lab 2 - Addition of Vector Forces Purpose: To practice...

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6 Addition 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) x y Scale 1 cm = 1 Newton Figure 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 2 2 y + x = R r . (eq. 1) The angle which the vector makes relative to the x axis can be found by using o 180 arctan ± = x y . (eq. 2)
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7 There are two main methods used to sum vectors and to give their magnitude and direction . The resultant is the name given to the sum of a set of vectors. The two methods are the graphical method and the component method. The graphical method is accomplished by drawing the vectors on graph paper in a special way. Two vectors are added together graphically by placing the tail of the second vector at the head of the first vector. A third vector is added by placing its tail at the head of the second vector, and so on. All of these vectors must have the proper magnitude and direction relative to the x axis direction and the graph scale. To draw the proper direction of a vector you need a protractor while drawing the vector to scale requires a ruler. To illustrate this, two vectors, vectors a and b , are added together as shown in Figure 2. The third vector c is the resultant. To determine the magnitude and direction of vector c the ruler is aligned with the resultant and then laid against the scale of the graph.
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This note was uploaded on 08/25/2011 for the course PHYS 164 taught by Professor Johnjames during the Fall '09 term at MO St. Louis.

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lab 2 - Addition of Vector Forces Purpose: To practice...

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