# Term Paper: Mechanics and Dynamics Life

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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.

Predictions regarding the growth of cracks can be inferred with an understanding of the fracture properties of the materials with accurate stress analysis. The principle is further extended to analyze the metal fatigue. Besides the Mechanics of Deformable Materials also studies the Elasticity i.e. stress and strain in three dimensional elastic bodies, the Visco-elasticity in terms of stress proportional to strain and strain rate. This branch also deals with Engineering Materials the properties of the material, the mechanism of deformation the criteria for failure etc. including composite materials. Moreover the Experimental stress Analysis, Non-destructive Evaluation and Failure Analysis and Prevention is also constitute important sphere of study under this branch. The mechanical behavior of the engineering materials and their strength constitute the study of the branch Strength of materials.

The strength of a material is adjudged in three jargons namely, compressive strength, tensile strength and shear strength. The compressive strength…
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