition to the meter-kilogram-second (MKS) system in the early marked a pivotal shift toward larger-scale practical applications in physics. Proposed by Giovanni Giorgi in 1901 to integrate mechanical and electrical units coherently, the MKS system expressed as kilogram-meter per second squared, initially without a dedicated name, facilitating broader adoption in engineering and where CGS units were often impractically small. The ongoing evolution of the profoundly shaped force measurement in physics experiments by emphasizing coherence and decimal scalability, enabling seamless integration across disciplines like and from the late onward. This progression from ad hoc units to systematic frameworks reduced errors in calculations and supported advancements in precise instrumentation, such as balances and dynamometers used in gravitational and inertial studies.

Standardization and Naming

The standardization of the newton as the unit of force within the metre-kilogram-second (MKS) system commenced in the mid-20th century through decisions by international metrology bodies. In 1946, the International Committee for Weights and Measures (CIPM), during its 41st meeting, formally defined the MKS unit of force as the force that gives a mass of one kilogram an acceleration of one metre per second squared, expressed as kg⋅m⋅s−2kg \cdot m \cdot s^{-2}. This definition built on earlier efforts to establish a practical system of units, providing a coherent measure for force in mechanical contexts. The 9th General Conference on Weights and Measures (CGPM), held in 1948, ratified the CIPM's 1946 resolution on the MKS unit of force and officially adopted the name "newton" (with symbol N) for it, honoring the English physicist and mathematician Sir Isaac Newton for his foundational contributions to . The naming took effect immediately, marking the transition from a descriptive term ("MKS unit of force") to a named unit, and it aligned with broader efforts to standardize nomenclature in the evolving metric framework. In 1960, the 11th CGPM established the International System of Units (SI) through Resolution 12, incorporating the newton as the coherent derived SI unit for force, derived from the base units of mass (kilogram), length (metre), and time (second). This ratification solidified the newton's role within a comprehensive, internationally agreed system. The 26th CGPM in 2019 revised the SI by fixing the numerical values of key physical constants to define the base units more precisely, which indirectly enhanced the stability and realizability of derived units like the newton without changing its fundamental expression as 1 N=1 kg⋅m⋅s−21\ \mathrm{N} = 1\ \mathrm{kg \cdot m \cdot s^{-2}}. This update ensures the newton's definition remains invariant and exact, supporting ongoing advancements in precision measurement.

Magnitude and Examples

Everyday Examples

To grasp the magnitude of the newton in daily life, consider the weight of a typical small apple, which masses about 100 grams; under Earth's standard of approximately 9.81 m/s², this exerts a force of roughly 0.98 newtons (approximately 1 newton) on a surface. Similarly, lifting a 1-kilogram object, such as a liter of , against requires applying about 9.81 newtons of force to overcome its . For a larger scale, the average adult human, with a body mass of around 62 kilograms, experiences a downward gravitational force of approximately 608 newtons when standing on . These examples highlight how the newton quantifies gravitational force via the relation F = m · g, where m is mass and g is gravitational acceleration, though the unit measures any force, including those from pushing or pulling in non-gravitational contexts. In routine activities, forces in the range of 1 to 10 newtons are common; for instance, pressing a thumbtack into a corkboard or pushing open a standard interior typically involves exerting such a force.

Engineering and Scientific Applications

In engineering applications, the newton is essential for specifying the load-bearing capacities of equipment, where are typically rated for major axis strengths between 20 and 27 kN to ensure safety under dynamic falls and static loads, as per UIAA standards. For instance, a standard locking carabiner might be certified at 24 kN along its primary axis, allowing it to withstand forces equivalent to several times the climber's body during high-impact scenarios. In , systems operate at vastly larger scales, with thrusts measured in meganewtons (MN) or even gig newtons (GN) for heavy-lift vehicles. The F-1 engines of the , for example, each produced approximately 6.77 MN of at , enabling the total first-stage output to reach over 33 MN to overcome Earth's gravity. Modern examples include the Falcon 9's nine Merlin 1D engines, collectively generating about 7.7 MN at liftoff, highlighting the newton's role in quantifying immense propulsive forces for . Material testing in relies on the newton to measure tensile strength, particularly for structural components like cables used in bridges, cranes, and elevators. A typical 12 mm 6x19 might exhibit a minimum breaking strength of around 100 kN, determined through standardized pull tests that assess ultimate load capacity before failure. These measurements guide design safety factors, ensuring cables can handle repeated stresses without catastrophic rupture. At the nanoscale, physics experiments such as (AFM) employ piconewtons (pN) to nanonewtons (nN) to probe intermolecular forces and surface properties. In AFM, tip interactions with samples generate forces on the order of 1-10 nN during indentation, allowing precise mapping of material stiffness and at atomic resolutions. This sensitivity underscores the newton's utility across scales, from macroscopic to quantum-level investigations. In , the newton quantifies muscle contractile forces, often in millinewtons (mN) for isolated tissue preparations. During isometric contractions, a single fiber bundle might produce peak forces of 0.5-5 mN, depending on cross-sectional area and stimulation frequency, as measured in setups to study excitation-contraction coupling. Such data inform models of neuromuscular function and rehabilitation strategies for conditions like .

