D-Alembert's Principle :
Consider arigid body acted upon by a system of forces. The system may be reduced to a single resultant force (P) acting on the body whose magnitude is given by the product of the mass of body (m) and the linear acceleration (a) of the centre of mass of the body.
Newton's Laws of Motion
1) Newton's first law of motion. It states that everybody continues in the state of rest or of uniform motion, in a sraight line, wnless it is acted upon by some external force.
2) Newton's second law of motion. It states that the rate of change of momentum is directlyr popotional to the inmpressed force, and takes place in the same direction, in which the force acts
3)Newton s third law of motion. It states that to every action, there is always an equal and opposite resction
Laws of Static Friction :
Following are the laws of static friction:
1)The force of friction always acts in a direction, opposite to that in which the body tends to move
2)The magnitude of force of friction is exactly equal to the force, which tends the body to move
3)The magnitude of the limiting friction bears a constant ratio to the normal reaction between the two surfaces.
4)The force of friction is independent of the area of contact between the two surfaces.
5)The force of friction depends upon the roughness of the surfaces.
Laws of Dynamic or Kinetic Friction :
Following are the laws of dynamic or kinetic friction:
1) The force of friction always acts in a direction, opposite to that in which the body tends to move.
2) The magnitude of the kinetic friction bears a constant ratio to the normal reaction betweenh the two surfaces.
3) For moderate speeds, the force of friction remains constant. But it decreases slightly with the increase of speed.
Friction :
A force acting in the opposite direction to the motion of the body is called force offriction simply friction. It is of the following two types:
1. Static friction; and
2. Dynamic friction.
Static friction :
The friction, experienced by a body, when at rest, is known as static friction
Dynamic friction :
The friction experienced by a body, when in motion, is called dynamic friction. It is also call kinetic friction. It is of the following two types:
(a) Sliding friction; and
(b) Rolling friction.
Sliding friction :
The friction, experienced by a body, when it slides over another body, is known as sliding friction
Rolling friction :
The friction experienced by a body, when balls or rollers are interposed a surfaces known as rolling friction.
Moment of a Force :
It is the turning effect produced by a force, on the body, on which it acts. The moment of a force is equal to the product of the force and the perpendicular distance of the point, about which the moment is required and the line of action of the force.
Lami's Theorem :
It states that if three coplaner forces acting at a point be in equilibrium then each force is proportional to the sine of the angle betwee the other two forces.
System of Forces:
When two or more than two forces act on a body, they are said to form a system of forces
Following are the various system of forces:
Coplaner forces :
The forces, whose lines of action lie on the same plane are known as coplaner forces.
Concurrent forces :
The forces, which meet at one point, are known as concurrent forces.
Coplaner concurrent forces :
The forces, which meet at one point and their lines of action lies on the same plane, are called coplaner concurrent forces.
Coplaner non-concurrent forces :
The forces, which do not meet at one point but their lines action lie on the same plane, are known a coplaner non-concurrent forces.
Non-coplaner concurrent forces :
The forces, which meet at one point but their lines of action do not lie on the same plane are known as non-coplaner concurrent forces.
Non- coplaner non-concurrent forces :
The forces, which do not meet at one point and their lines of actions do not lie on the same plane are called non-coplaner non-concurrent forces.
Resultant Force :
It is a single force which produces the same effect as produced by all the given forces actung on a body. The resultant force may be determined by the following three laws of forces
Parallelogram law of forces:
It states that if two forces, acting simultaneously on a particle be represented in magnitude and direction by the two adjacent sides of a parallelogram, then the result may be represented in magnitude an direction by the diagonal of a parallelogram which pass through their points of intersection
Triangle law of forces:
It states that if two forces, acting simultaneously on a particle,be representing magnitude and direction by the two sides of a triangle taken in order, then their resultant may be represented in magnitude and direction by the third side of the triangle taken opposite order
Polygon law of forces:
It states that if a number of forces, acting simultaneously on a particle,be represented in magnitude and direction by 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 opposite order.
Introduction:
The Engineering Mechanics is that branch of Engineering-science which deals with the principleof mechanics along with their applications to engineering problems.
It is sub-divided into following two main groups:
(b) Dynamics
(a) Statics
Statics
The Statics is that branch of Engineering Mechanics which deals with the forces and their,effect while acting upon the bodies at rest.
Dynamics:
The Dynamics is that branch of Engineering Mechanics which deals with the forces and their,effects while acting upon the bodies in motion.
It is further sub-divided into the following two
i) Kinetics, and (ii) Kinematics
Kinetics :
The Kinetics is that branch of Dynamics, which deals with the bodies in motion due to the application of force
Kinematics:
The Kinematics is that branch of Dynamics which deals with the bodies in motion without taking into account the forces which are responsible for the motion.
