APPLIED MECHANICS Introduction to Applied Mechanics Mechanics or Engineering Mechanics Branches of Mechanics SI system of Units, Basic units, Derived units Body, Rigid body, particle Scalar quantity, vector quantity Force and Graphical representation of force. Moment of forces Couple and moment of couple Law of Parallelogram of forces

Law of transmissibility of forces Varignon’s theorem, Composition of forces Coplanar force system Coplanar Non-concurrent force system Analytical method Graphical Method: Triangle law of forces, polygon law of forces Bow’s notation Problems Problems on calculation of resultant  

Problems on Varignon’s Theorem Applied Mechanics: It is the branch of engineering which studies the effect of external forces applied in any manner on a particle or a body. Engineering Mechanics/ Mechanics: It is the branch of physical science which deals with the behavior of a body when the body is at rest or in motion. Depending upon the body to which the mechanics is applied, the Engineering Mechanics/ Mechanics is classified as a) Mechanics of solids b) Mechanics of fluids Mechanics of solids (rigid bodies) further classified in two groups: 1 Resolution of Coplanar Forces

Statics: It is a branch of Mechanics which deals with the studies of the bodies or rigid bodies in equilibrium under the action of external forces. Dynamics: It is a branch of Mechanics which deals with the studies of the bodies or rigid bodies in motion. Dynamics has two parts: Kinematics b) Kinetics Kinematics: The study of the body in motion, when the forces which cause the motion are not considered, is called as Kinematics. Kinetics: The study of the body in motion, when the forces which cause the motion are considered, is called as Kinetics.

SI system of Units: It is an internal system of units SI system of Units: It is an internal system of units. It is universally approved and accepted. It is adopted by large number of countries. System: Measuring systems are adopted for the measurement of physical quantities. Unit/Quantity: It is standard for the measurement of physical quantities.

Basic Unit/ Fundamental units/ Basic quantities: Basic quantities/ Basic Unit: The quantities which do not depend upon other quantities for their measurement is known as basic quantities and their corresponding units are known as the basic units. Eg. Length, Mass, Time, Temperature, Electric current, plane angle etc. Derived quantities/ Derived Unit: The quantities which depend upon one or more basic quantities for their measurement is known as derived quantities and their corresponding units are known as the derived units. Eg. Velocity, Acceleration, Force, Work & Energy, Power etc. Body: A body is defined as an object, which cannot retain its shape and size under the action of a force system. Rigid body: A rigid body is defined as a body, which can retain its shape and size even if subjected to external forces. In practice, there is small deformation of body under the action of a force system. Such deformation is neglected and the body is treated as rigid body.

Particle: A particle is defined as a very small amount of matter, which may be assumed to occupy a single point in space. Practically, any object having very small dimensions as compared to its range of motion can be called as a Particle. Eg. Stars, planets, Rockets, Bullets etc. Scalar quantity: It is the quantity having magnitude only. It has no direction. Eg. Mass, speed etc.

Vector quantity: It is the quantity having magnitude and direction Vector quantity: It is the quantity having magnitude and direction. It is shown by vector. Eg. Force, Velocity, acceleration etc. Force: The external agency, which tends to change the state of a body is known as force. A force is completely defined only when the following four characteristics are specified: - Magnitude - Point of application - Line of action - Direction A force (F) is a vector quantity which is represented graphically by a straight line say ‘ab’ whose length is proportional to the magnitude of force and the arrow shows the direction of force ‘ab’ . Unit of force is Newton (N). Force System: When several forces of different magnitude and direction act upon a body, they constitute a system of forces. Main types of force systems are as follows: 1) Coplanar Force System: Lines of action of all the forces lie in the same plane in this system.

Collinear Force System: Lines of action of all the forces lie in the same straight line in this system .3) Concurrent Force System: Lines of action of all the forces meet at a point in this system. The concurrent forces may not be collinear or coplanar. 4) Parallel Force System: Lines of action of all the forces are in parallel as shown in Fig. (D) above. 5) Non- Coplanar Force System: Lines of action of all the forces does not lie in the same plane . 6) Non- Concurrent Force System: Lines of action of all the forces do not meet at a point in this system .

7) Non-Parallel Force System: Lines of action of all the forces are not in parallel . 8) Coplanar Concurrent Force System: Lines of action of all the forces lie in the same plane and meet at a point. 9) Coplanar Non-Concurrent Force System: Lines of action of all the forces lie in the same plane, but do not meet at a a point.