Dear Students, Please study the theoretical pre-lab materials, check the recommended educational website and YouTubc videos given below, and try to follow the step-by-stcp instruction. If you still have any questions regarding this lab, I will also be available by Skype, Zoom.com video conference or email during our regular class time and beyond in order to provide all the necessary assistance and guidance. Please contact me at liubushka.iu@gmail.com with any questions, but please keep in mind that it might take me some considerable time to respond, especially if I receive too many of your messages at the same time. 1 Theory Projectile. motion is a form of motion experienced by an object or particle (a projectile) that is projected near the Earth's surface and moves along a curved path under the action of gravity only. Sometimes, the air resistance should be considered noticeable and included into the equations of motion. 1 .1 Acceleration Since the only force acting on the moving projectile is the gravity force F}, = my}, where g = 9.81m/s is the gravitational acceleration near the Earth surface, its horizontal acceleration equal to zero, and the vertical one - to _q (downward direction): 2 n, (1) \"r; = g. a, 1.2 Horizontal and vertical velocities The two component of the initial velocity \"At = (l) and e_.,(f = 0) could be found if the initial launch angle 6.. is known: \"0,1: = 1!\" CUB g\" . (2) 'Uu'y 'UU Sill. 6\" . The horizontal component- of the velocity of the object remains unchanged throughout the motion. The vertical component of the velocity changer-i linearly, because of the two components of acceleration given in Eq. (1). Using the velocity equation{s) for a uniform acceleration motion, we can write a; 2 \"it: = on cos 6'\" = const, (3] ii\" = en sin I91] gt . The magnitude of the velocity obtained under the Pythagorean theorem is Utof(t) = 1/ of, + try\")? = (ea cos 6'0)2 + (on sing 902. (4) It obviously depends on time. 1.3 Horizontal and vertical displacements: Once again, we use the fact that the horizontal motion of the projectile is a uniform motion (with a constant speed), and the vertical - uniformly accelerated motion. At any time t, the projectile's horizontal and vertical displacement are: x = vot cos Go , (5) y = Vot sin 60 2gt2 1.4 Total time of motion Time of flight or total time of the whole journey is obtained from the y-component of Eq. (5) by setting y = 0 (the projectile hit the ground): t = 200 sin do . (6) 1.5 Maximum height and range The greatest height that the object will reach is known as the peak of the object's motion. The increase in height will last until vy = 0, that is, Vo sin 2 00 . H = 29 (7) The horizontal range L of the projectile is the horizontal distance it has traveled when it returns to its initial zero height (y = 0) g L = 0 sin(200) . (8) The range L has its maximum value when sin(20) = 1, which necessarily corresponds to 00 = 7/4 = 45.00. The range and the maximum height of the projectile does not depend upon its mass. 2 Useful resources 2.1 Educational websites . https://courses . lumenlearning. com/physics/chapter/3-4-projectile-motion . https://en . wikipedia. org/wiki/Projectile_motion . https://www. physicsclassroom. com/class/vectors/Lesson-2/What-is-a-Projectile 2.2 YouTube videos . https://www. youtube. com/watch?v=8NLzuURxFWY . https://www. youtube. com/watch?v=pZZt357pk-I . https://www. youtube. com/watch?v=aY8z2q044WA and many-many others available online.Procedure 1. Open our present online lab by clicking on the following link: https : f/phet . colorado . edu/en/simulation/proj ectile-mot ion 2. Select Vectors window at the center of your initial menu screen. 3. Set the initial speed of your projectile to be 1'0 : 17.0 m/s and the initial launch angle 90 = 400. 4. Disable the Air Resistance checkrnark D A\" Resistance A , add Velocity vectors 8 WW Vectors Acceleration vectors 8 Acceleration Vectors 21> and Force vectors 8 Force Vectors at the right side of your screen. Launch the projectile. 5. With the vectors on1 go through the projectile's path to see the relationship between the compo nents of its velocity and acceleration and view the launch in the slow motion. Your screen should now look as follows: F'n_.|u_--:_Ii!