Composition and Resolution of Forces

INTRODUCTION

The force is an important factor in the field of Mechanics, which may be broadly *defined as an agent which produces or tends to produce, destroys or tends to destroy motion. e.g., a horse applies force to pull a cart and to set it in motion. Force is also required to work on a bicycle pump. In this case, the force is supplied by the muscular power of our arms and shoulders.

Sometimes, the applied force may not be sufficient to move a body, e.g., if we try to lift a stone weighing 2 or 3 quintals, we fail to do so. In this case we exert a force, no doubt, but no motion is

produced. This shows that a force may not necessarily produce a motion in a body ; but it may, simply, tend to do so. In a tug-of-war the two parties, when balanced, neutralize each other’s force. But the moment one party gets weaker, the other party pulls off, in spite of first party’s best effort to destroy motion.

EFFECTS OF A FORCE

A force may produce the following effects in a body, on which it acts :

1. It may change the motion of a body. i.e. if a body is at rest, the force may set it in motion. vAnd if the body is already in motion, the force may accelerate it.

2. It may retard the motion of a body.

3. It may retard the forces, already acting on a body, thus bringing it to rest or in equilibrium We shall study this effect in chapter 5 of this book.

4. It may give rise to the internal stresses in the body, on which it acts. We shall study this effect in the chapters ‘Analysis of Perfect Frames’ of this book.

CHARACTERISTICS OF A FORCE

In order to determine the effects of a force, acting on a body, we must know the following characteristics of a force :

1. Magnitude of the force (i.e., 100 N, 50 N, 20 kN, 5 kN, etc.)

2. The direction of the line, along which the force acts (i.e., along OX, OY, at 30° North of East etc.). It is also known as line of action of the force.

3. Nature of the force (i.e., whether the force is push or pull). This is denoted by placing an arrow head on the line of action of the force.

4. The point at which (or through which) the force acts on the body.

PRINCIPLE OF PHYSICAL INDEPENDENCE OF FORCES

It states, “If a number of forces are simultaneously acting on a *particle, then the resultant of these forces will have the same effect as produced by all the forces. ”

PRINCIPLE OF TRANSMISSIBILITY OF FORCES

It states, “If a force acts at any point on a †rigid body, it may also be considered to act at any other point on its line of action, provided this point is rigidly connected with the body.”

SYSTEM OF FORCES

When two or more forces act on a body, they are called to form a system of forces. Following systems of forces are important from the subject point of view :

1. Coplanar forces. The forces, whose lines of action lie on the same plane, are known as coplanar forces.

2. Collinear forces. The forces, whose lines of action lie on the same line, are known as collinear forces.

3. Concurrent forces. The forces, which meet at one point, are known as concurrent forces. The concurrent forces may or may not be collinear.

4. Coplanar concurrent forces. The forces, which meet at one point and their lines of action also lie on the same plane, are known as coplanar concurrent forces.

5. Coplanar non-concurrent forces. The forces, which do not meet at one point, but their lines of action lie on the same plane, are known as coplanar non-concurrent forces.

6. Non-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.

7. Non-coplanar non-concurrent forces. The forces, which do not meet at one point and their lines of action do not lie on the same plane, are called non-coplanar non-concurrent forces.

RESULTANT FORCE

If a number of forces, P, Q, R ... etc. are acting simultaneously on a particle, then it is possible to find out a single force which could replace them i.e., which would produce the same effect as

produced by all the given forces. This single force is called resultant force and the given forces R ... etc. are called component forces.

COMPOSITION OF FORCES

The process of finding out the resultant force, of a number of given forces, is called composition of forces or compounding of forces.

METHODS FOR THE RESULTANT FORCE

Though there are many methods for finding out the resultant force of a number of given forces, yet the following are important from the subject point of view :

1. Analytical method.

2. Method of resolution.

ANALYTICAL METHOD FOR RESULTANT FORCE

The resultant force, of a given system of forces, may be found out analytically by the following

methods :

1. Parallelogram law of forces.

2. Method of resolution.

PARALLELOGRAM LAW OF FORCES

It states, “If two forces, acting 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 intersection.” Mathematically, resultant force,