You will have to make a physics report.

Your work will require to include all these following items:

1. GOALS (briefly but precisely state the goals of the experiemnt)
2. THEORY (formulas, derivations, etc.) and DIAGRAMS/FIGURES
3. PROCEDURE and DRAWINGS/PHOTOS of THE EXPERIMENTAL SET UP
4. DATA (measurements, expressed individually and/or in tables)
5. GRAPHS, MUST be computer-generated. (Plot a Graph in Excel") MUST INCLUDE 3 GRAPHS
6. CALCULATIONS and RESULTS (extracting information from tables and graphs, and ERROR calculations)
7. CONCLUSIONS and DISCUSSION

Lozrans DATE Lab # 1 cont. 09 / 13 / 2023 8) Using x vs + graph, calculate the average velocity ( for displacement around 70 cm ) Vav = Av Yay =" (0. 136) - 10.587)_ -0-451. (0 . 85 - 62 . 0 ) - -- 1.2 - = 0.376 m/ s XO = 0.8+ = vo= 0. 136 m/s X = 2. 0 +. = 1 = 0.587 m/s 9 ) Calculate the average velocity using the vist graph for the same two times used in part (B ) : Var = Z ( VitVF ) + = 0.85 + = 2.05 = z ( Vo+ v ) Var = = (0 . 136 + 0. 587 ) Var = 4 (0. 136 + 0.587) Var = 0.362 m/s Var =0.362 m/s 30 M 290 10 ) The Logger Pro software is able to calculate average of the quantity that is graphed . To do this , highlight the appropriate portion of the vist graph and use this option marked stat to find the average of velocity . - Does this agree w/ part ( 8 ) + (9 ) ? V yes 11) Verify the geometric rules: (Use software: top page symbol of a curve a ) Slope of X = V , lie , the slope of the tangent line to * Vs + curve at any point = instantaneous velocity at that point ) * Picture taken b)slope of v= a, lie, the slope of the tangent line to V vs + Arve at any point = instantaneous acceleration at that point )Lab 1 1-D Kinematics Objectives: 0 Study 1-D kinematics (motion on a straight line with constant acceleration) 0 Collect data as a cart moves freely on the smooth (almost frictionless) track 0 Study motion graphs x '05. t, I: vs. t, and :1, vs. t, understand the significance of positive and negative signs for position, velocity, and acceleration 0 Calculate average velocity using the motion graphs 0 Calculate instantaneous velocity and acceleration as slopes of the position and velocity curves. 0 Calculate acceleration due to gravity using a free-falling ball 0 Observe a special motion with variable (non-constant) acceleration using an oscillating mass attached to a vertical spring INTRODUCTION We use Vernier Dynamic Track system equipped with a motion detector which is interfaced to a computer using Logger Pro software. The data is then processed by the computer and appropriate graphs are generated for further analysis. A brief review of 1-D kinematics will be done in the lab prior to the experiment. PROCEDURE . Connect the motion detector to channel 1 of the Logger Pro data acquisition (interface) device (which is connected to a computer). Run the Logger Pro software on the computer and select motion detector on the interface: Experiment -)Set Up Sensors 9Lab Pro I 9Motion 9Motion Detector Normally you would see 2 graphs: one for position and one for velocity. You need to use the insert option to insert a graph for acceleration as well. (Before doing that, decrease the size of the 2 graphs so you can fit in the 3rd one on the screen!) Note: there is switch inside the motion detector for choosing Cart or Ball (larger moving objects). If not doing experiment with the cart on track, it is recommended to select Ball for better accuracy. . Place the motion detector at the end of the track, as close as possible to 0 cm mark, facing along the track. Click Collect (green button on top of the page) on the software to start collecting data. Move your hand back and forth in front of the detector to get a sense for how the system works. The goal is to understand how a coordinate system (an X-axis) is set: see the graphs on the computer screen and understand where the origin is and which way the positive sense of the X-axis is