Mechanics and dynamics in physical systems

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 rotate of spin with a particular application of force. Torque is the attribute of a force that causes rotation of the object. The product of the perpendicular distance between the line of the force and the axis of rotation gives the magnitude of torque. Friction arises out of opposing torque that resists the motion. The frictional forces arise when other forces are applied or the body is already in motion. The friction is normally seen to be a negative force and seems to be undesirable. However its usefulness cannot be denied in respect of car brakes to slow down a car by its brake. The application of Laws of Mechanics assumes isolation of the body from its extraneous forces and influences and takes into consideration only the forces acting on it.

Scientists take into consideration in most of the cases the center of gravity of the object where actually the entire weight rests rather than the behavior of the entire object. The center of gravity is a point of the object where actually all the forces applied to it act upon. A torque is created when the force is exerted along a line that does not pass through a body's center of gravity. The body is said to be in equilibrium when it is in complete rest as a result of balance between all forces tending to move the center of gravity and all torques. A body is said to be in stable equilibrium, if it tends to return to its original position when a torque is applied. Similarly it is said to be in unstable equilibrium when the object turns to a new position after the torque ceases to act. If the body comes to rest when the torque is removed wherever it may be, the body is said to be in neutral equilibrium. [Introduction to Physics]

The Dynamics is that branch of physical science and sub-division of Mechanics related to the motion of the objects with the influence of force, mass, momentum, energy etc. Galileo Galilei by experimenting with a smooth ball rolling down an inclined plane derived the law of motion for falling bodies which laid the foundation of Dynamics in 16th Century. Only he could, at first, realize that force is the cause of changes in the velocity of a body. This fact led Sir Isaac Newton to propound the second law of motion in 17th century. Dynamics has two divisions Kinematics and Kinetics. The Kinematics deals with the geometrically possible motion in terms of velocity, position and acceleration of a body without consideration of the causes and effects like forces, torques and masses.

The Kinematics describes the spatial position of bodies or systems of material particles, the rate of movement of particles, and the rate of change of their velocity. Disregarding the causative forces motions are possible only with the particles having constrained motion that moves on a predetermined path. The forces influence the shape of path for unconstrained motion. It is possible to express positions of a particle moving on a straight line in terms of time with the help of a mathematical formula. Two or three dimensional considerations are necessary to describe the positions of a particle moving on a curved path. Kinetics deals with the effect of forces and torques on the motion of bodies having mass.

The principles of classical mechanics were involved in creation of simple machines, which traces their origin to the antiquity and formed the basis for many components of modern machinery. The lever, the wheel and axle, the inclined plane, the screw, and the rope and pulley system are the common machines developed involving the basic principles of classical mechanics that is exertion of force over certain distances for movement of weights overcoming resistances. Lever is a simple machine, with a stiff bar that rotates about a fixed point known as fulcrum (F) used to lift a weight (R) of larger magnitude with an effort (E) of comparative smaller magnitude. Exertion of effort at point E. lifts weight at point R. overcoming the resistance. The length between effort and fulcrum (E-F) is called the effort arm and the length between the fulcrum and the resistance (F-R) is called as the resistance arm.

The lever is categorized into three groups depending upon the position of effort, fulcrum and resistance along the lever bar. The first class lever position the fulcrum in between the effort and resistance as is in a pair of scissors. The resistance is between fulcrum and the effort, in the second class levers as in a wheelbarrow. The arm bending at elbow with a view to lifting a weight is an example of third class lever which positions the effort between fulcrum and the resistance. The efficiency of the lever depends upon the distance through which points E. And R. move while turning around the fulcrum. This constitutes the Law of Ideal Machines which in its crude form states the efforts applied multiplied by the effort arm is equal to the resistance multiplied by resistance arm. The resistance divided by the effort gives the mechanical advantage of levers. According to the Law, mechanical advantage is favorable when the effort arm is more than resistance arm.

Next to lever a rope and pulley system is another simple machine. Pulling a rope over a single fixed pulley hardly generates any mechanical advantage. However, a single rope over a series of pulleys generates mechanical advantage by replacing the lever arms with wheels. The mechanical advantage increases with number of strands running through the moving pulleys. The mechanical advantage in a pulley system is calculated by isolating the pulley to which the weight is attached and counting the number of strands of rope that leads to the isolated pulley. Inclined plane is another simple machine mechanical advantage of which is seen in case of locomotive pushing freight cars up an incline of height than to hoist it straight. Mechanical advantage here is equivalent to the ratio of the length of the plane to its height. A wedge is formed by setting to inclined planes back to back. The resistance other than weight can be overcome by the wedge. Screws are seen as inclined plane wrapped around a cylinder. Its application is seen in vise where jaws are drawn together to hold materials tightly. Gears with some variation of screw also provide mechanical advantage when they are of varied sizes. [Introduction to Physics]

Engineering mechanics is the branch of Engineering science that provides indispensable tools and theories for more applied engineering sciences. The Engineering Mechanics is concerned with the influences of forces and torques on particles, rigid bodies or deformable media. The modern Engineering Mechanics traces its origin into the classical laws of motions. Timoshenko is said to be the father of modern engineering mechanics who brought into light the applications of the laws of motions to its sphere. The Engineering Mechanics in this line has been subdivided into several branches like static's, dynamics, strength of materials, Fluid mechanics, mechanics of deformable bodies etc. Importing the idea of equilibrium of the bodies at rest the static's deals with the algebra of vectors, equilibrium, and equivalency of force/torque systems free body diagram etc. It also studies the concepts of friction, machines and trusses.

The part Dynamics in Engineering Mechanics deals with the study of acceleration, velocity and displacement of the bodies resulting out of the effects of un-equilibrated force and torque systems. It also includes the study on harmonic motion, caused by a restoring force, linearly dependent on displacement. This is the basis for explaining vibrations. The applications of Newtonian Laws of motions and energy principles are prominent on this part of the study. The Mechanics of Deformable Materials is concerned with stress- the internal distribution of force per unit area, Strain -- the local normalized deformation and the response of the materials in terms of strain, strain rate and temperature to the stress. The Mechanics of Deformable Materials studies the strength of materials in terms of stretching, bending, and twisting of long thin, elastic bodies, Hooke's law yielding and fracture.