SCHWEITZER_LAB_1

7 e

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Unformatted text preview: hink is the advantage to using a perpendicular coordinate axes (where the angle between x and y axes is 90°) over another coordinate system where the axes are not perpendicular? By using a perpendicular coordinate system, we can use th e Pythagorean theorem and other trigonometric functions when analyzing vectors. It also allows us to calculate the different components of a vector because the x and y components of a vector are measured in relation to the x and y axes. Also, computing the to use these functions. Additional Analysis 1. 11 using only the magnitudes and angles of the multiple path vectors (no components). How does your answer compare to adding them via components? Be sure that you include a sketch or plot indicating the vectors and angles used for the determination. Given the triangle in figure e below, the Law of Cosines states that for any triangle, c2 = a2 + b2 2abcos(C). Because of this law, we can determine r11 using only the magnitudes and angles of the multiple path vectors. Our calculated value using path vectors was 15.03, and our calculated value using the Law of Cosines was 13.18. The actual measured value of r11 was 14.9, so the path vector method was more accurate. See the figure below for calculations. 7 (e) 2. magnitude (Ax |A|, Ay |A|) is a function of sin and cos functions. Show that your individual vectors from your measurements fit this plot. As the table below shows, the cos ­1 of Ax |A| and the sin ­1 of Ay |A| equal the fact a function of the sin and cos functions. As the table shows, our data proves this relationship to be true for our experimental results. 8 Experiment #2: Vectors in Alternative Coordinate Systems Procedure In this experiment, we specified positions on a vector square. To do this, we found the magnitude and angle of vectors from the origin to specifically marked positions on the square. Using the vector's magnitude and angle we measured and recorded the x and y components for each vector. A summary of the data gathered is shown in the table below. Data from Table 2.3: Origin 2 was obtained from a fellow classmate, because we were unable to gather this data ourselves due to time restraints. However, for the purpose of this lab, we referred to these calculations as our own. Data Analysis 1. Use the information you recorded to calculate the angle through which the vector ­ square was rotated. To calculate the angle through which the vector ­square was rotated, we compared the difference between each of the correspon...
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