pointing to (Le, away or toward the detector?) (Hint: the Auto Scale option on top of the computer screen of the software (square with letter A on it) is very helpful!) . Push (briey) the cart gently away/toward from the detector and try to create a constant positive and negative velocity for the cart while collecting data. Take a screen shot of the 3 graphs of position, velocity, and acceleration vs. time (x, o, and :1, vs. 1*) to include in your lab report. A very useful app to create custom screen shots in Windows is called Snipping Toolr and can be found easily by searching for it under the Start button on Windows. (WARNING: The cart and the detector are very sensitive devices and can be damaged easily! Stop the car appropriately at the end of the track and avoid any collision! You may want to use the Stopper at the end of the track! . Increase one side of the track few inches to create a mild incline. This provides a small constant acceleration when the cart is pushed up the ramp or released to slide down the ramp. 5. Now create the following 4 cases, while collecting data and save screen shots of the 3 graphs (x, v, and a, vs. t) for each case: (a) Speeding up in the positive direction (1:!) Slowing down in the positive direction (c) Speeding up in the negative direction (d) Slowing down in the negative direction Include the 3 graphs for each in your report (label them appropriately!) 6. Make sure your findings agrees with the following table that we have studied in the lecture. ' Direction of ' Away ' Away ' Toward ' Toward Motion Si of v + + - - Sign of a + - + - Result Speeding Up Slowing Down Slowing Down Speeding Up 7. Collect a new set of data for the following case: speeding up moving away from the detector. Start the cart around 20 cm mark from the detector, i.e., the cart's black reector plate is about 20 cm mark, if the detector is at 0 cm mark (the origin). Release the cart and collect data for a displacement of about 70 cm. (You Do not need to stop the cart at 90 cm, nor stop collecting data when the cart is at 90 cm. Once the graphs were generated by the computer, you may simply focus on the portion of the graph corresponding to displacement of roughly from 20 cm to 90 cm.) Note: When the detector is on the table touching the 1} cm mark on the track, the actual detecting part is about 3 to 4 mm behind the 0 cm mark! This means the actual positions are off by this amount. You should double check this: leave the cart at rest a specific mark on the track and measure its position by collecting 10. 11. data and observe the position graph. (In any case, this would not be important if you are measuring the displacements.) Using the x vs. t graph, calculate the average velocity (for a displacement around 70 cm via: x 1'11:: = E Now calculate the average velocity using the I) vs. t graph for the same two times used in part (8) via: 1 \"at: = 2 (vi + vf) Your result here should agree with your result in part (8). (Recall that equation in part (9) is correct when the acceleration is constant, which is the case here! The Logger Pro software has the capability of calculating average of the quantity that is graphed. To do this, highlight the appropriate portion of the v vs. t graph and use the option (on top of the page) marked Stat to find the average of velocity. Does the result agree with your findings in parts (8) and (9) ab0ve? Verify the geometric rules: (a) Slope of x = "0 (Le, the slope of the tangent line to x vs. t curve at any point = instantaneous velocity at that point) (b) Slope of o = a (i.e., the slope of the tangent line to I: vs. t curve at any point instantaneous acceleration at that point) You may measure the slope of the tangent line using the software: it is the button on top of the page that has a symbol of a curve with a tangent line next to letter M). Choose 2 different points on you position graph (i.e., at different times). Then nd the corresponding