6Addition of Vector Forces Purpose: To practice vector addition by putting objects in equilibrium. Use the graphical method and component method of adding vectors to show the sum of the forces equal zero. Apparatus: Force table, String, Hanging masses, Protractor, Ruler, graph paper. Background on Vectors: Vectors are used to indicate size and direction of such things as forces, velocities, accelerations etc. The direction of the vector is specified by an angle from one of the primary axes. The magnitude is indicated by its length. Figure 1 below illustrates this idea of a single vector. θ(x,y)xyScale1 cm = 1 NewtonFigure 1. A force vector defined by the length of the vector and the angle θ. The magnitude of a single vector can be determined by measuring the vector and using a scale to determine the actual magnitude. The magnitude can also be determined mathematically by using the Pythagorean theorem, and measuring the x and y components 22y+x=Rr. (eq. 1) The angle which the vector makes relative to the x axis can be found by using o180arctan±⎟⎠⎞⎜⎝⎛=xyθ. (eq. 2)
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