| hypothenuse | = | √(base2 + altitude2) | (4) |
| (5 | = | √(42 + 32)) | |
| base | = | √(hypothenuse2 - altitude2) | (5) |
| (4 | = | √(52 - 32)) | |
| altitude | = | √(hypothenuse2 - base2) | (6) |
| (3 | = | √(52 - 42)) |
Representation of Forces by Lines.—A single force may be represented in a drawing by a straight line, 1, the point of application of the force being indicated by an extremity of the line, 2, the intensity of the force by the length of the line, and 3, the direction of the force by the direction of the line, an arrow head being placed at an extremity defining the direction.
Thus in fig. 1,310, the force necessary to balance the thrust on the steam piston may be represented by the straight line f whose length measured on any convenient scale represents the intensity of the force, and whose direction represents the direction of the force.
Fig. 1,310.—Diagram illustrating the representation of forces by straight lines. If 80 lbs. of steam be applied to a piston of 4 square inches area, the total pressure acting on the piston is 4 × 80 = 320 lbs. This may be balanced by an equal and opposite force. To represent the latter by a line, select any convenient scale whose divisions represent any convenient number of pounds—1, 3, 5 or, as here taken, 25 lbs. If the scale selected be divided into inches with ¼-inch divisions, then each ¼ inch represents a force of 25 lbs.; or, as usually stated, 1" = 100 lbs. Strictly speaking 1" is equivalent to 100 lbs. Draw the line f = 3.2 ins., then its length represents the magnitude of the force or 320 lbs., that is, 3.2 × 100 = 320 lbs.
Composition of Forces.—This is the operation of finding a single force whose effect is the same as the combined effect of two or more given forces. The required force is called the resultant of the given forces.
The composition of forces may be illustrated by the effect of the wind and tide on a sailboat as in fig. 1,311. Supposing the boat be acted upon by the wind so that in a given time, say half an hour, it would be moved in the direction and a distance represented by the line AB, and that in the same time the tide would carry it from A to C. Now, lay down AB, to any convenient scale, representing the effect of the wind, and AC that of the tide, and draw BD equal and parallel to AC, and CD equal and parallel to AB, then the diagonal AD will represent the direction and distance the boat will move under the combined effect of wind and tide.
Fig. 1,311.—Parallelogram of forces for boat acted upon by both wind and tide.