values on the velocity graph for the same 2 points in time. Repeat the process for the velocity and acceleration graphs. Record your findings in the lab report. Briey but precisely state the GOAL(S) of the experiment. Include a short but complete and self-contained account of the THEORY behind the experiment. Here you must begin with the basic physical principles and concepts and relevant equations (normally given in the text and/or the lab hand out) and use them to derive any specific formula used in the experiment. (The theory is described in the text, lab handouts, and will also be covered briey at the beginning of each lab session on the board). You must also include in this section any FIGURE or DIAGRAM that is related to the formulas and experiment. These are simple figures and drawings containing important information such as some of the symbols used in the equations. 4. Next you will need to include the PROCEDURE for the experiment in clear and distinguished NUMBERED STEPS. (e.g. we set the device X to measure the quantity Y, n-times etc). You need to include the necessary drawings or photos of the experimental setup in this section. (Perhaps you could take a pic with your cell phone camera.) 5. The tables of data and other numeric results of measurements (DATA) come next. Make sure you include the physical units for all date presented. Data must be TABULATED- avoid including the data within the text. 7. Often you will need to calculate the slope of your graph (if it is a straight line) to extract information about a physical quantity you are measuring. Excel (or similar software) does this easily. You may NOT calculate the slope by hand. (a) In general, you will use the value of the calculated slope to calculated EXPERIMENTAL VALUE of the physical quantity you are after. We use the subscript \"exp\" for this value. (b) The THEORETICAL VALUE (or sometimes the actual value provided otherwise) for the quantity in question is known or given some other way. We use the subscripts \"th\" for the theoretical value. You will need to compare the experimental and theoretical value and measure the ERROR (as described below) (c) The ABSOLUTE ERROR (Also see item (e) below) Let's denote the physical quantity we are measuring by X . Then if we use X exp and X m for experimental and theoretical values respectively, the absolute error is Eabs:|X1h _ Xexp where the vertical lines indicate absolute value. Note that Em has the same unit as X exp or X m. In some cases (where there is no graph of data and no slope calculation) X6x13 is the AVERAGE value of results of several runs (measurements) on the quantity X . ((1) Almost always we are interested in PERCENT ERROR, which is dened by E \"I\" x 100 % XI}: %E= The result should be presented as a percentage. As a rough rule of thumb, a percent error of more than 10% indicates a serious problem with your measurements or calculations. Note that the percent error is a quantity with no dimension or unit and it is reported as a positive value. (e) In certain circumstances a theoretical value is not available. In these cases, we measure the quantity of interest using two different experimental methods. Each experiment may itself include a number of repetitions but the average of all runs in each method is to taken as the nal result for that method. Suppose that the final results of the two methods are labeled as X 1 and X 2. The percent error is then defined by: | X1 X 2 | Xl + X2) 2 8. Finally you will need to briey discuss the possible sources for errors and include a short summary related to the goal(s) and the result(s) of the experiment. %E= x100% Logger Pro - slowing down in negative direction.cmbl File Edit Experiment Data Analyze Insert Options Page Help X OGBO Page 1 Collect Latest Time Position Velocity 1.0- (S) (m) (m/s) 0.8- 0.05 1.006 0.000 0.10 1.006 0.001 0.6- Position (m) 0.15 1.006 0.001 0.4- 0.20 1.007 0.000 0.2- 0.25 1.006 -0.001 0.30 1.006 0.000 N- 0.35 5 1.006 0.000 8 Time (s) 0.40 1.006 0.000 9 0.45 1.006 0.001 10 0.50 1.007 0.000 0.5- 11 0.55 1.006 -0.003 12 0.60 1.006 0.000 13 0.65 0.0- 1.006 0.001 Velocity (m/s) 14 0.70 1.006 0.000 15 0.75 1.006 0.000 -0.5- 16 0.80 1.006 -0.002 17 0.85 1.006 -0.002 18 0.90 1.006 0.000 19 0.95 N- 1.006 0.001 W - 4 5 20 1.00 1.006 -0.001 Time (s) 21 1.05 1.006 -0.013 22 1.10 1.006 -0.040 Acceleration (mis?) Position m 2 3 Time (s) Type here to search Micros... File Ex. e Pace U. Logge. 