Newton
Hold a small apple in your palm, about a hundred grams. Your palm pushes up on it with a force of roughly one newton. That is exactly enough to keep the apple from falling.
In 1687 Isaac Newton published the «Mathematical Principles of Natural Philosophy». It says that a change in motion is proportional to the force applied. Today this is written as F = m·a. The unit of force was named after Newton only in 1948. One newton speeds up one kilogram by one metre per second every second.
| Notation | N |
| Through the base units | kg·m·s⁻² |
| Weight of 1 kg | 9.806 65 N at standard g · on the Moon 1.62 N |
| Named | after Isaac Newton · CGPM 1948, in the SI since 1960 |
| Standards | ISO 80000-4 · SI Brochure 9th ed. · ISO 376 (force-proving instruments) |
| Typical values | 1 nN — tip of an atomic force microscope · 1 N — apple of 102 g · 35 MN — thrust of Saturn V |
01 · Definition
A kilogram, a metre and two seconds
A newton is the force that gives a body of mass 1 kg an acceleration of 1 m/s². The newton has no standard of its own. It is built from the kilogram, the metre and the second, and it is exactly as precise as they are.
Weight is a force too. It is the force with which a body presses on its support. On Earth a kilogram weighs about 9.8 N, on the Moon six times less, while the mass stays the same. That is why a spring scale shows a different number on the Moon, and a beam balance shows the same one.
How much sand weighs one newton
The pan holds exactly enough sand for the spring to read 1 N. The weaker the gravity, the more sand is needed. The height of the heap is the mass of sand; the blue line is the 1 N mark on the scale. It is the same on every celestial body.
A shopper cares how much substance is in the pack, and that is mass. Weight depends on the place: at the equator a pack weighs half a percent less than at the pole. Shop scales measure force, but they are calibrated with weights on site. So the display shows grams.
The same newton holds a load and speeds up a cart
On the left is a spring balance. The red arrow is the weight of the object, the blue one is the force of the spring. When they are equal, the load hangs still. On the right is a cart on a rail. A propeller at the back pushes it with a constant force, shown by the blue arrow. Dots on the tape are marked every 0.1 s. The farther apart the dots, the faster the cart goes. The green line is the finish 1 m away. The celestial body changes the weight of the load and the friction, but not the propeller thrust.
An apple of 102 g weighs 1.00 N on Earth. The same newton speeds up a one-kilogram cart by 1 m/s² every second.
02 · Conversion
| Unit | Value | Where it is met |
|---|---|---|
| {n} | {v} | {note} |
A kilogram-force is the weight of a kilogram at standard g. It is exactly 9.806 65 times a newton.
The dyne of the CGS system is a hundred thousand times smaller than a newton. It speeds up a gram by 1 cm/s².
In the USA the thrust of jet engines is still written in lbf: 100 000 lbf is 445 kN.
03 · Orders of magnitude
04 · Measuring instruments
05 · Writing rules
06 · Neighbouring units
07 · Historical section
Free fall is too fast to time with a pendulum. In 1784 George Atwood hung two almost equal weights over a pulley. The small difference pulls the system slowly, so the acceleration can be measured in seconds. This was the first tabletop test of Newton's second law.
The newton rests on the kilogram. Since 2019 the kilogram has been defined through the Planck constant, so force can now be realised without weights: a Kibble balance offsets weight with an electromagnetic force. National laboratories realise large forces with deadweight machines of up to 1 MN and calibrate force-proving instruments to ISO 376.
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