Resultant Of Concurrent Coplanar Forces – Engineering mechanics

Resultant Of Concurrent Coplanar Forces

Engineering mechanics is that branch of science which deals with deals with the system of forces, effect produced by these forces on rigid object.Mechanics can be divided into two main branches – Statics and Dynamics. Statics  is that branch of Engineering mechanics, which deals with the study of system of forces and effect produced by these forces on rigid bodies, which are at rest and remains at rest. Dynamics is that branch of Engineering mechanics, which deals with the study of system of forces and motion produced by these forces on rigid bodies.There are two sub division of Dynamics

• Kinematics is the study of motion of a body without considering the  effect of its mass and forces acting on it.
• Kinetics deals with the problems which requires determination of the effect of forces on the motion of the body.

Body, A portion of matter which occupies a finite space. A body is made of atoms and molecules arranged in complex but continues manner. Rigid Body,A body which dose not change its size and shape when subjected to external load .In some case  the deformation is negligible and assume that it is rigid. Deformable Body,A body which change its size and shape when subjected to external load. Actually solid bodies are never rigid, they deform under the action of applied forces. In those cases where this deformations negligible compared to the size of the body, the body may be considered to be rigid.

Portion of matter having smallest size or its dimensions. A body whose dimensions are negligible as compared to distance travelled by it during motion may also be treated as particle. For example, while studying the motion of sun and earth, they are considered as particles since their dimensions are small when compared with the distance between them.

Force

It is that agent which causes or tends to cause, changes or tends to change the state of rest or of motion of a mass.

A force is fully defined only when the following four characteristics are known:
(i)Magnitude
(ii)Direction
(iii)Point of application
(iv)Sense.

Scalars and Vectors

• A quantity is said to be a ‘scalar ‘if it is completely defined by its magnitude alone.Example: Length, Area, and Time
• A quantity is said to be a ‘vector ‘if it is completely defined only when its magnitude and direction are specified .Example : Force, Velocity, and Acceleration.

Principle of Transmissibility

It is stated as follows : ‘The external effect of a force on a rigid body is the same for all points of application along its line of action’.

For example, consider the above figure. The motion of the block will be the same if a force of magnitude P is applied as a push at A or as a pull at B.