Using the Component Addition Method

Classical Physics - Physics theories and other related topics
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Vectors COMPONENT ADDITION METHOD Rev. 0 Page 21 CP-02 3. Mathematically combine all y-axis components (+y at 270 = -y at 90 ). o o 4. Resulting (x,y) components are the (x,y) components of the resulting vector. The following examples illustrate vector addition using the component addition method. Example 1: Given the following vectors what are the coordinates of the resultant vector, that is, the sum of the vectors? F = (4,10), F = (-6,4), F = (2,-4), and F = (10,-2) 1 2 3 4 Step 1. Determine the x- and y-axes components of all four original vectors. x-axes components = 4, -6, 2, 10 y-axes components = 10, 4, -4, -2 Step 2. Mathematically combine all x-axis components. F = 4 + (-6) + 2 + 10 x F = 4 - 6 + 2 + 10 x F = 10 x Step 3. Mathematically combine all y-axis components. F = 10 + 4 + (-4) + (-2) y F = 10 + 4 - 4 - 2 y F = 8 y Step 4. Express the resultant vector. The resultant components from the previous additions are the coordinates of the resultant, that is, F = (10,8). R Example 2: Determine the resultant, F . R Given: F = 30 lbf at 0 , 10 lbf at 90 1 o o F = 50 lbf at 0 , 50 lbf at 90 2 o o F = 45 lbf at 180 , 30 lbf at 90 3 o o F = 15 lbf at 0 , 50 lbf at 270 4 o o

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