Mechanics

 

Mechanics is that branch of science which deals with the bodies when they are at rest or in motion.When the bodies are at rest, the branch of mechanics is known as Statics and if the bodies are in motion, the branch of mechanics is known as ‘Dynamics. Dynamics is further divided into two parts namely (i) Kinematics and (ii) Kinetics. Kinematics is the branch of mechanics which deals with the study of rigid bodies in motion without considering the forces, which cause motion. Kineticsis the branch of mechanics which deals with the study of rigid bodies in motion, taking into consideration the forces.   1. Force is that action which moves or tends to move a body. The units of force are (i) newton (N) in S.I. units, and (ii) dyne in C.G.S. units. 2. Newton is a force which acts on a mass of one kilogram and produces an acceleration of one metre per second square.   Dyne is a force which acts on a mass of one gram and produces an acceleration of one centimetre per second square. The relation between newton (N) and dyne is given by 1 N = 105 dyne   Force is a vector quantity which means it is having magnitude and direction. A single force which produces the same effect as a number of forces acting together is called the resultant of these forces. If the forces are acting in a straight line, their resultant is equal to the algebraical sum of the forces. If the forces are acting in different directions, their resultant is obtained by:   (a) Law of triangle of forces, (b) Law of parallelogram of forces, and (c) Law of polygon of forces.   (a) Law of triangle of forces states that if two forces acting on a body are represented in magnitude and direction by the two sides of a triangle taken in order, then their resultant is given by the third side of the triangle taken in the opposite order.    (b) Law of parallelogram of forces states that if two forces, acting at a point of a body, be represented in magnitude and direction by the two adjacent sides of a parallelogram, their resultant may be represented in magnitude and direction by the diagonal of the parallelogram, which passes through their point of intersection. (c) Law of polygon of forces states that if a number of forces acting on a point of a body are represented in magnitude and direction by the sides of a polygon, taken in order, then their resultant is represented in magnitude and direction by the closing side of the polygon taken in the opposite direction. Conversely, if any number of forces acting at a point can be represented in magnitude and direction by the sides of a polygon taken in order, the forces are in equilibrium.   3. The forces acting on a body may be: (a) Coplanar, (b) Non-coplanar, (c) Concurrent, (d) Non-concurrent, (e) Coplanar concurrent, and ( f ) Collinear etc.   4. Coplanar forces are those forces, whose lines of action lie on the same plane. Non-coplanar forces are those forces whose lines of action do not lie in the same plane. Concurrent forces are those forces, which meet at a point and if the forces do not meet at a point, the forces are called non-concurrent. If the lines of action of the forces lie in the same plane and they meet at a point, those forces are called coplanar concurrent forces. Collinear forces are those forces, whose lines of action lie on the same line.   5. Lami’s theorem states that if three coplanar forces acting at a point be in equilibrium,then each force is proportional to the sine of the angle between the other two.   6. Moment of a force about a point is the product of the magnitude of the force and perpendicular distance of its line of action from the point.   7. When a number of forces acting on a rigid body are in equilibrium, then the sum of moments of the forces which tend to turn the body in one direction about any given axis is equal to the sum of the moments of the forces which tend to turn the body in the opposite direction about the same axis. This is known as Principle of Moments.   8. When a number of coplanar forces are acting on a particle, the algebraic sum of the moments of all the forces about any point is equal to the moment of their resultant force about the same point. This is known as Varignon’s theorem of moments.   9. A system of coplanar forces will be in equilibrium if the sum of the resolved components of the forces of the system in any two perpendicular directions is zero separately and the sum of the moments of the forces about a point in their plane is zero. Conversely, if a system of coplanar forces is in equilibrium, the sum of the resolved components of the forces of the system in any two perpendicular directions must be separately zero and also the algebraic sum of their moments about any point in their plane must be zero. 10. A couple consists of two equal, opposite and parallel forces acting on a body.   The perpendicular distance between the two parallel forces is called the arm of the couple. The moment of a couple is equal to the product of the magnitude of one of the forces and the sum of the couple.   The couple tends to rotate a body. If two couples are acting on a body, the body will be in equilibrium if both the couples have equal moments, are acting in the same plane and their directions of rotation are opposite Written by : Sarwaidi. ST.MT