Figure 3 The opposite vector of a resultant vector is called equilibrium vector or the equilibrant. An equilibrium vector has the same magnitude but opposite in direction to the resultant vector. > =R VlP'l'UGl Lab: In this lab, we will use a virtual vector lab in the link below: httpszphetcoloradoedu/sims/htmI/vectoraddition/Iatest/vectoraddition en.htm| Part 1- Graphical Method of finding the resultant vector 1-Open the link above, click \"Explore 2D" [3 Vector Values 2- Turn off the vector values 3 Select and place a vector on the graph, with the vector's tail at the origin Questions: 1- A velocity vector 45 above the positive X-aXis has a y-component of 10 m/s. What is the value of its x-component? 2- A vector quantity can be (a) positive, (b) negative, or (c) zero. Which of these (a, b, or c, or all) apply to the magnitude of a vector? Explain in details. 8. Place the tail of the second vector on the tip of the first vector, check the \"sum\" box, and drag and place the resultant vector created with its tail at the origin. Click on \"Components\" button to obtain components of the vectors, record them in the Table 2 below, and compare the components of the resultant vector, its magnitude and direction to those obtained analytically in 7 and 8 above. Copy and paste your vector diagram below. Table 2 Vector Magnitude Direction X-component y-component First Second Resultant (virtual) 9. Copy and paste your vector diagram below. Part 3- Equilibrium Vector 1- Using the virtual lab, graphically obtain vectors j , E , and E, here if is the equilibrium vector, such that O = Al + E + E". Note: Use an orange colored vector for your equilibrium vector. (see example in figure 6 of the lab instruction handout) 2- Copy and paste the graph from step 1, in your report 3- Check your answers in step 1 analytically. Show all steps. 4- How does the equilibrium vector obtained relate to the resultant of the two vectors Al and E ? 3. Select the vector and turn on the \"Vector Values\Questions : 1- A velocity vector 45 above the positive xaxis has a ycomponent of 10 m/s. What is the value of its x-component? Z-A vector quantity can be (a) positive, (b) negative, or' (c) zero. Which of these (a, b, or' c, or' all) apply to the magnitude of a vector? Explain in details. Table 1 Vector Magnitude Direction x-component y-component First Second Resultant (Analytical) 9. Calculate the magnitude and direction of the resultant vector, and record it in the Table 1 above. 10. Place the tail of the second vector on the tip of the first vector, check the \"sum" box, and drag and place the resultant vector created with its tail at the origin. 11. Click on \"Components" button ' to obtain components of the vectors, as seen below, record them in the Table 2 below, and compare the components of the resultant vector, its magnitude and direction to those obtained analytically in 7 and 8 above. BSumb a m 29.0 a 46.4 s, 20.0 51,210 DSum> y 8 Values 1 [it Ar; 8 . Components 1- Using the virtual lab, graphically obtain vectors [1) , B , and B, here B is the equilibrium vector, such that 0 = A + B + E. Note: Use an orange colored vector for your equilibrium vector. (see example in figure 6) 2- Copy and paste the graph from step 1, in your report 3- Check your answers in step 1 analytically. Show all steps. 4- How does the equilibrium vector obtained relate to the resultant of the two vectors A and B ? , ESumb : m 27.6 a 7133.5 v. 719.0 r. 720.0 DSW_, 1. [Z Values E4 AB 8 iii Whole Universe > Measurement > Physical Quantities /\\ Scalar Vector Scalar quantity: A scalar quantity can be specified by a single number with a unit. Examples are mass, time, speed, temperature etc. Vector quantity: A vector quantity (or a vector in short) has direction as well as magnitude and a unit. Examples are force, velocity, acceleration, displacement etc. A vector is usually represented graphically by an arrow. The length of the arrow is the magnitude of the vector, while the tip of the arrow shows the direction of the vector, Graphical Method: To graphically add two given vectors shown in Figure 1, we simply choose one vector first, A , and draw it at the origin. After that, we draw second > vector B , such that its tail is on the tip of 14:. To find the sum, we draw a vector from the tail of [Z to the tip of This vector is called the resultant vector 13, and is as shown in Figure 1. Figure 1 Component or analytical method: As shown in Figure 2, a vector A can be split into two perpendicular vectors called the components of A, using trigonometry: Ax = A cos 0 Ay = A sin 0 A = Ax + Ay 0 = tan Ar 20 A 10 Ay 36.9. Ax 30 Figure 2 Figure 3 shows that the x component of the resultant, Rx, is the sum of the x components of vectors A and B; the y component of the resultant, Ry, is the sum of the y components of vectors A and B; Rx = Ax + Bx Ry = Ay + By R = RX + Ry4- Place The Tail of The Second vector on The Tip of The first vecTor, check The \"sum' box, and drag and place The resultant vector 57 created wiTh its Tail at The origin. 5- Copy and pasTe your diagram in your lab reporT. Part Z-Analytical Method of finding the resultant vector 1. 2. 3. Open The link above, and SelecT \"Lab" El Vector Values Turn off The vector values Select and place a vector on The graph, with The vector's Tail at The origin, check The boxes (values, and The angle) as shown below, and drag and move The Tip to obTain a lengTh between 15 and 20, and angle beTween 20 and 40. E] Sum > [3 Vector Values Cl Sum I Evaluas BA~ E' Camponanis