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:

• $F_n$ is the normal force
• $F_r$ is friction
• $F_a$ is the applied force
• and $W$ being 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 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.

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 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.

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

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

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.

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

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.

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