retarded; such is the motion of a train of cars when coming to rest, or that of a body thrown vertically upwards. When the spaces passed over in equal times are continu ally increased or decreased by the same quantity, the motion is uniformly accelerated, or uniformly retarded. The mo tion of a body falling in a vacuum, is uniformly acceler ated; that of a body shot vertically upwards in a vacuum, is uniformly retarded. The velocity of a body having varied motion at any time, is the rate of the body's motion at that time. In varied motion the velocity is continually changing. 19. Forces, Powers, and Resistances. tends to set it If a body is at rest, any cause that in motion, is called a Force; if a body is in motion, any cause that tends to make it move faster, or slower, or to change its direction, is called a Force. A Force, then, is any cause that tends to change the state of a body, with respect to rest or motion. The attractions and repulsions between the molecules of bodies are forces; the muscular efforts of men or animals, employed in accomplishing any kind of work, are forces; the elastic efforts of gases and vapors are forces. Forces which act to produce motion are called Powers; those which act to prevent or destroy motion are called Resistances. The effort of steam employed in moving a train of cars is a power, whilst friction and the inertia of the air, which tend to retard the motion, are resistances. Powers tend to accelerate motion, and are for that reason called Accelerating Forces. Resistances, on the contrary, tend to retard motion, and are for that reason called Retarding Forces. Examples. Define uniformly accelerated and uniformly retarded motion. Examples. (19.) What is a Force? Examples. Define Powers and Resistances. Examples. By what other names may they be called? 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. 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 repre Jented? Example. tion of the force. Having assumed some unit of length, say one tenth of an 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 (21.) What is a Resultant of several forces? The separate forces are called Compo their 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. 25), 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 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 Composition of Forces; the reverse operation is called Resolution of Forces. When two forces B are applied at the Fig. 9. 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. 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. |