 # Resource: Forces overview

A general brainstorm for relevant and common-seen forces is listed below. Symbols are shown where often used and formulas where known and useful. (Be aware of vector versus magnitude notation, $\vec F$ and $F$, in formulas.) Symbols used:

• $\mu_k$ and $\mu_s$ are friction coefficients,
• $k$ the spring constant,
• $\Delta s$ elongated/compressed length (difference from natural/relaxed length),
• $C_D$ aerodynamic/drag coefficient,
• $\rho$ fluid density,
• $A$ frontal/projected area in direction of motion,
• $v$ speed and $\vec v$ velocity,
• $V$ submerged volume,
• $g$ gravitational acceleration,
• $m$ and $M$ two different masses,
• $G$ gravitational constant
• $r$ distance (orbit radius or charge separation)
• $q$ and $Q$ two different charges
• $\vec E$ electric field
• $\varepsilon_0$ vacuum permittivity
• $l$ length of wire carrying current $\vec I$
• $\vec B$ magnetic field
Mechanical forces (internal or needing contact)
Tension$$\vec T$$... in taut strings Compression... in lifting walls Normal force$$\vec n$$... when a surface “holds back” against something Kinetic friction$$\vec f_k$$... between sliding surfaces $$f_k=\mu_k n$$
Static friction$$\vec f_s$$... between surfaces about to slide $$f_s\leq \mu_s n$$
Elastic force /
spring force
(Hooke's law)
$$\vec F_\text{elastic}$$... in stretched rubber bands or pressed springs $$\vec F_\text{elastic}=-k\;\Delta \vec s$$

Other usual forces such as kicking forces, throwing forces, chewing forces, etc. are included in those already listed.

Fluid forces (in liquids or gasses)
Drag$$\vec D$$... on flying planes and sailing submarines $$D=C_D\rho Av^2$$
Buoyancy$$\vec B$$... pushing up the light bathing ring $$B=\rho V g$$
Diffusion 1... causing absorption and mixing Surface tension /
cohesion[2,3]
... causing water to form round rain drops Field forces (at a distance)
Weight$$\vec w$$... when gravity pulls you down $$w=mg$$
Gravitational force$$\vec F_g$$... when gravity attracts $$F_g=G\frac{mM}{r^2}$$
Electric force
(Coulomb's law)
$$\vec F_e$$... charge attraction and repulsion $\displaystyle\vec F_e=q\vec E$
$\displaystyle F_e=\frac 1{4\pi\varepsilon_0}\frac{qQ}{r^2}$
Magnetic force$$\vec F_B$$... magnetic pole attraction and repulsion $\displaystyle\vec F_B=q\vec v\times \vec B$
$\displaystyle \vec F_B=l\vec I\times \vec B$
Strong nuclear force... holds the atom together Weak nuclear force... causes breakdown of atoms Weight and the gravitational force are in fact the same thing, we just must input $g=\frac{GM}{r^2}$.

The electric and magnetic forces are usually combined into one electromagnetic force (called the Lorentz’ force): $\vec F_L=q\vec E+q\vec v\times \vec B$.

Chemical forces
Adhesion... when tape sticks and paint adheres Bonding force2... holding materials together Capillary force... when liquid by itself sucks into a straw Many of the forces can be differently categorised, such as intermolecular forces (bonding force, strong nuclear force etc.).

References:

1. Encyclopædia Britannica’ (encyclopedia), www.britannica.com

## Proof 37: Elastic potential energy

In a spring that is elongated/compressed the distance $\Delta L=L_\text{end}-L_\text{relaxed}$, an elastic force (due to Hooke’s law) $F_\text{elastic}=k\Delta L$ is pushing/pulling on the surroundings in…

## Proof 36: Gravitational potential energy

Small falling object due to weight A flower pot falls down from a window sill due to gravity. This i because gravity does work $W_g$…

## Proof 24: Newton’s 2nd law in rotation

Get some friends to help you push the stuck carousel with your daughter sitting in it. Each applies a force on her. Friction and other…

## Resource: Often-used units

Often-used units converted into SI units. Units are listed for length, time, mass, quantity (amount of substance), temperature, angle, area, volume, velocity, energy and power.…

## Resource: Geometric shapes

References:‘Encyclopædia Britannica’ (encyclopedia), www.britannica.com