141EE0402-Engineering Mechanics. UNIT- I : Basics and Statics of Particles

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1 141EE0402-Engineering Mechanics UNIT- I : Basics and Statics of Particles

2 Force Force is an agent which produces or tends to produce, destroys or tends to destroy the motion of body or particles. Vector Quantity, Unit : Newton

3 Forms and Characteristics of Forces It has four characteristics I. Direction II. Magnitude III. Point on which it acts IV. Line of action

4 Line of Action of force The line of action of a force f is a geometric representation of how the force is applied. It is the line through the point at which the force is applied in the same direction as the vector f.

5 System of forces When two are or more forces acts act on a body, 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

7 Coplanar Force System 2D

8 Non- Coplanar Force System 3D

9 Concurrent and Non Concurrent Force system Concurrent Forces Non- Concurrent Forces

10 Collinear and Non- Collinear Force system Collinear Forces Non Collinear Forces

11 Parallel Force system

12 Examples

13 Just Identify Force system

14 Particle A Particle may be defined as a portion of a matter which is infinitely small in size in all directions. It has no size, but it has mass Example : For astronomical Calculation, the earth may be assumed to be particle. For mathematical description, a particle denotes a body in which all the materials are concentrated at point.

15 Resultant Force If a number of forces acting on a particle simultaneously are replaced by a single force, which could produce the same effect as produced by the given forces, that single force is called Resultant Force. It is an equivalent force of all the given forces. Example:

16 Example Find the resultant of force system shown in figure

17 Procedure Step 1 : Find algebraic sum of the horizontal components Step 2 : Find algebraic sum of vertical components

18 Cont d Step 3 : Find the magnitude of Resultant force Step 4: Find the direction of Resultant Force

19 Example: Three coplanar concurrent forces are acting at a point as shown in figure. Determine the resultant in magnitude and direction.

20 Cont d Four coplanar concurrent forces are acting at a point as shown in figure. Determine the resultant in magnitude and direction.

21 Equilibrium of Particle in 2D If the resultant of a number of forces acting on a particle is zero, the particle is in equilibrium. The set of forces, where resultant is zero, are called Equilibrium Forces. Equilibrant: (E) is equal to the resultant force (R) in magnitude and direction, collinear but opposite in nature.

22 Conditions of Equilibrium

23 Example

24 Free body Diagram (FBD) In equilibrium analysis of structures/machines. It is necessary to consider all the forces acting on the body and exclude all the forces which are not directly applied to it. The problem becomes much simple if each body is considered in isolation. Such a body which has been so separated or isolated from the surrounding bodies is called free body The sketch showing all the forces (both external and reaction) and moments acting on the body is called as the free body diagram

25 Example - FBD Action and Reaction

27 Example

28 Example 2

29 Resultant and Equilibrium of forces in 3D (Non-Coplanar) Mainly used to convert force magnitude to force vector by multiply with unit vector. Methods used to express force as Cartesian vector: Three angles and force magnitude Coordinates and force magnitude

30 3D Cartesian Coordinate system

31 Type 1: Three angles Given

33 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

34 Example Find coordinates with respect to origin Position vector = OP = (PO- OO) Unit vector = OP / mag of OP Force vector = Force magnitude x Unit vector

35 Cont d

36 Cont d

37 2D- Concurrent Force System Resultant of two concurrent forces It is calculated by Parallelogram law of forces

39 2D Equilibrium Lamis Theorem

TEST-1 MEACHNICAL (MEACHNICS)

1 TEST-1 MEACHNICAL (MEACHNICS) Objective Type Questions:- Q.1 The term force may be defined as an agent t which produces or tends to produce, destroys or tends to destroy motion. a) Agree b) disagree