Physics Laboratory Worksheet in Vector Addition In this Worksheet, we are going to :1- Understand the Nature of vectors 2- Learn how to Add Vectors 3- Calculate the Resultant force from two vectors using Phet Simulation Firstly, what is a Vector? A Vector in physics, is a quantity that has both magnitude and direction. ... It is typically represented by an arrow whose direction is the same as that of the quantity and whose length is proportional to the quantity's magnitude. Vectors could or could not be exactly on the x or y axis, But we can still calculate the Resultant Force regardless. There are a few ways to show the direction of a vector ; x and y components, polar coordinates, up and down, and left and right. A great example to distinguish a scalar from a vector is to compare distance (a scalar) with displacement (a vector). If a person walks for 250 m North and then 250 m South then the Distance he’d covered would be 500 m, but if we were to calculate the displacement in the same exact example, then it would be 0 because his starting point was the same as his end’s. Example #1: Percy walks 7 meters to the east, then 8 meters north, and then 4 meter west. The graph below shows this progression. Andreas has travelled a total distance of 18 meters, because 5 m + 6 m + 7 m = 18 m. To find his displacement we need to determine how far his final position is from his initial position, and in what direction he would have had to travel to get from the start to the finish. (For now, we will not worry about the direction.) You add up all the east-west components (remembering that east is positive and west is negative) and you get a total x-component of 3 m. You only have one north-south component, so that is 8 m. To find the resultant vector, which is the displacement, you make a new triangle with the total x –component ((1 m) and the total ycomponent (7 m) and you find the hypotenuse, 8.5 m. Find the total Distance and Displacement covered in each of the following scenarios:- 1- Bailasan walks for 3 km north, 1 km west and 5 km east (calculate in km) 2- A bird flies 12 blocks north, 5 south, 2 west and 7 east (calculate in blocks) 3- A person walks 12 m east and , 6 m west (calculate in meters) 4- Usain Bolt runs for 590 m west ,43000 cm east and 1.2 km west (calculate in meters)(100 cm = 1 m)(1000 m = 1 km) Solving vectors with x and y components :Another way to write this type of problem is to use x and y –component notation instead of using the compass directions. This is when you write things in the form (x,y). To solve this type of problem you need to add up all the x-components and, separately, add up all the y-components. Sometimes you will be asked to put the result on a graph, other times you can just write the result in x and y – component notation. Keep in mind that sometimes you will be given vectors with certain angles from which you will have to manually extract the values of the x and y components and then add them up (x1 + x2 = X resultant) to calculate the magnitude of the Resultant force or degree if necessary. Example :A force of 15 N with a degree of 31.6o is implied on an object And, another force of 14.3 N with a degree of 77.9o is implied on the same object. - Calculate the MAGNITUDE and DEGREE of the Resultant Force. X1 = 15.3cos(31.6) = 13 N X2 = 14.3cos(77.9) = 3 N Y1 = 15.3sin(31.6) = 8 N Y2 = 14.3sin(77.9) = 14 Xr = X1 + X2 = 16 N Yr = Y1 + Y2 = 22 N Resultant Force = √162 + 222 =27.2 N Angle of the Resultant vector = tan-1(22/16) = 54o We can also use the graphical simulation Phet to expand our knowledge in Adding Vectors and explore how vectors are added geometrically (you can calculate analytically and approve your work from phet) - Visit this link “ https://phet.colorado.edu/sims/html/vectoraddition/latest/vector-addition_en.html ” and select either ‘Explore 2D’ or ‘Lab’ (shown in Figure 1.1) - Adjust the origin of the graph to be in the center (shown in Figure 1.2 below) - Familiarize yourself with the website and adding vectors. - When adding vectors make sure you use the head to tail method to get the correct resultant vector (elaborated in Figure 2.1) then make sure to click on the Sum box to display the resultant vector Figure1.1 Figure 1.2 Figure 2.1 Data Analysis:Use the givens in the chart below to calculate x and y components of each vector in order to find the magnitude and degree of the resultant vector. 1- Write the resultant vector using head to tail method (graphical method). 𝑠⃗ = .................N θR = .................... 2- Write the magnitude and direction of 𝑎⃗ and 𝑏⃗⃗ in table (1), and then calculate the resultant force 𝑠⃗ using the analytical method. Magnitude Direction (N) (degree) 𝑎⃗ 17.7 16.4 𝑏⃗⃗ 12.4 104.0 Force (N) x-component y-component 𝑠⃗ If the statement is correct, check with mark with and if incorrect - Vectors have magnitudes only, and scalars have both magnitudes and degrees ( ) - The resultant Vector is the sum magnitudes of all vectors and their directions ( ) - The total displacement can NOT be equal to zero ( - The resultant vector has a magnitude and a degree ( ) ) - The total distance covered CAN be equal to zero in a scenario where at least one 1 m is covered in any direction and another 1m in a another random direction ) ( ) - The equilibrant vector has the same magnitude and opposite direction of the Resultant vector ( ) Questions:1- What is the difference between Scalars and Vectors 2- If a person walked 10 m in a random direction and then another 10 m in another random direction, could his displacement be equal to zero? If yes, demonstrate 3- In the second question, could the person’s distance be equal to zero? If no, explain why 4- What are the conditions for two vectors to be equal? Critical thinking question:- If the resultant force vector is of 10 N magnitude in the positive y axis direction (North), find the Equilibrant Force. (like shown in figure 3.1) Figure 3.1