When two forces, having the same point of application, act at the same time upon a body, we can imagine someone force, called the resultant, that would have the same effect as the two actual forces, which are called components. The direction and intensity of this resultant force may be found as follows:

• When the forces act in the same direction. - Suppose two forces act upon a body, tending to move it toward the east. Let one of them be a force of 2 dynes and the other of 3 dynes. Select a point A as the position of the body. Draw a line Ax (Fig. 1) to represent the direction in which the forces act. Take any convenient scale and lay off AB to represent 2 dynes, and AC to represent 3 dynes. Since the forces AB and AC are acting upon the same body at A and along the same line, Ax, and since each force produces its own effect, their resultant must be equal to the sum of AB and AC; hence it will be the force AD, representing 5 dynes.

 The resultant of two forces acting in the same straight line, in the same direction, is the sum of the given forces.

• When the forces act in opposite directions. - Suppose the two forces to act, one toward the east and the other toward the west, as in Fig. 2. It is evident that the force AB will act against AC, and that the resultant will be AD, their difference. The resultant of two forces acting in the same straight line, but in opposite directions, is the difference of the given forces and acts in the direction of the greater. It two equal forces act upon a body in opposite directions, their resultant will be zero, the forces will be in equilibrium, and the body will be at rest.

• When the forces act at an angle to each other. - THE PARALLELOGRAM OF FORCES

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(1) Suppose the force P(Fig. 3), of 3 dynes, to act toward the east, at a right angle to the force Q, of 2 dynes, acting toward the south. Represent P by AC, and Q by АB. Complete the parallelogram by drawing the dotted lines BD and CD (parallel to AC and AB, respectively), and their intersection will locate the point D and determine both the magnitude and the direction of the resultant, AD. For D is the only point that is as far east as C and as far south as B. In each figure all lines representing forces must be measured by the same scale.

(2) Suppose the force to act at an angle CAB to the force P (Fig. 4). Complete the parallelogram to determine the point D. Then, for reasons similar to the above, AD or R will be the resultant required.

The resultant of any two forces acting at an angle to each other may be found by completing the parallelogram upon the forces as sides and drawing the diagonal from the common point of application.

• When there are more than two forces. -The resultant of any number of forces can be found by a repetition of the parallelogram of forces. Suppose three forces, P, Q, and S (Fig. 5), to be acting on a body at A. Complete the parallelogram ACDB; then AD or R' will be the resultant of P and Q. Find the resultant of S and R' by completing the parallelogram ADHЕ; then A H or R will be the resultant of P, and S.

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