# Newton

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The newton (symbol: N) is the SI derived unit of force, named after Isaac Newton in recognition of his work on classical mechanics.

### Definition

The newton is the unit of force derived in the SI system; it is equal to the amount of force required to accelerate a mass of one kilogram at a rate of one meter per second per second. In dimensional analysis, F=ma, multiplying m (kg) by a (m/s2), the dimension for 1 newton unit is therefore:

### Examples

• 1 N is the force of Earth's gravity on an object with a mass of about 102 g or 1/9.81 kg (such as a small apple).
• 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 kg corresponding to 10 N is sometimes used as a rule of thumb in everyday life and in engineering.
• The force of Earth's gravity on a human being with a mass of 70 kg is approximately 686 N.
• The 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.
• An amusing rule of thumb to help remember the Newton: On earth, a N is equivalent to ~100 g; coincidentally, this is about the mass of an apple. So, you can think of a N as getting hit on the head with an apple.

### 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

Three approaches to mass and force units

 System Gravitational Engineering Absolute Force (F) F = m·a F = m·a/gc = w·a/g F = m·a Weight (w) w = m·g w = m·g/gc ? m w = m·g Units English Metric English Metric English Metric Acceleration (a) ft/s2 m/s2 ft/s2 m/s2 ft/s2 m/s2 Mass (m) slug hyl pound-mass kilogram pound kilogram Force (F) pound kilopond pound-force kilopond poundal newton

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