Engineering Principles for Electrical Technicians: The Commonwealth and International Library: Electrical Engineering Division

By K. M. Smith and P. Holroyd

Engineering Principles for Electrical Technicians serves as an introduction to basic engineering principles. This book discusses several topics, including rectifier equipment, pole systems, capacitors, electrical energy, and operating torque. Organized into 23 chapters, this book begins with an overview of the different applications of forces, including gravitational, friction, accelerating, shear, tensile, and compressive force. This text then defines the center of gravity as the point through which the resultant weight acts in whatever position the body is placed. Other chapters consider the efficiency, velocity, and mechanical advantage of simple machines. This book discusses as well the value of the factor of safety that depends on the material being used and the circumstances under which the material will work. The final chapter deals with thermionic emission that is concerned with the production of charged particles at a heated surface. This book is a valuable resource for electrical, mechanical, and telecommunications technicians.

• Language: English
• Publisher: Elsevier Science
• Release date: Oct 22, 2013
• ISBN: 9781483140308

Book preview

Course.

Symbols, Units and Abbreviations

CHAPTER 1

Forces and Equilibrium

Publisher Summary

When we think of forces we usually consider the action of lifting a weight, bending a piece of wire or setting a vehicle in motion. Whenever we move, or move other objects around us, then forces are brought into play. One of the most important forces is the one that causes objects to fall downwards, the Force of Gravity. This chapter discusses the types of force, effects of forces, and the equilibrium of forces. The effect of a number of forces acting on a body depends not only on the magnitude of the forces and their directions, but also on the points at which the forces are applied to the body. This action of the force turning about an axis or fulcrum is called the turning moment or moment of the force, or torque. The chapter also presents the experiment to find the coefficient of friction between two surfaces in contact.

1.1 Types of force

When we think of forces we usually consider the action of lifting a weight, bending a piece of wire or setting a vehicle in motion. Whenever we move, or move other objects around us, then forces are brought into play. In fact, approximately three centuries ago Sir Isaac Newton gave us a definition of a force which includes all the forces that we can imagine. Force changes or tends to change the state of a body’s rest or uniform motion in a straight line. One of the most important forces we meet is the one which causes objects to fall downwards, the Force of Gravity.

It has been found that between all bodies there is a force of attraction defined as the gravitational force. The larger the bodies the greater the attraction between them, but as the distance between the bodies increases the attraction decreases. Normally bodies on the surface of the earth do not show this attraction between themselves because the force is very small, but if we consider two masses, one of which is the earth, then the force of attraction between these masses can be considerable. The earth being the larger body will not move perceptibly and therefore the smaller body, if free to do so, will move towards the centre of the earth. This force of gravity acting on the body is called its Weight.

It should be understood that not all the forces we meet are gravitational forces. Friction forces are introduced when two surfaces slide over each other; inertia forces occur when a mass has to be accelerated; tensile, compressive and shear forces are considered in dealing with the strength of materials (Fig. 1.1). The idea of the gravitational force can be used to give us a unit of measurement of a force.

FIG. 1.1 Different applications of forces. The gravitational force causes all bodies to fall towards the centre of the earth. An accelerating force causes a body to change its speed or velocity. When two surfaces slide over each other the resistance to motion is called the friction force. A pair of scissors cuts paper by a shearing force. A tensile force is introduced into a rope when pulling a box along the ground. The stool legs are subject to a compressive force when anyone sits on the stool.

1.2 Unit of force

If we wish to compare forces, then we must have a standard of reference. In England a cylinder of platinum of a certain size is kept at the Board of Trade in London representing a mass of one pound. The gravitational force exerted on this mass at mean sea level is called the pound-force. Other weights are then made to compare with the standard and distributed to Weights and Measures offices throughout the country from which the weights you see in shops or factories are checked. See Fig. 1.2.

FIG. 1.2 The U.K. Standard One Pound Mass. A cylinder of platinum kept at the Board of Trade represents the United Kingdom Primary Standard one pound mass. Five copies of this are distributed to various other offices in London. Secondary standards are made to compare with the authorised copies and tertiary standards are compared to the secondary standards. In each town and city a set of local standards are kept and periodically checked with the tertiary standards. The Weights and Measures Officer uses a set of working standards for checking tradesmen’s weights which he maintains by checking with the local standards. This flow enables a continual check to be made on the accuracy of all weights used in the country.

Another standard of mass used on the Continent is the kilogramme, represented by a cylinder of platinum-iridium kept in France. The gravitational force exerted on this mass is called the kilogramme-force.

The relationship between the pound-force and the kilogramme-force is

or

We can use multiples of these forces or weights.

The pound-force is related to the ton-force (tonf) such that

Similarly

1.3 Effects of forces

If we consider a mass of 5 lb hanging from a rope (Fig. 1.3) we should say that the force in the rope is 5 lbf. If we now support the rope over a pulley and hang a 5 lb mass on each end (Fig. 1.4) would the force on the rope now be 5 lbf? If you are in doubt, cut the string and insert a spring balance in the system (Fig. 1.5) and take a reading from the balance. This should be 5 lbf. Now ask yourself why this is only 5 lbf and not 10 lbf. The answer was given again by Sir Isaac Newton, who stated: To every action there is an equal and opposite reaction.

