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Physics 1 Lab Lawrence Technological University LAB 4 - DATA MODELING Goals: • Record data for a cart going up and then back down a tilted ramp. • Match the real world data to a computer model from a spreadsheet. Part 1 Up and Down the Ramp Making a cart accelerate down a steep ramp is similar to dropping a ball from a height. In this activity, you will give the cart a push up the ramp and let it return. This is similar to throwing a ball straight up in the air, but the motion is slower and easier to study. Predictions Suppose you throw a ball straight up in the air. Qualitatively, what is the velocity at the moment that the ball reaches its highest point and is about to start back down? At this same moment, is the acceleration positive, negative or zero? (Assume that the positive direction is downward.) Velocity: _______________ Acceleration: _______________ If you give the cart a push up the ramp and release it, what will the velocity be at the moment that the cart reaches its highest point and is about to start back down? At this moment, is the acceleration positive, negative or zero. (Assume that the positive direction is down the ramp-- away from the detector.) Velocity: _______________ Acceleration: _______________ Sketch your predictions for the velocity-time and acceleration-time graphs for the cart moving up and down the ramp. Velocity (m/s) Acceleration (m/s2) Figure 1 - Prediction graphs for Up/Down cart motion Now you will test your predictions. Rev 09/01/08 Copyright © 1992-2008 Scott Schneider Lab 4 Data Modeling - Page 1 of 9 Physics 1 Lab Lawrence Technological University Preliminary activities 1. Prepare equipment. Connect the Motion detector to the USBLink and then to the laptop. It would be very helpful to look at the online help page for this lab. Start the DataStudio software. 2. Load the experiment file. Load the DataStudio file Lab04_DataModel.ds from the Physics1 folder. 3. Prepare program for graphing. Make sure the graph layout is set to display two graphs - Velocity and Acceleration – and the time axis is set for at least 10 seconds. Note there is one common time axis for both graphs. [See the graph layout help page for information on how to make these changes in DataStudio if necessary.] 4. Preparing track and cart. Set up the ramp similar to the way you did in the previous lab. (One end should be tilted up off the table--use the “high tilt” position - about 6-7 cm high). We will be starting the cart at the bottom of the ramp, giving it a push upward, and letting it naturally slow to a stop, and then roll back down (catching it as it reaches the bottom). Try a few sample starts to get a feel for how much of a push is needed to move the cart close to, but not closer than 0.5 meters from the detector. 5. Starting the graphing process. When you are ready to start graphing, click START and then release the cart when the clicking sound starts. Give the cart a push up the ramp, but release it quickly, and keep your hand free of the detector. Make sure that the program is graphing before you let go of the cart. (Also, make sure the detector doesn’t “see” your hands.) 6. Sketching graphs. When you get a good run, sketch the graphs on the axes below. Do not use a run where the cart came closer than 0.5 meters to the detector. Sketch the graph on the Data/Question Sheets. Save your experiment (Call it UPDOWN.ds). Leave DataStudio running! 7. Questions. Move to the Data/Question sheets to answer a series of questions concerning your sketch. INSTRUCTOR-GROUP DISCUSSION: Discuss the above questions with the class. Part 2 : Introduction to the current data graphs You should have graphs that look similar to the ones shown here: (Note, the two regions of interest, described on the next page, are shown in the rounded rectangles in this image.) Figure 3 – Graphs of Up/Down cart motion Rev 09/01/08 Copyright © 1992-2008 Scott Schneider Lab 4 Data Modeling - Page 2 of 9 Physics 1 Lab Lawrence Technological University During the first part of the motion, the cart was Top of incline - cart moving up the incline (velocity is negative -- toward reverses direction. the detector), it stopped and came back down the incline (velocity is positive). Considering the Acceleration vs Tim acceleration data, we see a nice "constant" region of 1 positive acceleration in the middle of the run. Looking 0.5 Acceleration closely, you will see that there are two relatively 0 distinct magnitudes, one for the way up, and one for -0.5 the way down the incline. This is also reflected in the -1 -1.5 slight "kink" in the slopes of the velocity vs. time 0 0.6 1.2 1.8 2.4 3 3.6 4.2 4.8 Time curve. We will investigate these different accelerations. High accel. Low accel. To do this, we will introduce the methods of up incline down incline "data modeling." When analyzing data, it is sometimes important to see if it fits a certain model, or at least fits a Figure 4 – Different Accelerations certain function. We have two excellent opportunities in this data set -- a straight-line relationship between velocity and time, and a quadratic relationship between distance and time. We have to split the data set in half, because we have two different constant acceleration values. The two different accelerations can be explained as follows: • On the way up, there is a component of gravity acting down the incline, and there is a component of friction acting opposite the motion {also down the incline.