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 = [frac up=”Q sin θ” down=”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 [frac up=”2 P cos θ” down=”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.