FIG. 1.3

FIG. 1.4

FIG. 1.5

In Fig. 1.3 the support is providing an upward force of 5 lbf to balance the weight hanging downwards, therefore in Fig. 1.4. to keep the system balanced, a mass of 5 lb must be attached at each end of the string. If one mass were taken away then the other would fall to the ground. This situation occurs when anything rests on the ground. If you weigh 145 lbf and you are standing on the ground, then the earth is pressing upwards with an equal force of 145 lbf to keep you at rest. When you stand on the bathroom scales, the scales are sandwiched between your feet and the floor so that pressure is exerted on the top and bottom of the scales to enable a reading of your weight to be taken. If you attempted to jump off a high diving board with the scales strapped to your feet then no reading would be registered until you hit the water, with disastrous results to the scales.

1.4 Equilibrium of forces

In the previous paragraph we considered someone standing on the ground and the ground pressing upwards with a force equal to the weight of the person. Under these conditions no movement occurs. If the person steps off the high diving board, then there is nothing to provide an upward force to stop the person falling and motion occurs. In the first case we say the forces acting are in equilibrium, and in the second case they are not in equilibrium.

Now imagine two tug-of-war teams straining on a rope. Each team pulls away from the centre of the rope and if both teams are as strong as each other then no movement occurs. If, however, one team is stronger than the other then the rope moves towards the stronger team and the system becomes unbalanced and ceases to be in equilibrium.

When you ride a cycle on a level road, the action of pedalling is to overcome the resistance due to friction of the moving parts and any air resistance. See Fig. 1.6.

FIG. 1.6 Equilibrium conditions. A state of equilibrium can occur if the forces are stationary such as a tug-of-war when both teams are pulling with equal forces. Alternatively if a cyclist is moving along a road at a constant speed then he is in equilibrium when the propelling force is equal to the friction force plus the force due to air resistance.

If you are travelling at a constant speed then the force pushing you forward due to pedalling is equal to the resistance tending to stop the motion and the system is in equilibrium. If you stop pedalling the cycle retards, or if you pedal harder the cycle goes faster. In either case the system is unbalanced and ceases to be in equilibrium. Equilibrium can occur if a body remains stationary under the action of a number of forces or alternatively if a body is moving at a uniform speed.

1.5 Scalar and vector quantities

Quantities involving magnitude only, e.g. money, time, temperature, resistance, speed, etc., are called SCALAR quantities and can be expressed by a number and the appropriate unit. If, however, direction is involved in addition to magnitude, e.g. velocity, acceleration, force, etc., then they are called VECTOR quantities.

Scalar quantities can be added together or subtracted arithmetically but vector quantities require special treatment.

1.6 Representation of a force

When a force acts on a body, the effect the force has on this body depends on (a) the magnitude, (b) the direction, (c) the point of application and (d) the sense of the force. Figure 1.7 shows how these quantities may be represented on a simple diagram called a space diagram.

FIG. 1.7

The vector representation of the force will be made by drawing a straight line to a suitable scale of force, say 1 inch to represent 20 lbf, in the same direction as the force is applied to the body and placing an arrow head on the line to indicate the sense (Fig. 1.8).

FIG. 1.8

1.7 Addition of forces

Figure 1.9 shows forces of 3 lbf and 4 lbf acting on a mass Mis drawn to represent the 4 lbf, 2 inches long in the same direction as the 4 lbf, and the arrow is placed on the vector. Now vectorially:

FIG. 1.9

gives the result of the addition. If the diagram, (Fig. 1.10) is drawn carefully the answer is found to be 5 lbf. Therefore a force of 5 lbf acting in a direction 37° to the 4 lbf will have the same effect on the mass M as the 4 lbf and 3 lbf acting at right angles. This single force is called the RESULTANT of the two forces.

FIG. 1.10

The RESULTANT of a set of forces is that single force which will replace the system of forces and have the same effect.

For two forces to be in equilibrium they must be (a) equal in magnitude, (b) acting in the same direction, (c) of opposite sense and (d) passing through the same point.

If now we have a number of forces acting through a point and we wish to put the system of forces in equilibrium by the use of a single force, all we need to do is to find the resultant of the system and balance the resultant. This single force which balances a number of forces is called the EQUILIBRANT.

The equilibrant is exactly the same as the resultant except for the sense.

EXAMPLES

Find the resultant of forces A and B (Fig. 1.11), stating clearly the magnitude and direction relative to force A.

FIG. 1.11

[(a) 12·7 lbf, 29°; (b) 57 lbf, 52°; (c) 20 kgf, 46°; (d) 24·75 kgf, 24°; (e) 5 tonf, 53°; (f) 9·9 lbf,