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What is theoretical mechanics?
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The progress of technology confronts the engineer with a wide variety of problems connected with structural design (buildings, bridges, canals, dams etc.), the design, manufacture and operation of various machines, motors, and means of locomotion, such as automobiles, steam engines, ships, aircraft, rockets and spaceships. Despite the diversity of problems that arise, their solution, at least in part, is based on certain principles common to all of them, namely, the laws governing the motion and equilibrium of material bodies. The science which treats of general laws of motion and equilibrium of material bodies and of the resulting mutual interactions is called theoretical or general mechanics. Theoretical mechanics constitutes one of the scientific bedrocks of modern engineering. Theoretical mechanics treats of general laws of motion and interaction of material bodies, i.e. laws which can be applied equally, for example, to the earth’s motion around the sun or to the flight of rocket or an artillery projectile. Other branches of mechanics cover a variety of general and specialized engineering disciplines treating of the design and calculation of specific structures, motors and other machines and mechanisms or their parts. All these disciplines are based on the laws and methods of theoretical mechanics.
By motion in mechanics we mean mechanical motion, i.e., any change in the relative positions of material bodies in space which occurs in the course of time. By mechanical interaction between bodies is meant such reciprocal action which changes or trends to change the state of motion or shape of the bodies involved (deformation). The physical measure of such mechanical interaction is called force. According to the nature of the problems treated, mechanics is divided into statics, kinematics and dynamics. Statics studies the forces and the conditions of equilibrium of material bodies subjected to the action of forces. Kinematics deals with the general geometrical properties of the motion of bodies. Dynamics studies the laws of motion of material bodies under the action of forces. According to the nature of objects under study, theoretical mechanics is subdivided into: (a) mechanics of a particle, i.e., of a body whose dimensions can be neglected in studying its motion or equilibrium, and systems of particles; (b) mechanics of a rigid body, i.e. a body whose deformation can be neglected in studying its motion or equilibrium; (c) mechanics of bodies of variable mass (i.e. bodies whose mass changes with time, due to the change in the number of particles constituting the body); (d) mechanics of deformable bodies (the theory of plasticity and elasticity); (e) mechanics of liquids (fluid mechanics); (f) mechanics of gases (aerodynamics). The general course of theoretical mechanics conventionally treats of the mechanics of particles and rigid bodies and general laws of motion of particles. Theoretical mechanics is one of the natural science and is based on laws derived from experience that reflect a specific class of natural phenomena associated with the motion of material bodies.
Comprehension check. Ex.1. Answer the following questions: 1. What does general mechanics treat of? 2. What is motion? 3. What is mechanical interaction? 4. How many parts is mechanics divided into? 5. What does statics study? 6. What does kinematics deal with? 7. What is the subject of dynamics?
Ex.2. Say whether the following statements are True or False. 1. Mechanics is divided into statics and dynamics. 2. Statics deals with the general geometrical properties of the motion of bodies. 3. Mechanics of a particle is the mechanics of a body whose dimensions can be neglected. 4. Mass of a body changes with time due to the change in the number of particles constituting the body. 5. Theoretical mechanics is based on laws derived from experience.
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