1.1 What is mechanics?
Mechanics may be defined as the science which defines and predicts the action of forces on bodies. Under the influence of forces, bodies may may either be in motion or at rest, relative to assigned system or frame of reference. The part of mechanics which deals with the motion of solid body is called dynamics, and that concerned with solids at rest is called statics. Dynamics has two distinct parts – kinematics, which is the study of motion without reference to the forces which cause motion, and kinetics which relates to the action of forces on bodies to their resulting motions. The corresponding parts of the subject dealing with fluids are known as hydrodynamics and hydrostatics respectively.
Mechanics as applied science, purposes to explain and predict physical phenomena and thus lay the foundation for engineering applications.
1.2 Basic Concepts and Principles:
The basic concepts used in mechanics are space, time, mass, force, particle and rigid body.
Space is the geometric region occupied by bodies. The concept is associated with the motion of the position of a point. The position of the point may be defined by three lengths measured from a certain reference point, origin in three given directions. These lengths are known as the co-ordinates of the point. To define an event, it is not sufficient to indicate it’s position in space. The time of the event should also be given.
Time is a measure of the succession of events and is considered an absolute quantity.
Mass is the quantity measure of the inertia or resistance to change in motion of a body. Two bodies of the same mass, for example, will be attracted by the earth in the same manner, they will also offer resistance to Change in translational motion. Mass is also the property which gives rise to gravitational attraction.
Force is a representation of the action of one body on another. It may be exerted by actual contact or at a distance, as is the case of gravitational forces and magnetic forces. A force has a point of application, magnitude, direction and is represented by a vector.
In Newtonian mechanics, space, time and mass are absolute concepts, independent of each other. The principle of Newtonian mechanics indicates that the resultant force acting on a body is related to the mass of the body and to the manner in which the velocity varies with time.
1 . A particle is a very small amount of matter which may be assembled to occupy a single point in space. Also when the dimensions of a body are irrelevant to the description of its motion or to the action of forces acting on it, the body may be treated as a particle.
2. A rigid body is a combination of a large number of particles occupying fixed positions with respect to each other.
The study of mechanics rests on the following fundamental principles:
a). The parallelogram law for the addition of forces which states that two Force acting on a particle may be replaced by a single force, called resultant, obtained by drawing the diagonal of the parallelogram which has sides equal to the given forces.
b). The principle of Transmissibility states that the conditions of equilibrium or of motion of a rigid body will remain unchanged if a force acting at a given point of the rigid body is replaced by a force of the same magnitude and the same direction but acting at a different point, provided that the two forces have the same line of action.
C). Newton’s Laws: Newton’s three laws are stated as follows.
Law 1: Everybody continues in a state of rest or uniform motion in a straight line except there is unbalanced force acting on it.
Law 2: The acceleration of a particle is proportional to the resultant force acting on it and is in the direction of this force.
Law 3: To every action there is always an equal and opposite reaction, or, the mutual actions of any two bodies are always equal and oppositely directed.
Newton’s second law forms the basis for most of the analysis in dynamics. For a particle of mass m subjected to a resultant force F, the law may be states as F = ma..
Where a is the resulting acceleration measured in a non accelerating frame of reference.
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