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Rigid-body Mechanics

Principle

Statics: deals with equilibrium of bodies under action of forces (bodies may be either at rest or move with a constant velocity).

Theory

Rigid-body Mechanics •

Dynamics: deals with motion of bodies (accelerated motion) Mechanics: Fundamental Concepts Length (Space): needed to locate position of a point in space, & describe size of the physical system  Distances, Geometric Properties Time: measure of succession of events  basic quantity in Dynamics Mass: quantity of matter in a body  measure of inertia of a body (its resistance to change in velocity) Force: represents the action of one body on another  characterized by its magnitude, direction of its action, and its point of application  Force is a Vector quantity. Mechanics: Fundamental Concepts Newtonian Mechanics Length,


Time, and Mass are absolute concepts independent of each other Force is a derived concept not independent of the other fundamental concepts. Force acting on a body is related to the mass of the body and the variation of its velocity with time. Force can also occur between bodies that are physically separated (Ex: gravitational, electrical, and magnetic forces) Mechanics: Fundamental Concepts Remember:

• Mass is a property of matter that does not change from one location to another.

ʉۢ Weight refers to the gravitational attraction of the earth on a body or quantity of mass. Its magnitude depends upon the elevation at which the mass is located

• Weight of a body is the gravitational force acting on it. Mechanics: Idealizations To simplify application of the theory Particle: A body with mass but with dimensions that can be neglected Size of earth is insignificant compared to the size of its orbit. Earth can be modeled as a particle when studying its orbital motion Mechanics: Idealizations Rigid Body: A combination of large number of particles in which all particles remain at a fixed distance (practically) from one another before and after applying a load. Material properties of a rigid body are not required to be considered when analyzing the forces acting on the body. In most cases, actual deformations occurring in structures, machines, mechanisms, etc. are relatively small, and rigid body assumption is suitable for analysis Mechanics: Idealizations Concentrated Force: Effect of a loading which is assumed to act at a point (CG) on a body.

• Provided the area over which the load is applied is very small compared to the overall size of the body. Ex: Contact Force between a wheel and ground. 40 kN 160 kN Mechanics: Newton’s Three Laws of Motion First Law: A particle originally at rest, or moving in a straight line with constant velocity, tends to remain in this state provided the particle is not subjected to an unbalanced force. First law contains the principle of the equilibrium of forces  main topic of concern in Statics Basis of formulation of rigid body mechanics. Mechanics: Newton’s Three Laws of Motion Second Law: A particle of mass “m” acted upon by an unbalanced force “F” experiences an acceleration “a” that has the same direction as the force and a magnitude that is directly proportional to the force. m F = ma Second Law forms the basis for most of the analysis in Dynamics Mechanics: Newton’s Three Laws of Motion Third law is basic to our understanding of Force  Forces always occur in pairs of equal and opposite forces. Third Law: The mutual forces of action and reaction between two particles are equal, opposite, and collinear. Mechanics: Newton’s Law of Gravitational Attraction 

Conclusion

F = mutual force of attraction between two particles G = universal constant of gravitation Experiments  G = 6.673x10-11 m3/(kg.s2) Rotation of Earth is not taken into account m1, m2 = masses of two particles r = distance between two particles 2 1 2 r m m F = G Weight of a body (gravitational force acting on a body) is required to be computed in Statics as well as Dynamics. This law governs the gravitational attraction between any two particles. Gravitational Attraction of the Earth 2 r mM W G e = W = mg Weight of a Body: If a particle is located at or near the surface of the earth, the only significant gravitational force is that between the earth and the particle Let g = G Me /r 2 = acceleration due to gravity 

Published Date

05 Mar, 2018

BY- Sandeep singh

DE Electronics & Communications Training Program