Introduction of mechanics of solid and coplanar forces
- 2. Engineering Mechanics Mechanics is the branch of science which deals with the state of rest or motion of particles and bodies under the action of forces
- 3. Idealizations In Mechanics Particle: It is an idealized body which may have negligible mass and whose size ad shape can be neglected. Rigid body: A body is said to be rigid if the relative distance between the particles of the body remain same before and after appliction of force
- 4. Deformable body: a body is said to be deformable if its size and shape changes under application of external forces. Continuum: It is defined as an idealized body whose matter is assumed to be totally continuous ,homogenous and non-porous.
- 5. Newton's first law: Every body continues the state of rest or uniform motion unless its compelled to change that by external force
- 6. Newton’s second law of motion: the acceleration of body is proportional to the impressed force and takes place in the direction in which the force acts
- 7. Newton’s third law of motion: For every action there is always an equal and opposite reaction
- 8. Coplanar and Concurrent forces Force: An agent which produces or tends to produce, destroy or tends to destroy motion of a body is called force.
- 9. Parallelogram Law Of Forces: If two, forces simultaneously on a particle 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 interaction.
- 11. Principle Of Superposition Of forces If two equal , opposite and collinear forces are added to or removed from the system of forces ,there will be no change in the position of the body .this is known as principle of superposition of forces.
- 12. Triangle law of forces If two forces acting at a point be represented in magnitude and direction by two sides of triangle taken in order , their resultant may be represented in magnitude and direction by the third side of triangle, taken in opposite order.
- 13. Principle of resolution It is often convenient to split a force in two perpendicular components Consider a force f being split into to components fx and fy Therefore fx=fcosѲ fy=fsinѲ
- 14. Polygon Law of Forces If a number of forces acting at a point be represented in magnitude and direction by the sides of a polygon taken in order ,then the resultant of all those forces may be represented in magnitude and direction by the closing side of the polygon taken in order
- 15. Here F is the resultant
- 16. Lami’s Theorem If three coplanar forces acting at a point be in equilibrium , then each force is proportion to the sine of angle between the other two