Force
Force may be defined as an agent which produces or tends to produce, destroy, or tends to destroy the motion of a body. A force while acting on a body may
(a) change the motion of a body.
(b) retard the motion of a body.
(c) balance the forces already acting on a body. And
(d) give rise to the internal stresses in a body.
To determine the effects of a force acting on a body, we must know the following characteristics of a force:
(0) The magnitude of the force.
(ii) The line of action of the force.
(i) The nature of the force, i.e., push or pull, and
(iv) The point at which the force is acting.
In the M. K. S. system of units, the magnitude of the force is expressed in kilogram-force (briefly. written as KGF), and in the S.I. system of units, the force is expressed in newtons (briefly written as N). It may note that
1 kgf = 9.81 N
Resultant Force
It is a single force that produces the same effect as all the given forces acting on a body.
The resultant force may be determined by the following three laws of forces:
1.Parallel 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, their results may be represented in magnitude and direction by the diagonal of a parallelogram their points of intersection.
For example, let ses consider two forces and act at angle 0, as shown in Fig.
The resultant is given by
R=√P2+Q2+2PQcosθ
If the resultant (R) makes an angle α with the force P, then.
tanα =Qsinθ⁄P+cosθ
2. Triangle law of forces:-
It states that if two forces, acting simultaneously on a particle, be represented in magnitude and direction by the two sides of a triangle taken in order, their results may be represented in magnitude and direction by the third side of the triangle opposite order.
3. Polygon law of forces:-
It states that if several forces, acting simultaneously on a
particle, be represented in magnitude and direction by sides of a polygon taken in order, then there
resultant is represented in magnitude and direction by the closing side of the polygon taken in
opposite order
Notes:
1. The resultant of more than two intersecting forces may be found by resolving all the forces horizontally and vertically. In such cases, the resultant of the forces is given by
R = √(ΣH)2+(ΣV)2
ΣH = Sum of resolved parts in the horizontal direction, and
ΣV = Sum of resolved parts in the vertical direction.
If the resultant (R) makes an angle α with the horizontal, then.
tanα = ΣV/ΣH
2. If the resultant of several forces acting on a particle is zero, the particle will be in equilibrium. Such a set of forces, whose resultant is zero, are known as equilibrium forces. The force, which brings the set of forces in equilibrium is called an equilibrium. It is equal to the resultant force in magnitude but spposite in direction
3. Several forces acting on a particle will be in equilibrium when ΣH= 0 and ΣV = 0.
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