Mechanics and Dynamics Term Paper

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Mechanics and Dynamics

Life without motion is better explained as death. A living being is said to be having life only when the walls of the heart engage in pumping the blood, when the blood circulates through the entire body, when nerves impulse electrically from brain to toe, lungs move to bring oxygen, food transports through the stomach and intestines, when the iris expands and contract, when the eyeball rotates, etc. Not only in the living beings, the riddles of the non-living items like recoiling of a fired gun, acceleration of an automobile, action of a spinning top, the motion of a space rocket can also be broken down in terms of the analysis of motion.

Dynamics" is a branch of study of motions and "Mechanics" contrary to the general idea of referring to people in uniforms with name over his pocket and having a tool box in his hand, refers to a branch of study that analyses motions in relation to objects. The Mechanics as a branch of study deals with the influence of forces acting on bodies and dynamic responses of bodies to the imposition of those forces. The principles underlying mechanics apply alike to all the bodies large or small, solid or fuel, stationery at Earth's surface or traveling in outer space. The roots of engineering mechanics trace back its origin to the likes of Archimedes, Galileo, and Sir Isaac Newton etc. Mechanics is said to be the first exact science that has ever developed. It successfully accounted for the quantitative details of the motions of the celestial bodies like Moon, the Earth etc. even in its earliest form.

The field of mechanics broadly has three branches- Statics that studies the behavior of bodies at rest or if in motion but with constant velocity, Kinematics describing possible motions of the bodies and Kinematics that explain and predict the motion that occurs at a given situation. Specialized branches have been evolved in order to describe further subdivision. The dynamics of liquid and gases are described by Fluid Mechanics, the high speed flow of gases is explained by Gas Dynamics, the stress and deformations experienced by bodies with application of forces are described by Mechanics of materials-Hydraulics and so on to mention a few.

It may not be an exaggeration to say that engineers must start with the classical laws of mechanics in order to have a better understanding of the forces that act constantly to move and deform the structures built by them and to provide proper support like arches, buttresses and trusses etc., to counter act those forces and enable the structure to stand against. The application of the classical principles of mechanics has been observed distinctly in three broad realms of phenomena. They are the accurate calculation of the motions of celestial bodies, uniform applicability of the principles in earthly objectives irrespective of their sizes, and finally, its application to study the behavior of matter and electromagnetic radiation on the atomic and sub-atomic scale. [Statics and Mehcanics]

Classical mechanics is the study of motion of bodies under the influence of forces or the study of static's that is a state of equilibrium of bodies with all the forces exerted is balanced. The classical mechanics is an elaboration and application of basic postulates propounded by Sir Isaac Newton during the 17th century, better known as "Laws of Newton." The classical mechanics is said to revolve around three basic concepts of force, mass and motion. The amount of matter in body is Mass. The weight of body, measured in scales is the pull of gravity upon matter. The unit of measurement of mass is kilograms (KG) and force is Newton (N) in metric scheme. The rate of the change in the velocity of a body refers to acceleration. Acceleration is both slowing down and speeding up thus includes the common term deceleration also The mass is, thus, a measurement of that attribute of a body which puts a resistance to the changes in its state of motion. Forces bring a change in the state of motion of bodies to which they are applied. The interaction and counteraction of these effects forms the basic theme of classical mechanics. In addition to these three Newton's laws encompass three more concepts energy, momentum and angular momentum. The importance of these three lies in the fact that the in aggregate the total amount remains constant. The basic principles of mechanics were reduced to three laws by Newton with the help these concepts.

The First Law of Newton envisages that unless compelled by forces impressed upon, every body continues to be in a state of rest or of uniform motion in a straight line. The first law thus envisages that the moving body is at rest, as long as its motion continues at the same speed and in the same direction. It is due to this that the celestial bodies keep on flying through the empty spaces forever; in absence of any force compelling them to change their motion. According to the Second Law of Newton the change of motion of an object is proportional to the force impressed and is made in the direction of the straight line in which the force is impressed. The second law thus envisages the net force acting on a body is equal to the product of the body's mass times the resulting acceleration. Using letters for force mass and acceleration it can be stated as: f = ma. This principle thus makes it clear that an impressed force compels a change in the body's motion i.e. both speed and direction and the direction is always towards the direction of the acting force.

The Third Law of Newton explains that to every action there is always an opposed and equal reaction; or, the mutual actions of two bodies upon each other are always equal and directed to contrary parts. The bootstrap pulls down on him as he pulls up on his own bootstrap. At this moment the action and reactions are counter balanced due to their equality and opposite in nature. The Jet propulsion works under this principle. The first law of Newton is said to be a modification of the principle of inertia propounded by Galileo. As per the second law, momentum is the product of mass of a particle and velocity. The rate of the change in momentum is proportional to the force acting on the particle. Thus it envisages that assuming a state of constant force acting on a particle for a given period of time, the change in momentum is proportional to the product of fore and the time interval.

Conversely, the amount of time required for a constant force to bring a particle to rest is its momentum. The sum of the momenta of each particle in the body is the momentum of a rigid body. Assuming a rotating body in a plane, the momentum of each particle has a moment about any point in the plan. All these moments of momenta altogether constitute the angular momentum of the body about the point. The angular momentum is equal to the product of the moment of inertia of the body and the angular velocity of the body. The rate of change of the angular momentum of a body in relation to a point is equal to the moment of the forces applied at the point. The Third Law explains that no net force as a whole is produced out of interaction of two bodies. There is a pair of equal and opposite forces in terms of action and reactions acting on each other. Irrespective of the state of the body- rest, uniform motion or in accelerated motion, the application of the Third Law is quite visible. In accordance with the second law it can be explained that the body undergoes accelerated motion if it has net force acting on it.

In absence of net force as a result of no forces at all acting on the body or all forces being acted upon are counter balanced by contrary forces, the body is said to be in the state of equilibrium. For instance, a massive object comfortably rests on a table in a state of equilibrium with the counterbalance of the gravitational forces that pulls the object downward by the exertion of an equal and opposite upward force of the table on the object. Forces and velocities are represented as vectors i.e. quantities having specific magnitude of size and strength as well as direction. In this consideration speed is only a magnitude of velocity vector though both are being used interchangeably. The simultaneous application of two forces at a particular point is equal to the same effect as a single equivalent force. Addition of two respective vectors arrives at the magnitude of the resultant force.

Moreover, the same forces may have different effects. The effects of same force depend on their application and on the object, which it is applied to. A body may…[continue]

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