-: \"Johan Figure 1: (Color online) Schematics for Step 5. D Air Resistance A 6. Include the Air resistance by clicking on button and set the Diameter m OII' of the projectile 1 \"'. '. L to D : 0.9m. Repeat Step 5, discuss how the path of your cannonball has changed in the presence of a nite air resistance, as well as its velocity and acceleration at the different points of the trajectory. 7. What are the magnitude and direction of the Drag Force at the different locations of the trajectory of the projectile and how is it related to its velocity? 3.1 Horizontal and vertical displacements of a projectile 8. Choose Lab window on the right side of your screen. 9. Set the initial speed of your projectile to be 1'0 2 15.0 m/s and the initial launch angle 90 = 45 0. Fire the projectile. 10. When you re the cannon, the path of the projectile is shown and with a marker drawn at. every 0.1366 of the projectile motion time, as show in Fig. 2 i I ' ' 1mm 15111.1 . r:- - 0 A I'D Figure 2: {Color onliue} Schematics for Step 5. 11. Using both equations {5}, calculate the horizontal and vertical position of the pro- jectile at the following time: 0.2 360, 0.4360, 0.6360, 0.8360, 1.0560, 1.2360, 1.4360, 1.6360, 1.8360, 2.0860. Record your results in Table 1: \"mm (t), m r.(t)= m | | | | l Table 1. Theoretical, or calculated results for the horizontal t} and vertical y(t} displacements of the projectile after each 0.2360. .. 12. Use the tracer tool to gather the data about. the pro jectile's range and height at every other marked point of its trajectory which corresponds to 0.2 360-incre1nent. Record the obtained results into Table 2: 1,, 360 0.2| 0.4| 0.6 0.8 1.0 1.2 1.4| 1.6| 1.8 2.0 (am I | | | (t), m I I I I Table 2. Experimental {measured} data for the horizontal .r(t) and vertical y(t} displacements of the projectile after each 0.2360. 13. Are the theoretical and experimental results in Table 1 and Table 2 identical or just close to each other? 14. For the initial velocity and launch angle accepted and used in Step 9, calculate the maximum height of the projectile trajectory using Eq. (7) and its range from Eq. (8). ~ In 15. Verify your calculated results from the previous Step 14 using the tracer tool at the highest and the terminal points of the investigated trajectory. A green clot at the top of the path shows the apex (or the highest point} of the path of our projectile. 4 Lab Report I am not going to demand any specific format or presentation style of your lab reports. This is completely up to you: you can type it in MS W'ord, Latex, onlinc Google documents, you can just scan the handwritten notes or even take the pictures on your phone. However, it is crucial that you: 1. Do and properly explain all Steps which are printed in bold font in the Procedure section. Each such Step or a task (printed in Bold in you manual) should be properly addressed in your lab report in all detail. Provide sample calculations which include all the equations, numbers and units for every calculation which you have performed for your lab experiment. Sample calculations means that you don't need to repeat it in all detail if the same calculation is performed multiple times, such as filling a table for different. values of a parameter. However, you will still need to do the calculation each time and put. in the results into the table. Conclusions, or main physics learning points from this experiment. Here, you should briey discuss which laws of physics you have learned and experimentally tested, what kind (s) of phenomena you have dealt with, as well as your calculations and mathematical equations. Is this experiment helpful for your science. education in general and why? Discuss the precision of your results and the percent errors, make any other comments you might think of (no one will be penalized for making critical comments regarding our course). This section should not exceed 15 lines. Here, I will specically value its originality, your own words and thoughts which are not copied from a textbook or someone else\"s report. Also, there are no specic requirements regarding the size of your lab report and, in fact, you cannot nd a professor who wants to receive and grade 30page reports but. all the questions need to be answered completely and in a lot of cases your score depends directly on the amount of relevant. and original information which you provide within a specific response. The report should be submitted to Blackboard as an Assignment on or before the posted date or (as an exception, if the Blackboard submission system failed] sent by email to liubushka. iutgmail . com