fundamental concepts

FUNDAMENTAL CONCEPTS

At the outset, certain fundamental concepts have to understood before starting the study of Mechanics of Machines. Table 0.2 summarises few such concepts.

Table 0.2. Fundamental concepts

1. Space:

• Space is a region, which extends in all directions and contains everything in it.

• Reference system: The position of a body in space is determined with respect to a reference system.

• Examples:

(i) The position of aircraft in space is determined with respect to earth.

(ii) The position of an object on the earth surface is determined with reference to a fixed or immovable station on the earth by taking linear and angular measurements.

2. Time: Time is a measure of the succession of events.

3. Matter: Any substance which occupies space is called matter. It is made up of atoms.

4. Body: Any matter that is bounded by a closed surface is called a body.

5. Rigid body: A rigid body is that which does not change its shape or size when subjected to external forces.

6. Deformable body: A deformable body is that which changes its shape or size when subjected to external forces.

7. Mass: The mass of a body is the quantity of matter it contains. Mass of a body does not vary with the location and orientation of the body.

8. Particle: A body of negligible dimension is called a particle. A particle occupies no space i.e., it has not size, but has a definite mass concentrated at a point.

9. Inertia: The resistance offered by a body to any change of its state of motion or rest is called inertia.

10. Solid: A substance possessing a definite shape and a definite volume is called a solid.

11. Force:

• Force is a pull or push, which acting on a body changes or tends to change, the state of rest or of uniform motion of the body.

• A force is completely characterized by its point of application, its magnitude and direction.

12. Forced system: When a number of forces act on a body, they are called a force system or a system of forces.

13. Weight:

• The weight of a body is the force with which the earth attracts the body towards its centre.

• By Newton's second law of motion, the weight of a body is given by

where

m = Mass of the body, in kg, and

g = Acceleration due to gravity i.e., 9.81 m/s².

• Since the value of 'g' is known to vary with the location of the body. Thus the weight of the body varies with the location and orientation of the body.

14. Equilibrium: A body acted upon by a system of forces is said to be in equilibrium, if it either remains in a state of rest or continues to move in a straight line with uniform velocity.

15. Motion: A body is said to be in motion, when it changes its position with respect to a reference system. Thus the relative change in position is called motion. Motion involves both space and time.

16. Trajectory:

• The motion of any body takes place along a definite path with respect to a reference system. The path followed by a body during its motion is called its trajectory, which may be a straight line or curve.

• If the path is a straight line, the motion is said to be rectilinear. In case it is a curve, the motion is called curvilinear.