# Newton

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The newton (symbol: N) is the SI derived unit of force. It is named after Isaac Newton in recognition of his work on classical mechanics, specifically Newton's second law of motion.

## DefinitionEdit

The newton is the SI unit for force; it is equal to the amount of net force required to accelerate a mass of one kilogram at a rate of one meter per second squared. Newton's second law of motion states: F = ma, multiplying m (kg) by a (m/s2), The newton is therefore:[1]

${\rm N = kg~\frac{m}{s^2}}$

Units used:

N = newton
kg = kilogram
m = meter
s = second
$\textrm{Force} = \frac{\bold M \bold L} {{\bold T^2}}$

where

M = Mass
L = Length
T = Time

## ExamplesEdit

• 1 N is the force of Earth's gravity on a mass of about 100 g = (1/9.81 kg).
• On Earth's surface, a mass of 1 kg exerts a force of approximately 9.8 N [down] (or 1.0 kilogram-force; 1 kgf = 9.80665 N by definition). The approximation of 1 kgf corresponding to 10 N (1 decanewton or daN) is sometimes used as a rule of thumb in everyday life and in engineering.
• The force of Earth's gravity on (= the weight of) a human being with a mass of 70 kg is approximately 686 N.
• The dot product of force and distance is mechanical work. Thus, in SI units, a force of 1 N exerted over a distance of 1 m is 1 N·m of work. The Work-Energy Theorem states that the work done on a body is equal to the change in energy of the body. 1 N·m = 1 J (joule), the SI unit of energy.
• It is common to see forces expressed in kilonewtons or kN, where 1 kN = 1,000 N.

## Common use of kilonewtons in constructionEdit

Kilonewtons are often used for stating safety holding values of fasteners, anchors, and more in the building industry. They are also often used in the specifications for rock climbing equipment. The safe working loads in both tension and shear measurements can be stated in kilonewtons. Injection molding machines, used to manufacture plastic parts, are classed by kilonewton (i.e., the amount of clamping force they apply to the mold).

On the Earth's surface, 1 kN is about 101.97162 kilogram-force of load, but multiplying the kilonewton value by 100 (i.e. using a slightly conservative and easier to calculate value) is a good rule of thumb.[2]

## Conversion factorsEdit

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 mass and force units[3][4]
Base force, length, time weight, length, time mass, length, time
Force (F) F = m·a = w·ag F = m·agc = w·ag F = m·a = w·ag
Weight (w) w = m·g w = m·ggc ≈ m w = m·g
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, also called “metric slug” or “TME” lbm kg lb g t kg
Force (F) lb kp lbF kp pdl dyn sn N
Pressure (p) lb/in2 at PSI atm pdl/ft2 Ba pz Pa