} • On the way down, the gravity force is still down the incline, but now the frictional contribution has reversed and acts up the incline, so the magnitude of the acceleration is less. Part 3 - Data Preparation Before we export the data (so that we can import it into Excel), it would also be useful to know the time ranges in which we will investigate. The two ranges that we want to use are shown in the diagram to the right. Figure 5 - Up and down regions on Acceleration graph 1. Looking for the “best” regions. Use the Smart Tool on the acceleration graph, and locate a reasonable start/stop point for each of the motions: up incline and down incline. Pick regions where the acceleration is reasonably constant - avoid the “junk” at the beginning and end of the region (and avoid the “dip” in the middle). We will record these values below, so that we can pinpoint those times in the Excel worksheet. Fill in the chart below: Up incline: start time ________ end time _________ (higher acceleration) Down incline: start time ________ end time _________ (lower acceleration) Rev 09/01/08 Copyright © 1992-2008 Scott Schneider Lab 4 Data Modeling - Page 3 of 9 Physics 1 Lab Lawrence Technological University Part 4 - Moving the Data from DataStudio to Excel 1. Launch Excel. We will use Excel to analyze the data. We can easily add equations and graphs to the spreadsheet, and it allows us to change numbers and see the result on the graph immediately. To ensure that the data can be structured the right way, there is a “template” already created to help us through the modeling process. 2. Sliders and Security settings. The template we will use makes use of sliders to change the variables for the model. [The spreadsheet should work without needing any “macro security settings” to be changed – but follow those directions on the online help page if necessary.] 3. Load the modeling template. In the DataStudio PHYSICS1 folder you’ll find the excel spreadsheet P1Lab04_Modeling_ds.XLS – load that into Excel. [Location: C:\Program Files \DataStudio\ LTU_Physics\Physics1]. You might want to save it under a new name, as a working copy. 4. Description of the modeling spreadsheet. There is an Information sheet, and then three data sheets in the file (“Data from DataStudio”, “Up Incline”, and “Down Incline”). We will copy the data from DataStudio onto the second sheet “Data from DataStudio”. Then we will copy the sections we identified in step 3.1 to the other two sheets. 5. Copying the data from DataStudio to Excel. Follow the directions on the first page of the Excel file, or on the online help page for this lab – copy the active data run onto the first page of the Excel file. Then save the file (under your new filename). As long as you have identified the time ranges you need for the “up incline” and “down incline” sections in Part 3.1, you can now close DataStudio. At this point, you have the DataStudio data in 6 columns on the “Data from DataStudio” page. We will copy the appropriate sections of that data to the “Up Incline” and “Down Incline” pages (which contain equations and graphs for us to use in the modeling process). You recorded the start time and end time for the two sections of interest ... we will use that information to shift that data into pre-formatted template pages. There is a diagram indicating the information that will be copied on the Online Help page. Part 5 – Moving the data into the Excel pages Copying data to the Excel sheets: 1. Copying the Up Incline data. On the “Data from DataStudio” page, highlight the cells that make up the range you identified as the UP INCLINE section (use the time range from Part 3). Select COPY from the Edit menu. Switch to the “Up Incline” sheet, click in the A2 cell, and select PASTE from the Edit menu. 2. Copying the Down Incline data. On the “Data from DataStudio” page, highlight the cells that make up the range you identified as the DOWN INCLINE section (use the time range from Part 3). Select COPY from the Edit menu. Switch to the “Down Incline” sheet, click in the A2 cell, and select PASTE from the Edit menu. Rev 09/01/08 Copyright © 1992-2008 Scott Schneider Lab 4 Data Modeling - Page 4 of 9 Physics 1 Lab Lawrence Technological University Copying formulas down the columns: 3. Formulas on the Excel pages. On each sheet, in the cells H2-K2 there are special formulas that will calculate our new T (calc), X (calc), T (calc) and V (calc) for our model. [You might wonder why there are two T(calc) columns .. If you look at the DataStudio data, you’ll notice that the time values for the Position and the Velocity are not exactly the same {but they are in the same time base} – having two T(calc) columns means we can keep the Position and Velocity on their own “graphing” scales (even though they both refer to the same absolute time scale).] We need to copy each of these formulas down the column. “Click and drag” to select the four cells, copy them, and then paste them down as far as the DataStudio data exists to the left of the calculation columns. The cells in those columns will fill in “zeros” (except for the Tcalc columns, which should now have an increasing time count). The graphs should light up with two curves each .. but, they are most likely NOT similar since the calculated curves depend on the M and Q values – which have random default values at the moment! Part 6 - Modeling the data on Page Up_Incline The “Up Incline” page should now contain data columns for the DataStudio data and for the calculated (model) data. There are two graphs that will display the DataStudio data against the calculated (model) data. There are also some cells labeled M1, M2, and Q1, Q2, and Q3. We will change these variables of our model equations by using the sliders. (The equations in columns H-K point to these M and Q cells.) Once you start changing the M and Q cell values, the calculated columns will contain more reasonable data, and the graphs will start to “line up”. 1. Automatic graphing. The graphs should automatically graph any data in the first 100 rows (much more than we need). There should be no need to edit the Series for the graphs, but if it is necessary, click on the graph, then right click and select SOURCE DATA and then the SERIES tab, and then edit them appropriately. [Note: This should not be necessary for the normal use of the graphs.] Picking variables for the model The point of this lab is to “model” (or simulate) the real-world data from the ULI motion. We now have equations that match the graphical look of the two data sets (a straight line or a quadratic curve). The equations have random variables attached to them (via the sliders) - we have to experiment with them. Using the sliders, we can adjust the numbers in those boxes (next to the labels M1, M2, and Q1, Q2, Q3) until the true data and the model data line up together. The best way to see this is with the graphs. (Info on using the sliders is on the online help page.) 2. Modeling the Velocity curve. We are now ready to begin the modeling process. The ULI data shows a straight line on the graph. The model equations for the V (calc) column fit the format of V=M1+M2*t. Changing the values in M1 and M2 will change the shape of the V (calc) graph. Your goal is to figure out which values should be used in M1 and M2 so that the two velocity curves line up as closely as possible. 3. Modeling the Distance curve. The model equations for the X (calc) column fit the format of of a quadratic curve -> X=Q1+Q2*t+Q3*t2. Changing the values in Q1, Q2 and Q3 will change the shape of the X (calc) graph. Your goal is to figure out which values should be used so that the calculated curve lines up closely with the actual position curve. Rev 09/01/08 Copyright © 1992-2008 Scott Schneider Lab 4 Data Modeling - Page 5 of 9 Physics 1 Lab Lawrence Technological University M1 = Q1 = As you are adjusting the sliders – M2 = Q2 = Q3 = your curves will start lining up as shown. Your goal would be a “single color” curve as much as possible. (Note: the values in columns O and S are the “maximums” of the sliders – you may need to change the sign of them!) In case something happens to the equations in the (calc) columns, these are the Excel functions that should be typed into the cells listed: Cell Excel Equation Math Equation H2 +A2-$A$2 T-T0 (shifts time origin for position) I2 +$Q$1+$Q$2*H2 +$Q$3*H2*H2 X= Q1+Q2*t+Q3*t2 (quadratic) J2 +C2-$A$2 (yes A! – connects v to x) T-T0 (shifts time origin for velocity) K2 +$M$1+$M$2*J2 V= M1+M2*t (linear) 4. Save your model in progress. Keep saving your file periodically as you manipulate the model. After resizing the graphs (as suggested in the Excel sheet) – print this “UP” page for the report. Part 7 - Second data set (Down the incline): The steps are identical for the second data set, and you should have time to finish them within the class period. Notice that the “orientations” of the graphs are different for the cart coming down the incline (as they should be). After resizing the graphs (as suggested in the Excel sheet) – print this “DOWN” page for the report. Part 8 - Questions to consider for the Lab Report – See Data/Question sheet Answer on the Data/Question sheets. UP and DOWN the incline: a) Does your model match the real-world data exactly? What is your explanation for this? b) What quantity does the variable M1 correspond to in the “physics world”? c) What quantity does the variable M2 correspond to in the “physics world”? d) What quantity