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Theory Consider a vector A that lies in a plane. It can be expressed as the sum of two components. The components are usually chosen to be along two perpendicular directions. The vector A can be resolved in to its a- and y-components by drawing two lines perpendicular to the r- and y-axes. Then A, and Ay are the x and y components of A, respectively. Ax = Acoso, (1) Ay = Asine. where A = [A| = VA; + A, is the magnitude, or the absolute of the vector A. Let's consider vector C, which is a sum of two vectors A and B C = A+B (2) The magnitudes of the two vectors can not be added like regular numbers 3 However, the r- and y- components of these three vectors do satisfy such relations: C, = As + B. , (4) Cy = Ay + By , where A, = Acosta , (5) Ay = Asin a , By = Bcos du , By = B sino- After the components of vector C are known, its magnitude and angle to the a-axis could be determined by: C = ICI = \\/C+c3, (6) 0. = tan ' (). This online laboratory experiment will be largely devoted to finding the compo- nents, magnitudes and angles for a sum or difference of two vectors A and B. 2 Useful resources 2.1 Educational websites . https://www.grc. nasa. gov/Www/K-12/airplane/vectadd. html . https://www. physicsclassroom. com/class/vectors/Lesson-1/Vector-Addition 2.2 YouTube videos . https://www. youtube. com/watch?v-HseRUq-IACw . https://www. youtube. com/watch?v=165E_x0MgLc . https://www. youtube. com/watch?v=81y6cEyolaI and many-many others available online. 3 Procedure 1. Start by clicking on the following link: https://phet . colorado. edu/sims/html/vector-addition-equ latest/vector-addition-equations_en . html 2. Focus on a control panel in the upper right corner of your screen. Make the following modification to its settings: . Remove (disable) the V-checkmark for c-vector 7- . Enable the ticks for Values O Values and Angle 20 0 4. below the one. . Move down to the "Components section" and choose any available option to make the components visible (change the default "invisible" option to any other, such as K. ). . Move further down to the "Add (+) Base vectors" option Base Vectors and change the initial setting to any finite values (each of you is expected to choose different values of the vector components). Record your dz, by, a, and a, in your lab. report. 3. Now your screen should look similar to what is shown in Fig. 1. You may also take a snapshot of your screen and attach it to your lab report (optional). No vector selected Components - Blass Vectors 20 4 40 rector Addition: Equations PRET : Figure 1: (Color online) Schematics for Step 3. . Calculate the components, magnitude and the direction (ange to the horizontal) for vector c = a + b using Eqs. (4) and (6). Attach a detailed calculation to your lab. report. 5. Enable the uppermost checkmark for vector & - and compare the answer c and Oce (experimental) with the results co and fe,th (theoretical) which you obtained. You may not have exactly the same results due to some calculation error. Find the percent error as % error = 2 Cth Cel . 100%. (7) Cth + Ce and 10ce - dethl . 100%. % error = 2 dee + Beth (8)