Table of Contents

Forces

A force is an interaction that would change the motion of a given object. The diagram below shows the forces typical of an object in any given system.

Where:

Weight

Mass is the density of the object while weight is its resistance against gravity. Volume is related to mass via density. Weight is mass multiplied by gravity. $W = mg$

Applied Force

Applied force is the force exerted on an object in a system externally. Typically it's given to you. It can also be substituted with a force like tension.

Normal Force

The normal force is what is exerted when a object rests against another. Typically, this force is equivalent to the weight of the object1), unless it is a special situation like an incline plane. In those cases, the normal force may be offset from the weight.

Friction

Friction is a force caused by the collision of surfaces that are inherently uneven. It is mathematically defined as $F_r = \mu F_n$ where $F_r$ is friction, $F_n$ is the normal force2), and $\mu$ being the coefficient of friction3). The coefficient of friction is a uniform value4). There are two types of friction.

Static Friction

This type of friction prevents an object from sliding against another surface parallel to the contact area.

Kinetic Friction

This type of friction slows an object instead of preventing its movement. Direction is opposite to the object's net force.

Tension

See: Solving Tension Problems, also Solving Incline Plane Problems for Tension on an incline plane.

Tension is a force that a rope5) exerts pulling one object to another.

Finding Acceleration

The acceleration of tension can be calculated by summing the forces of each object under tension by the sum of their masses6).

Force of Tension

FIXME No clue if this is right, disregard if you're doing something important

You can use Newton's Second Law 7) to calculate the force of tension, with $F_{net}$ being the sum of all forces in the system ($\sum F$), $m$ being the mass of the two objects in tension, and $a$ being the value calculated before.

From Weight and Net Force

Tension can also be associated as equal to the net force of the system minus an acting force, typically weight $F_{net} = T - W$.

1)
$F_n = W$
2)
opposing force of weight when object is resting on a surface
3)
Newton's second law is useful here if you want to find the friction coefficient given an acceleration without mass present
4)
0-1 linear value
5)
/string/chain
6)
$a = \frac{\sum F}{m}$ where $F$ are the forces and $m$ is the total mass of the objects
7)
$F_{net} = ma$