INTRODUCTION
Engineering mechanics is a fundamental branch of physics that deals with the study of motion, forces, and energy. It provides the foundation for understanding and analyzing the behavior of objects and systems in various engineering disciplines. Knowledge of Engineering mechanics is essential for an engineer to plan, design and construction of various types of machine and structure.
The word Mechanics was coined by a greek philosopher Aristotle.
1.1 PARTS OF ENGINEERING MECHANICS :
The subject of Engineering Mechanics is divided into two parts. (a) Static, (b) Dynamic
(a) STATICS : It is the branch of Engineering mechanics, which deals with the forces and their effects, while acting upon the bodies at rest.
(b) DYNAMICS : It is a branch of Engineering mechanics, which deals with the forces and their effects, while acting upon the bodies in motion. It is further subdivided into the two branches, kinetics and kinematics.
(b.i) Kinetics : This branch of dynamics deals with the bodies in motion due to the application of forces.
(b.ii) Kinematics : This branch of dynamics deals with the bodies in motion without taking into account the forces which are responsible for the forces.
Particle: A particle is a body of infinitely small volume and is considered to be concentrated point.
Rigid Body: It is a body which can retain its shape and size, even if subjected to some external forces.
1.2 Force:
Force is an action which changes or maintain the motion of the body. To determine the effect of the force we must know.
1. The magnitude of the force.
2. Line of action of the force.
3. Push or pull force.
4. Acting point of the force.
System of Forces: When two or more forces act on a body, they are called to form a system of forces. Following are the system of forces.
| 1. Coplanar forces: The forces, whose lines of action lie on the same plane, are known as coplanar forces. |
2. Collinear forces: The forces, whose lines of action lie on the same line, are known as collinear forces.  |
| 3. Concurrent forces: The forces, which meet at one point, are known as concurrent forces. The concurrent forces may or may not be collinear. |
| 4. Coplanar Concurrent forces: The forces, which meet at one point and their lines of action also lie on the same plane, are known as coplanar concurrent forces. |
| 5. Coplanar Non-Concurrent forces: The forces, which do not meet at one point, but their lines of action lie on the same plane, are known as coplanar non-concurrent forces. |
| 6. Non-Coplanar Concurrent forces: The forces, which meet at one point, but their lines of action do not lie on the same plane, are known as non-coplanar concurrent forces. |
| 7. Non-Coplanar Non-Concurrent forces: The forces, which do not meet at one point and their lines of action do not lie on the same plane, are called non-coplanar non-concurrent forces. |
1.2.1 RESULTANT FORCE: It is a single force which produces the same effect as produced by all the given forces acting on a body. The resultant force may be determined by the three laws of forces.
- Parallelogram Law of Forces.
- Triangle Law of Forces.
- Polygon Law of Forces.
Parallelogram Law of Forces: The law states that, “if two forces, acting simultaneously at a point, are represented in magnitude and direction by the two adjacent sides of a parallelogram drawn from that point, then their resultant is represented in magnitude and direction by the diagonal of the parallelogram passing through that same point”.
To calculate the magnitude and direction of the resultant force analytically, we use trigonometry. Suppose two forces P and Q act at an angle θ to each other.
1. Magnitude of Resultant (R)
The magnitude of the resultant force is given by:
2. Direction of Resultant (α)
If the resultant force R makes an angle α with the force P, the direction is calculated as:
Method of Resolution of force:
1.4 Triangle Law of Forces: ” If two forces acting simultaneously on a particle are represented in magnitude and direction by two sides of a triangle taken in order, then the third side of the triangle taken in the opposite order represents the resultant force in magnitude and direction. “
Mathematical expression: If two forces F₁ and F₂ act at an angle θ between them, the magnitude of the resultant R is:
The direction (α) of the resultant with respect to F₁ is:
1.5 Polygon Law of Forces: The Polygon Law of Forces states that:
” If a number of forces acting simultaneously on a particle are represented in magnitude and direction by the sides of a polygon taken in order, then the closing side of the polygon taken in the opposite order represents the resultant force in magnitude and direction. “
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