# ENGINEERING MECHANICS

## IMPORTANT CONCEPTS TO LEARN

• The term force may be defined as an agent which produces or tends to produce, destroys or tends to destroy motion.
• A force while acting on a body may change its motion, balance the forces already acting on it and give rise to the internal stresses in it.
• In order to determine the effects of a force, acting on a body we must know the magnitude of the force, line of action of the forces and nature of the force.
• The unit of force in S.I. system of units is newton.
• One kg of force is equal t 9.8 N.
• A resultant force is a single force which produces the same effect as produced by all the given forces acting on a body.
• The process of finding out the resultant force is called composition of forces.
• The algebraic sum of the resolved parts of a number of forces in a given direction is equal to the resolved part of their resultant in the same direction. This is known as principle of resolution of forces.
• Vectors method for the resultant force is also called polygon law of forces.
• The resultant of two forces P and Q acting at an angle θ is √P2 + Q2 + 2PQ sin θ.
• If the resultant of two forces P and Q acting at an angle θ, makes an angle α with the force P, then tan α =  Q sin θ/P + Q cos θ
• The resultant of two forces P and Q (such that P > Q) acting along the same straight line, but in opposite direction is given by P – Q.
• The resultant of two equal forces P making an angle θ, is given by 2 P cos θ/2
• The resultant of two forces each equal to P and acting at right angles is √2P.
• The angle between two forces when the resultant is maximum and minimum respectively are 0° and 180°.
• If the resultant of two equal forces has the same magnitude as either of the forces then the angle between the two forces is 120°.
• The resultant of the two forces P and Q is R. If Q is doubled, the new resultant is perpendicular to P. Then Q = R.
• Concurrent forces are those forces whose line of action meet at one point.
• The forces which meet at one point and their lines of action also lie on the same plane are known as coplanar 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-coplanar concurrent forces.
• The forces which do not meet at one point and their lines of action do not lie on the same plane are known as non coplanar non concurrent forces.
• Coplanar concurrent forces are those forces which meet at one point and their lines of action also lie on the same plane.
• Non coplanar concurrent forces are those forces which meet at one point but their lines of action do not lie on the same plane.
• Non coplanar non concurrent forces are those forces which do not meet at one point and their lines of action do not lies on the same plane.
• According to lami’s theorem if the three forces acting at a point are in equilibrium, then each force is proportional to sine of the angle between the other two.
• Varignon’s theorem of moment states that if a number of coplanar forces acting on a particle are in equilibrium, then the algebraic sum of their moments about any point is equal to the moment of the resultant force about the same point.
• According to the law of moments, if a number of coplanar forces acting on a particle are in equilibrium, then the algebraic sum of their moments about any point in their plane is zero.
• The forces whose line of action are parallel to each other and act in the same directions are known as like parallel forces.