PARALLELOGRAM OF FORCES
Although a force is something that cannot be pictured it can be represented graphically by means of a line, letting the direction of the line represent the direction of the force and the length of the line the strength of the force. In Figure 58 we may measure off 3 inches from O to a to indicate the 3-pound force and 4 inches from O to b to represent the 4-pound force and 5 inches from O to c to represent the 5-pound force. Now if from a a line is drawn parallel to O b and from b a line is drawn parallel to O a we shall have a parallelogram a O b d, and if we extend the line O c it will bisect the parallelogram, running diagonally from O to d, and this diagonal will be found to measure exactly 5 inches which represents the 5-pound force. This is what is known as the parallelogram of forces. It shows us the resultant of any two forces that are not directly opposite and it gives us the direction as well as the strength or magnitude of this resultant. It is only because we happen to choose the forces 3, 4 and 5 that the angle at O is a right angle. In Figure 59, where the forces are all equal, our parallelogram is lozenge-shaped and the line O d is just as long as the line O a and O b, showing that its magnitude is the same as that of the two forces that balanced it.
FIG. 57.—BALANCED FORCES—UNEQUAL WEIGHTS
The greater the angle between the two lifting forces the less weight can they lift. If two men are carrying a ten-pound satchel, each will be lifting five pounds, if the pull is directly upward; but this is a rather inconvenient way of carrying the bag and usually they pull at a slight angle from the vertical, and so each must carry more than half the weight. If they move so far apart that the angle between them is more than 120 degrees, each will be carrying more than the full weight of the bag.
FIGS. 58 AND 59.—PARALLELOGRAMS OF FORCES