Force

Unit System	Unit	Definition
SI	Newton (N)	Force giving 1 kg mass acceleration of 1 m/s²
CGS	dyne	Force giving 1 g mass acceleration of 1 cm/s²
Imperial	pound-force (lbf)	Force giving 1 slug mass acceleration of 1 ft/s²

Conversion factors:

$1 \, \text{N} = 100{,}000 \, \text{dyne}$

$1 \, \text{lbf} = 4.45 \, \text{N}$

Newton's Third Law

Newton's third law describes the forces acting on objects interacting with each other:

"If one object exerts a force $F$ on another object, then the second object exerts an equal but opposite force $-F$ on the first object."

A body force acts on an object without direct physical contact between bodies. Common examples include:

Surface forces at supports or points of contact between bodies are called reactions.

System	Value
SI	$g = 9.81 \, \text{m/s}^2$
Imperial	$g = 32.174 \, \text{ft/s}^2$

A mass of 50 kg is accelerated with 2 m/s²:

$F = ma = (50 \, \text{kg})(2 \, \text{m/s}^2) = 100 \, \text{N}$

The weight of an apple with mass 50 g (0.050 kg):

$W = mg = (0.050 \, \text{kg})(9.81 \, \text{m/s}^2) = 0.4905 \, \text{N}$

A body with mass $m = 60 \, \text{kg}$ is hoisted by a cable with force $F_c = 700 \, \text{N}$ .

Weight:

$W = mg = (60 \, \text{kg})(9.81 \, \text{m/s}^2) = 588.6 \, \text{N} = 0.59 \, \text{kN}$

Net upward force:

$F_a = F_c - W = 700 \, \text{N} - 588.6 \, \text{N} = 111.4 \, \text{N} = 0.11 \, \text{kN}$

Acceleration:

$a = \frac{F_a}{m} = \frac{111.4 \, \text{N}}{60 \, \text{kg}} = 1.86 \, \text{m/s}^2$