does the variable Q1 correspond to in the “physics world”? e) What quantity does the variable Q2 correspond to in the “physics world”? f) What quantity does the variable Q3 correspond to in the “physics world”? g) What is the relationship between M2 and Q3? Comparing both data sets (up and down): Why is the acceleration for up the incline greater than down the incline? Rev 09/01/08 Copyright © 1992-2008 Scott Schneider Lab 4 Data Modeling - Page 6 of 9 Physics 1 Lab Lawrence Technological University QUESTION SHEET - LAB 4 - DATA MODELING Part 1 Up and Down the Ramp 3. Sketching graphs. When you get a good run, sketch the graphs on the axes below. Do not use a run where the cart came closer than 0.5 meters to the detector. + - Time + - Time + - Time Figure 2 - Observation graphs for Up/Down cart motion Questions Label the velocity and acceleration graphs with— "A" where the cart started being pushed. "B" where the push ended (where your hand left the cart). "C" where the cart reached the top (and is about to start down). "D" where the cart reached the bottom again. Rev 09/01/08 Copyright © 1992-2008 Scott Schneider Lab 4 Data Modeling - Page 7 of 9 Physics 1 Lab Lawrence Technological University Explain how you know where each of these points is. ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ Did the cart stop at the top? (Hint: Look at the velocity graph. What was the velocity of the cart at the top?) Does this agree with your prediction? How much time did it spend at the top before it started back down? Explain. ___________________________________________________________________________ ___________________________________________________________________________ According to your acceleration graph, what is the acceleration at the instant the cart reaches the top? Is it positive, negative or zero? Does this agree with your prediction? ___________________________________________________________________________ ___________________________________________________________________________ Explain the observed sign of the acceleration at the top. (Hint: Remember that acceleration is the rate of change of velocity. When the cart is at the top, what will its velocity be in the next instant? Will it be positive or negative?) ___________________________________________________________________________ ___________________________________________________________________________ Compare the average acceleration of the cart on the way up (but after you stopped pushing) and on the way down (but before reaching the bottom). Are they the same? Base your answers on your velocity and acceleration graphs. ___________________________________________________________________________ ___________________________________________________________________________ Challenge What forces act on the cart on the way up the ramp (after the push). Does any force have a different direction on the way up than on the way down? Explain any differences in the acceleration going up and coming down in terms of the forces on the cart. ___________________________________________________________________________ ___________________________________________________________________________ Rev 09/01/08 Copyright © 1992-2008 Scott Schneider Lab 4 Data Modeling - Page 8 of 9 Physics 1 Lab Lawrence Technological University INSTRUCTOR-GROUP DISCUSSION: Discuss the above questions with the class. Part 8 - Questions to consider for the Lab Report UP and DOWN the incline a) Does your model match the real-world data exactly? What is your explanation for this? _________________________________________________________________________ b) What quantity does the variable M1 correspond to in the “physics world”? ____________ c) What quantity does the variable M2 correspond to in the “physics world”? ____________ d) What quantity does the variable Q1 correspond to in the “physics world”? ____________ e) What quantity does the variable Q2 correspond to in the “physics world”? ____________ f) What quantity does the variable Q3 correspond to in the “physics world”? ____________ g) What is the relationship between M2 and Q3? ________________________________ Comparing both Why is the acceleration for up the incline greater than down the incline? ____________ _____________________________________________________________________ How do I write up this lab? … What is required for this lab report? Consult the Rubric for this experiment and the “Lab Report Instructions” document (both found on the Lab Schedule page). Questions/Suggestions -> Dr. Scott Schneider - S_SCHNEIDER@LTU.EDU Portions of this laboratory manual have been adapted from materials originally developed by Priscilla Laws, David Sokoloff and Ronald Thornton for the Tools for Scientific Thinking, RealTime Physics and Workshop Physics curricula. You are free to use (and modify) this laboratory manual only for non-commercial educational uses. Rev 09/01/08 Copyright © 1992-2008 Scott Schneider Lab 4 Data Modeling - Page 9 of 9