Multiples and Submultiples

Common Multiples

The common multiples of the newton are formed by applying standard SI decimal prefixes to the base unit, enabling the expression of larger forces in a concise manner. These prefixes, defined by the International Bureau of Weights and Measures (BIPM), multiply the newton (N) by powers of 10, with corresponding symbols attached to N. For instance, the prefix "kilo-" denotes a factor of 10310^3, "mega-" denotes 10610^6, and "giga-" denotes 10910^9. This system ensures consistency across all SI derived units, including force. The kilonewton (symbol: kN) is equal to 10310^3 N, or 1,000 newtons. It is widely used in structural engineering to quantify significant loads, such as the forces on bridge supports or beams, where point loads and distributed pressures are often specified in kN or kN/m² to assess material strength and stability. The meganewton (symbol: MN) equals 10610^6 N, representing one million newtons. This unit is applied to measure immense forces in contexts like heavy machinery and explosive events, including the thrust generated by large rocket engines; for example, the National Institute of Standards and Technology (NIST) employs a 4.45 MN deadweight machine to calibrate sensors for rocket propulsion forces exceeding one million pounds-force. The giganewton (symbol: GN) is defined as 10910^9 N, or one billion newtons. It is utilized in specialized domains involving extraordinarily large forces, such as astrophysical gravitational interactions or high-energy physics simulations, and in conceptual designs for large-scale systems where forces reach scales beyond typical applications.

Common Submultiples

Submultiples of the newton, formed using standard SI prefixes, quantify forces below 1 N and are essential in fields requiring high sensitivity, such as microscale and biological . These units enable precise of subtle interactions, from to , without altering the fundamental definition of force as mass times acceleration. The millinewton (symbol: mN) equals 10−310^{-3} N and is commonly used in precision instruments for tasks like component testing and haptic feedback systems, where forces in the range of delicate mechanical contacts must be controlled. In biology, millinewton-scale sensors support adhesion measurements in nanoindentation experiments on cellular and biomaterial interfaces, allowing quantification of surface interactions critical to tissue engineering. The micronewton (symbol: µN) is defined as 10−610^{-6} N and plays a key role in microelectromechanical systems (), where it measures forces in six-axis force-torque sensors for robotic manipulation and biomedical devices. These sensors, with resolutions down to sub-micronewton levels, facilitate applications like micrograsping of biomaterials, ensuring controlled interactions at the cellular scale without damage. The nanonewton (symbol: nN) corresponds to 10−910^{-9} N and is vital in for detecting forces in and similar tools. In cell adhesion studies, nanonewton measurements reveal the mechanics of cellular interactions, such as traction forces during migration, providing insights into processes like and cancer through techniques like and micropillar arrays. The piconewton (symbol: pN) equals 10−1210^{-12} and is employed to quantify molecular forces, particularly in experiments involving DNA interactions. For instance, piconewton-scale tensions are measured using DNA-based tension probes to study transient molecular bindings, such as those in integrin-mediated adhesions or protein-DNA complexes, advancing understanding of mechanotransduction in .

Conversions

To Other Force Units

The newton (N), as the SI unit of , is related to force units in other systems through defined conversion factors based on the relationships between their base units of , , and time. These conversions allow for in scientific and engineering contexts across metric, CGS (centimeter-gram-second), and FPS (foot-pound-second) systems. In the CGS system, the (dyn) is the unit of force, defined as the force required to accelerate a of one gram at one centimeter per second squared (g⋅cm⋅s⁻²). The exact conversion is 1 N = 10⁵ dyn, or equivalently, 1 dyn = 10⁻⁵ N. In the FPS system, the pound-force (lbf) is a gravitational unit defined as the force exerted by on one pound of , while the poundal (pdl) is the absolute unit defined as the force to accelerate one pound of at one foot per second squared. The conversions are 1 N = 0.224809 lbf (to six decimal places) and 1 lbf = 4.448222 N, or 1 N = 7.23301 pdl (to five decimal places) and 1 pdl = 0.138255 N.
UnitTo NewtonFrom NewtonSystem
(dyn)× 10⁻⁵× 10⁵CGS
Pound-force (lbf)× 4.448222× 0.224809FPS (gravitational)
Poundal (pdl)× 0.138255× 7.23301FPS (absolute)
These factors are derived from the precise definitions of the base units and (gₙ = 9.80665 m/s²) in each system.