2:41 PM 9/13/2023Logger Pro - Slowing down in positive direction.cmbl File Edit Experiment Data Analyze Insert Options Page Help X OGBO Page 1 Collect Latest Time Position Velocity 0.7- (S) (m) (m/s) 0.05 0.186 0.008 4 0.5- 0.10 0.186 -0.004 Position (m) 0.15 0.186 0.000 0.3- 0.20 0.186 0.000 0.25 0.186 0.000 0.1 - 0.30 0.186 0.000 0.35 0.186 0.000 8 Time (s) 0.40 0.186 0.001 9 0.45 0.186 1.0- 0.000 10 0.50 0.186 0.002 11 0.55 0.186 -0.002 12 0.60 0.186 0.001 13 0.65 0.186 0.000 Velocity (m/s) 14 0.70 0.186 0.0- 0.000 15 0.75 0.186 -0.001 16 0.80 0.186 -0.007 17 0.85 0.185 -0.011 OUL 18 0.90 0.186 -0.017 19 0.95 0.181 0.037 N- 20 1.00 0.181 (0.977, 0.52) 0.250 Time (s) 21 1.05 0.205 0.483 22 1.10 0.237 0.583 N Acceleration (mis?) Position m Time (s) Type here to search Micros... File Ex. B e Pace U. Logge. 2:43 PM 9/13/2023Logger Pro - speeding up away from sensor.cmbl X File Edit Experiment Data Analyze Insert Options Page Help OGBO Page 1 Collect Latest 1.0- Time Position Velocity (S) (m) (m/s) 0.8- Time: 1.00 s 20 Position Slope: 0.212 m/s 1.00 0.304 0.212 4 21 1.05 0.315 0.6- 0.231 Position (m) 22 1.10 0.327 0.252 0.4- 23 1.15 0.340 0.272 24 1.20 0.355 0.289 0.2- 25 1.25 0.369 0.307 0 N- C - 26 1.30 0.385 0.327 (0.998, 0.310) Time (s) 27 1.35 0.402 0.346 28 1.40 0.420 0.7- 0.363 29 1.45 0.438 0.383 Time: 1.00 s 30 1.50 0.458 0.402 0.5- Velocity Slope: 0.379 m/s/s 31 1.55 0.478 0.422 32 1.60 0.500 0.440 0.3- Velocity (m/s) 33 1.65 0.522 0.455 34 1.70 0.546 0.475 0.1- 35 1.75 0.570 0.495 36 1.80 0.595 0.511 37 1.85 0.621 0.529 -0.1- N - 38 1.90 0.648 0.550 39 1.95 0.676 0.568 Time (s) 40 2.00 0.705 0.587 41 2.05 0.735 0.606 o Time: - S Acceleration Slope: 8.796E-308 m/s /s Acceleration (mis?) Position 0.304 m N. Time (s) Type here to search Micros... File Ex. e Pace U. Logge. 2:45 PM 9/13/2023Logger Pro - Speeding up in negative direction.cmbl File Edit Experiment Data Analyze Insert Options Page Help X OGBO Page 1 Collect Latest Time Position Velocity 1.0- (S) (m) (m/s) 0.8- 0.05 1.005 0.004 0.10 1.005 -0.002 0.6- Position (m) 0.15 1.005 0.000 0.4- 0.20 1.005 0.001 0.2- 0.25 1.005 0.000 0.30 1.005 0.000 2 W - 0.35 1.005 0.001 Time (s) 8 0.40 1.005 0.002 9 0.45 1.005 0.003 10 0.50 1.005 0.000 0.0- 11 0.55 1.005 0.000 12 0.60 1.005 0.000 13 0.65 1.005 -0.001 Velocity (m/s) 14 0.70 1.005 -0.003 15 0.75 1.005 -0.008 -0.5- 16 0.80 1.005 -0.020 17 0.85 1.003 -0.038 18 0.90 1.001 -0.057 O -+ 19 0.95 0.997 -0.077 4 20 1.00 0.993 -0.095 Time (s) 21 1.05 0.988 -0.112 22 1.10 0.982 -0.129 Acceleration (mis?) Position m N- 3 Time (s) Type here to search Micros.. File Ex. e Pace U.. Logge. 2:44 PM 9/13/2023Logger Pro - Speeding up in positive direction.cmbl File Edit Experiment Data Analyze Insert Options Page Help X OGBO Page 1 Collect Latest Time Position Velocity 1.0- (S) (m) (m/s) 0.8- 0.05 0.183 0.0014 0.10 0.183 0.006 0.6- Position (m) 0.15 0.184 0.005 0.4- 0.20 0.184 0.000 0.2- 0.25 0.184 -0.008 O - 0.30 0.182 -0.006 N- Co- 0.35 0.183 0.000 8 Time (s) 0.45 9 0.50 10 0.55 0.5- 11 0.60 0.185 -0.008 12 0.65 0.180 -0.029 13 0.70 0.180 0.0+ 0.005 Velocity (m/s) 14 0.75 0.184 -0.011 15 0.80 0.178 -0.014 -0.5- 16 0.85 0.181 -0.001 17 0.90 0.179 -0.001 18 0.95 0.181 0.012 -1.0 19 1.00 0.181 0 0.007 N- 20 1.05 0.180 0.017 (0.627, 0.68) Time (s) 21 1.10 0.183 0.019 22 1.15 0.185 -0.019 Acceleration (m/s? ) Position m 2 C - Time (s) Type here to search Micros.. File Ex. @ Pace U. Logge. 2:44 PM 9/13/2023