141EE0402-Engineering Mechanics

UNIT- I : Basics and Statics of Particles

Force

•Force is an agent which produces or tends to produce,destroys or tends to destroy the motion of body orparticles.

•Vector Quantity , Unit : Newton

Forms and Characteristics of Forces

It has four characteristics I. DirectionII. MagnitudeIII. Point on which it actsIV. Line of action

Line of Action of force

•The line of action of a force f is a geometricrepresentation of how the force is applied.

• It is the line through the point at which the force isapplied in the same direction as the vector f→.

System of forces

When two are or more forces acts act on abody, they are called system of forces.1. Coplanar Force system – 2D and Non – Coplanar

system – 3D

2. Concurrent and Non – Concurrent Force system

3. Collinear and Non- Collinear Force system

4. Parallel – Like and Unlike

Coplanar Force System – 2D

Non- Coplanar Force System – 3D

Concurrent and Non – Concurrent Force system

Concurrent Forces Non- Concurrent Forces

Collinear and Non- Collinear Force system

Collinear Forces Non – Collinear Forces

Parallel Force system

Examples

Just Identify Force system

Particle

•A Particle may be defined as a portion of a matterwhich is infinitely small in size in all directions.

• It has no size, but it has mass

•Example : For astronomical Calculation, the earthmay be assumed to be particle.

•For mathematical description, a particle denotes abody in which all the materials are concentrated atpoint.

Resultant Force

• If a number of forces acting on a particlesimultaneously are replaced by a single force, whichcould produce the same effect as produced by thegiven forces, that single force is called ResultantForce.

• It is an equivalent force of all the given forces.

Example:

Example

•Find the resultant of force system shown in figure

Procedure

• Step 1 : Find algebraic sum of the horizontal components

• Step 2 : Find algebraic sum of vertical components

Cont’d

• Step 3 : Find the magnitude of Resultant force

• Step 4: Find the direction of Resultant Force

Example:

Three coplanar concurrent forces are acting at apoint as shown in figure. Determine the resultant inmagnitude and direction.

Cont’d

Four coplanar concurrent forces are acting at a pointas shown in figure. Determine the resultant inmagnitude and direction.

Equilibrium of Particle in 2D

• If the resultant of a number of forces acting on aparticle is zero, the particle is in equilibrium. The setof forces, where resultant is zero, are calledEquilibrium Forces.

•Equilibrant: (E) is equal to the resultant force (R) inmagnitude and direction, collinear but opposite innature.

Conditions of Equilibrium

Example

Free body Diagram (FBD)

• In equilibrium analysis of structures/machines. It isnecessary to consider all the forces acting on thebody and exclude all the forces which are notdirectly applied to it.

•The problem becomes much simple if each body isconsidered in isolation. Such a body which has beenso separated or isolated from the surroundingbodies is called free body

•The sketch showing all the forces (both external andreaction) and moments acting on the body is calledas the free body diagram

Example - FBD

Action and Reaction

Example

Example 2

Resultant and Equilibrium of forces in 3D (Non-Coplanar)

•Mainly used to convert force magnitude to forcevector by multiply with unit vector.

•Methods used to express force as Cartesian vector:Three angles and force magnitude Coordinates and force magnitude

3D –Cartesian Coordinate system

Type 1: Three angles Given

Type 2: Coordinates and Force Magnitude

• Find coordinates with respect to origin

•Position vector = OP = (PO- OO)

•Unit vector = OP / mag of OP

•Force vector = Force magnitude x Unit vector

Example

Find coordinates with respect to originPosition vector = OP = (PO- OO)Unit vector = OP / mag of OPForce vector = Force magnitude x Unit vector

Cont’d

Cont’d

2D- Concurrent Force System

•Resultant of two concurrent forces

• It is calculated by Parallelogram law of forces

2D – Equilibrium • Lamis Theorem