To Weight and Mass Equivalents

In the context of , which is the gravitational force acting on a near Earth's surface, the newton relates directly to via the equation W=mgW = m g, where WW is the in newtons, mm is the in kilograms, and gg is the local acceleration due to gravity in meters per second squared. For standardized conversions, the value gn=9.80665g_n = 9.80665 m/s², known as , is used; this represents a conventional average acceleration due to gravity at . A force of 1 thus corresponds to the weight of a mass m=1/gn≈0.10197m = 1 / g_n \approx 0.10197 kg, or approximately 102 g, under on . To determine the mass from a given (), the relation m = [F / g](/page/F&G) applies; for instance, a mass of 1 kg has a weight of 1×9.80665=9.806651 \times 9.80665 = 9.80665 under standard conditions. The actual value of gg varies slightly by location due to 's shape, rotational effects, and altitude: it reaches about 9.832 m/s² at the poles and drops to around 9.780 m/s² at the . Despite these differences, which amount to less than 0.5% variation, the standard gng_n ensures uniformity in unit conversions across scientific and applications. A frequent source of error is conflating with ; the measures mass only, while expressions like "kilograms of " are imprecise. The (kgf), defined as the gravitational force on 1 kg at and thus equal to exactly 9.80665 N, served historical purposes but is deprecated in the (SI), with the newton preferred for all measurements.

References

  1. https://www.bipm.org/documents/20126/41483022/SI-Brochure-9-EN.pdf
  2. https://www.nist.gov/pml/quantum-measurement/mass-and-force/proving-ring/what-force
  3. https://physics.nist.gov/cuu/pdf/sp811.pdf
  4. https://physics.nist.gov/cuu/pdf/sp330.pdf
  5. https://www.npl.co.uk/resources/q-a/what-is-the-si-unit-of-force
  6. https://hypertextbook.com/facts/2004/WaiWingLeung.shtml
  7. https://www.bipm.org/documents/20126/41483022/SI-Brochure-9-EN.pdf/2d2b50bf-f2b4-9661-f402-5f9d66e4b507?version=1.9&download=true
  8. https://www.nist.gov/pml/special-publication-811/nist-guide-si-chapter-8
  9. https://pubs.aip.org/aapt/ajp/article/79/10/1015/1043747/Is-Newton-s-second-law-really-Newton-s
  10. https://bipublication.com/files/IJCMS-V4I1-2013-14.pdf
  11. https://hep.physics.illinois.edu/home/serrede/P435/Lecture_Notes/A_Brief_History_of_the_Development_of_the_SI_Units.pdf
  12. https://www.bipm.org/en/committees/ci/cipm/41-1946/resolution-2
  13. https://www.bipm.org/en/committees/cg/cgpm/11-1960/resolution-12
  14. https://theuiaa.org/safety-standards/uiAA-121-connectors-karabiners/
  15. https://www.blackdiamondequipment.com/en_US/product/rocklock-screwgate-carabiner/
  16. https://ntrs.nasa.gov/api/citations/20160008869/downloads/20160008869.pdf
  17. https://www.wevolver.com/specs/merlin-engine-merlin-1d-falcon-9-falcon-heavy
  18. https://www.engineeringtoolbox.com/wire-rope-strength-d_1518.html
  19. https://www.nature.com/articles/s41598-017-05383-0
  20. https://www.frontiersin.org/journals/physiology/articles/10.3389/fphys.2022.937132/full
  21. https://www.bipm.org/en/measurement-units/si-prefixes
  22. https://www.structuralbasics.com/point-load/
  23. https://www.gsourcedata.com/navigating-load-calculations-for-modern-structures-bridging-theory-to-practice/
  24. https://www.nist.gov/how-do-you-measure-it/how-do-you-measure-thrust-rocket-engine
  25. https://unitconversionhub.com/force-converter/
  26. https://www.pi-usa.us/en/tech-blog/precision-force-control
  27. https://nanoindentation.oxinst.com/learning/view/article/adhesion-measurement-via-nanoindentation
  28. https://ieeexplore.ieee.org/document/4781621
  29. https://www.researchgate.net/publication/221070918_MicroNewton_Force-Controlled_Manipulation_of_Biomaterials_using_a_Monolithic_MEMS_Microgripper_with_Two-Axis_Force_Feedback
  30. https://www.sciencedirect.com/science/article/pii/S1878535215002518
  31. https://www.pnas.org/doi/10.1073/pnas.1904034116
  32. https://www.nist.gov/pml/special-publication-811/nist-guide-si-appendix-b-conversion-factors/nist-guide-si-appendix-b9
  33. https://physics.nist.gov/cgi-bin/cuu/Value?gn
  34. https://pwg.gsfc.nasa.gov/stargaze/Sfall.htm
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