Engineering Mechanics -system of Forces

Engineering mechanics or Applied mechanics is 

a branch of the physical sciences and the practical application of mechanics. 

Much of modern engineering mechanics is based on Isaac Newton's laws of motion while the modern practice of their application can be traced back to Stephen Timoshenko, who is said to be the father of modern engineering mechanics.  

Engineering Mechanics is divided into two parts Statics and Dynamics.

Statics:

It is a branch of mechanics which studies the effects and distribution of forces of rigid bodies which are and remain at rest.

In this area of mechanics, the body in which forces are acting is assumed to be rigid. 

The deformation of the body is treated in Mechanics in the name of Solid Mechanics or Strength of Materials.

Force - It may be defined as any action that tends to change the state of rest of a body to which it is applied. 

Newton's laws of motion are three physical laws that form the basis for classical mechanics. 

Newton's First law 

A body persists in a state of rest or of uniform motion unless acted upon by an external force. Newton's first law is often referred to as the law of inertia. 

Newton's second law 

Newton's second law states that the force applied to a body produces a proportional acceleration; the relationship between the two is F = ma 

where F is the force applied, m is the mass of the body, and a is the body's acceleration. 

Newton's third law: Or law of reciprocal actions

For every action there is always an equal and opposite reaction: or the forces of two bodies on each other are always equal and are directed in opposite directions.

Coplanar Forces : 

When a number of Forces lie in the plane they are said to be Coplanar Forces.
Concurrent Forces:
The Forces whose lines of action pass through a common point as said to be Concurrent Forces.
Components of a Force in XY Plane :

Forces acting at some angle from the the coordinate axes can be resolved into mutually perpendicular forces called components.

The component of a force parallel to the x-axis is called the x-component, parallel to y-axis the y-component, and so on.

         Fx = F cosθx and

 Fy = F sinθx

Resultant of a force system: 

Resultant is a force or a couple that will have the same effect to the body, both in translation and rotation, if all the forces are removed and replaced by the resultant. 

The equation involving the resultant of force system are the following : 

The x-component of the resultant is equal to the summation of forces in the x-direction. 

The y-component of the resultant is equal to the summation of forces in the y-direction.

The z-component of the resultant is equal to the summation of forces in the z-direction.

Note that according to the type of force system, one or two or three of the equations above will be used in finding the resultant. 

Resultant of Coplanar Concurrent Force System 

The line of action of each forces in coplanar concurrent force system are on the same plane. All of these forces meet at a common point, thus concurrent.

tanx = RxRy