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Construct a parallelogram with sides in the same direction as P and Q and lengths in proportion. Graphically evaluate the resultant which is equivalent in direction and proportional in magnitude to the diagonal. Trigonometric solution. Use the law of cosines and law of sines to find the resultant.
parallelogram law of addition (and the triangle law). Equivalent Vector: V= V1+ V2(Vector Sum) Ex: displacement, velocity, acceleration, force, moment, momentum
parallelogram law of forces: It states, “If two forces, acting simultaneously on a particle, be represented in magnitude and direction by the two adjacent sides of a parallelogram ; their resultant may be
law of vector addition. The vectors . A . and . B . can be drawn with their tails at the same point. The two vectors form the sides of a parallelogram. The diagonal of the parallelogram corresponds to the vector . C = A + B, as shown in Figure 3.2b. C = A + B B A (a) head to tail . A B C = A B (b) parallelogram . Figure 3.2a Figure 3.2b
Forces are drawn as directed arrows. The length of the arrow represents the magnitude of the force and the arrow shows its direction. Forces on rigid bodies further have a line of action. Forces (and in general all vectors) follow the parallelogram law of vector addition.
• Apply parallelogram law to obtain resultant force by adding the resultant of the x and y components.
A resultant force may be determined by following methods 1. Parallelogram laws of forces or method 2.
