Distinctive Characteristics of Forces.

20. In order that the effect of any force may be completely understood, three things must be known: its point of application, its direction, and its intensity.

The point of application of a force is the point where it exerts its action. Thus, in Fig. 6, which represents a child drawing a wagon, the force exerted by the child has its point of application at A.

Fig. 6.

The direction of a force is the line along which it acts; thus, in Fig. 6, the line AB is the direction of the force exerted by the child.

The intensity of a force is the energy with which it acts; thus, in the same example as before, the intensity of the force exerted is the energy which the child exerts in overcoming the resistance of the wagon.

The intensity of a force is measured in pounds; thus, a force of fifty pounds is a force necessary to sustain a weight of fifty pounds. The intensity of a force may be represented by a distance which is usually laid off on the line of direc

(20) What three elements determine a force? Define the point of application. The line of direction. The intensity. How is the intensity measured? How repreзented? Example.

tion of the force.

say one tenth of an

Having assumed some unit of length, inch, to represent one pound, this is set off as many times as the force contains pounds. In the example taken, if we suppose the force exerted to be seven pounds, and lay off from A to C seven tenths of an inch, then will AC represent the force both in direction and intensity.

Resultant and Component Forces.

21. When a body is solicited by a single force, it is evident, if no obstacle intervene, that it will move in the direction of that force; but if it is solicited at the same time by

several forces acting in different directions, it will not, in general, move in the direction of any one of them. For example, if two men on opposite sides of a river tow a boat by means of a rope, as represented in Fig. 7, the boat will not move either in the direction AB, or AC, but it will move in some intermediate direction, as AE; that is, it will advance as though it were solicited by a single force directed from A towards E. This single force, which would produce the same effect as the two separate forces, is called

9

(21) What is a Resultant of several forces?

their Resultant.) The separate forces are called Components of the resultant.

In general the resultant of any number of forces is a single force whose effect is equivalent to that of the whole group. The individual forces of the group are called Components.)

Parallelogram of Forces.

A

B

22. It is shown in Mechanics (Peck's Mechanics, Art. 27), that if AB and AD, Fig. 8, represent two forces acting at A, their resultant will be represented by AC. That is, if two forces are represented in direction and intensity by the adjacent sides of a parallelogram, their result

ant will be represented in

D

Fig. 8.

direction and intensity by that diagonal which passes

through their point of intersection.

This principle is

called the Parallelo

gram of Forces.

The operation of finding the resultant when the components are given is called Composi tion of Forces; the reverse operation is called Resolution

of Forces.

When two forces

are applied at the

same point, as shown in Fig. 9, we lay off distances AB

What are Components? Illustrate. (22) Enunciate the parallelogram of forces.

and AD to represent the forces, and having completed the parallelogram, we draw its diagonal AC; this will be their resultant. If the resultant AC is known, and the directions of its components are given, we draw through the lines CD and CB parallel to their directions; then will the intercepted lines AD and AB be components of the force AC.

Practical Example of Composition of Forces.

23. A bird, in flying, strikes the air with both wings, and the latter offers a resistance which propels him forward.

Let AK and AH, in Fig. 10, represent these resistances. Draw AB and AD equal to each other, and complete the parallelogram AC; draw also the diagonal AC. Then will AC represent the resultant of the two forces, and the bird will move exactly as though impelled by the single force CA.

How is the resultant found when the components are known? How are the components found? (23.) Explain the flight of a bird.

Practical Example of Resolution of Forces.

24. When a sail-boat is propelled by a breeze acting on the quarter in the direction va (Fig. 11), we may, by the rule in Art. 22, resolve the intensity of the wind into two components, one, ca, in the direction of the keel, and the

other, ba, at right angles to it. The first component alone is effective in giving a forward motion to the boat, whilst the second is partly destroyed by the resistance which the water offers to the keel, and partly employed in giving a lateral motion to the boat. This lateral motion is called lecway.

25. When two forces act in the same direction, as when two horses pull at the ends of a whiffle-tree to draw a wagon, their resultant is equal to the sum of the forces. (When they act in a contrary direction, as in the case of a steamboat ascending a river, where the force of the engine acts to propel the boat forward, whilst the current acts to

(24) Explain the sailing of a boat. (25.) What is the resultant of parallel forces when they act in the same direction? When they act in opposite directions? Examples.