Force is the name applied in Mechanics to whatever produces motion or pressure. Thus we have the forces of gravity and of elasticity, muscular force, and that of electricity and magnetism. These will be considered under the head Prime Movers; at present we shall confine ourselves to the general laws to which the application of force is subject When a force is applied suddenly to a body, and immediately ceases to act upon it, it is called an impulsive force; but when its action is continued so as to produce a constantly increasing motion or pressure, it is termed a constant or accelerating force. Examples of the first kind are seen in the blow with a hammer, and in the discharge of a gun; and of the second, in the action of gravity and in the motion of the wind. Impulsive forces produce uniform velocities. Thus, if a billiard ball be struck, and move along a smooth table, so that the resistance arising from friction may be small, it will be observed to pas3 over equal spaces in equal successive portions of time; or, in other words, if the ball pass over 1 foot in a second, it will pass over 2 feet in two seconds, 3 feet in three seconds, and so on. Constant forces produce accelerated velocities.
Thus, if a certain force, as that of gravity, act upon a body so as to impel it through 16 feet in one second of time, in the next second it would pass through three times sixteen, or 48 feet; in the third second through five times sixteen, or 80 feet, and so on, the constant addition being 32 feet, which is the velocity acquired at the end of the first second of time. Now if a force produce an uniform increase of velocity, as in this case, it is called an uniformly accelerating force; or if it produce a regular diminution of velocity, it is a uniformly retarding force. If, however, the increase or decrease of velocity be not constantly the same, it is caused by a variable accelerating or retarding force. In the application of forces, the chief considerations are intensity and direction. If a single force act upon a body, motion necessarily results in the direction in which the force acts, and with a velocity proportional to its intensity. If two or more forces are employed, motion may or may not result, according to the intensity and direction of the force.
If two equal forces applied to the same point act in opposite directions, they mutually annihilate each other; if, however, they act in the same direction, they produce the same effect as a single one equal in intensity to the sum of the two. Or, if they act in different directions, forming an angle with each other, a third force may be assigned, which shall be equivalent to the other two. In this case the two forces are called the components, and the third, the resultant. The process for finding the resultant of two or more forces is called the composition of forces, and the finding of two or more forces, which shall be equivalent to a single given force, is termed the resolution of forces. The propositions connected with this subject form a highly interesting and important branch of the science of mechanics. In the annexed cut let the line A B represent the intensity and direction of one force, and A C the intensity and direction of the other force. Complete the parallelogram A B D C, and the diagonal A D will represent the intensity and direction of the resultant; i. e. a force equal to A D, and, in the direction D A, would counterbalance the other two, and keep the point A at rest.
The same may perhaps be more clearly apprehended by considering the point A in motion; let a force act upon A so as, if alone, to drive it to the point E in one second, and at the same instant let a force act in the direction A C, that would, if unopposed, carry it to C in the same time; then if the two forces act together, the resulting motion will be in the line A D, and the body will read.
the point D in the same time that it would have taken to reach B or C by the action of either of the forces singly. In the composition of forces it will be seen that we are limited to one resultant; but in the resolution of force we may have an infinite number of components, any pair of which will be equivalent to the given force. Thus let a force, represented by the line A B, be resolved into two others by drawing two parallelograms around it, it will be manifest that the component forces may be either A C and A E, or A D and A F; and as an infinite number of directions may be given to the lines AC, AE, the number of components is also unlimited. In general, however, the required direction and intensity of one of the forces is given, and this determines the other. Suppose a man were required to raise a weight over a pulley, and the ropes, instead of being parallel, are in the directions A B A D, it will be evident that a part of his strength is employed uselessly in pulling horizontally.
Let B D represent the force necessary to sustain the weight B; resolve this into the two B C, B D, the one perpendicular, and the other parallel to the horizon, it will then be seen that the force which is employed in raising the body, is equal to B C, and as this is less than B D, the weight must fall, or the power be increased in the ratio of B C to B D. If three forces are employed, they may also be determined by drawing three lines parallel to their directions, so as to form a triangle. The three cords A D, B D, C D, will be kept at rest, when the three weights at A B C are proportional to the three lines D E, D F, and E F, either of which may be considered as the resultant of the other two. If a number of forces act upon a body, and a single resultant be required, it may be found by finding the resultant of one pair, and connecting this with another; then find the resultant of this pair and connect it with the next, and so on, till the last is obtained, which is the common resultant of the whole. Numerous examples are daily presented of the composition of forces.
When a boat is rowed across a river in which there is a rapid current, it will not pass directly across, nor down the stream, but will partake of both directions, proceeding in a direction intermediately between the acting forces. A body falling from the topmast of a vessel in full sail will not fall directly downward, for having a direction forward given by the motion of the vessel, and a downward direction by gravity, it will take a middle course, describing what is termed a parabolic curve. The tide and wind acting together upon a vessel, the two oars of a boat in rowing, the motion of a stone, an arrow, or a cannon ball through the air, are examples of the same kind. Another instance of a resultant motion may be adduced, in the reflection of elastic bodies from a smooth surface. Let A B be a smooth flat surface, and let an elastic ball strike it in the direction C D, then will it be reflected in the direction D E, making the angle of reflection E D F equal to the angle of incidence C D F. If C D represent the force of the ball in the direction C D, it may be resolved into two, which are proportional to C F and C B. The force C F being parallel to the plane A B, is not influenced by it, but C l) being perpendicular, is destroyed, and a motion impressed in the direction D F.
The body is still then under the influence of two forces, its retained velocity in the direction D A, and, the impressed force produced by the reaction of the board in the direction D F. Between these two the ball necessarily moves in the line D E. An application of this problem will account for the motion of billiard balls, and of ships sailing obliquely to the wind; also of windmill sails, and other daily occurrences in nature and art.