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Apr 3, 2024

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Lab DLT – Digital lab tools • The digital lab notebook Computers crash, that’s just a fact of life. Save your work regularly throughout the lab . Paper is not banned! Before we go into the digital notebook, we want to emphasize that sometimes, it is simply easier to figure out things with paper and pencil. You should always have them available during the lab. Just make sure that you then enter the information on the digital notebook. • Normal text The notebook is a Microsoft Word document. You can also edit it with Google Docs. Students are expected to be proficient with the most basic components. Your notes should in general be inside the provided gray spaces, so they are easy to distinguish from the rest. Enter your name in the box below. Marcus Skidmore For everything else that we expect students to need during the labs, there is an Icon on the Quick Access Toolbar at the very top of the window (when you use Word in the lab computers). α Quick Access: Or: Insert tab and select Symbol. Enter below one Greek letter, the symbol for infinity, and a minus sign (note that it is longer than a dash). Ω∞−

• Tables Quick Access: Or: Insert tab and select Table. Data should always be orderly displayed in tables, including proper labels and units. However, most of the time you should produce your data tables with Logger Pro, since this software provides data analysis and graphing tools, and is thus superior to a “static” table. In section 4 of this lab, we will go over the Logger Pro basics. • Equations Quick Access: Or: Insert tab and select Equation. Insert below the following formula: For long calculations, it is perfectly acceptable to do them on paper and insert a (good) photograph of the calculations. Even better: use a scanning app (like Adobe Scan) to turn the photograph into a clean scan before inserting it. It is NOT acceptable to use hard-to-read options like sqrt(t^2-alpha^2)/3. Your instructor is a regular human whose brain does not run on HTML. • Sketches, images and the Snipping Tool Digital notebooks are convenient and green, but sometimes we just need a space to sketch things. Each lab computer has a small graphical tablet to draw sketches and diagrams. You can also do your sketches on a piece of paper and insert a (good) photograph. Microsoft Word has a tool called Draw or Ink Tools, depending on the version. Using this tool, you can now draw anywhere on the page. Draw something below.

Sometimes you will just want to transfer an image (like a snapshot of a graph) to the notebook. You could always save a JPG or PDF file, and then insert it in the Word document. However, there is an easier and faster option: use the Snipping Tool (on the Taskbar at the bottom of the screen) or any similar screen-capture tool to take snapshots of any portion of your screen. Then, copy the snip and paste it into your notebook. Readjust the image as needed (resize, crop, etc.) Use the Snipping Tool to capture anything you would like and insert it below. • Data collection Data will be collected from a variety of sources. The methods go from simple processes like reading a ruler, all the way to digital sensors connected to the computer. When sensors are used, the data is automatically collected in a software called Logger Pro . This software is in all lab and help room computers, and we will use it for data analysis. You can also download and install Logger Pro on your computer. The links and instructions to do so are at the bottom of the home page on Canvas, under “Helpful stuff”. Alternative software: once you are home, you are allowed to use other data analysis softwares of your choice to complete the data analysis. We provide some basic guidance for Google Sheets (see “Helpful stuff” on Canvas), but instructors might not be able to help you with these alternative softwares. Please note that while in the labs, you must work with Logger Pro. • Logger Pro: collecting data through sensors Whenever we use sensors that send data directly to the computer, you will need to use Logger Pro for the data collection. If a .cmbl file(s) is provided on Canvas for the experiment , use that file to open the software, to ensure that you are working with the appropriate predefined settings. Example: On Canvas, this lab’s module includes a file called Sample.cmbl . Download it and open it. In a “real” lab, this will simply provide the appropriate settings for Logger Pro. In this case, we also included some data. What is the title of the graph? Enter it in the space below. Dampened Harmonic Oscillates

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• No sensors If the data is collected manually, you should enter it directly on LoggerPro (more details on the software below). • Data analysis • Basic Logger Pro tools Open the file Logger Pro Help.pdf . This document is included next to this notebook, but it is also posted under “Helpful Stuff”. The following tasks will guide you through the most basic procedures in Logger Pro. • Modify tables and enter data • On the table, double click on the Time column. In the Column Definition tab, change the units to minutes. • Double click on the Displacement ( x ) column. This is a Calculated Column. It is generated from the formula in the Expression box. We will work on an example of a Calculated Column below. In the meantime, in the Options tab, change the Point symbol to a different shape and select a different color. • On the top toolbar, select Data and Add Manual Column, with the following parameters: Name: Time 2 Short Nm: t2 Units: s Once the column is created, add 5 random values between 0 and 10. • Select Data again, and Add Calculated Column, with the following parameters: Name: Displacement 2 Short Nm: x2 Units: m Expression: , which should be entered as 3*”Time 2”+2+sin(“Time 2”) Note that “Time 2” can be either typed or selected from the drop menu of Variables (Columns). If you cut and paste from the notebook, you will get the wrong type of quotation marks and thus an error… • Modify graphs • Right-click on the graph and select Graph Options. In the Graph Options tab, and: • Change the title of the graph to whatever you fancy. • Explore the “Connect Points” option. As you can see, the connecting lines can be misleading if the data is not “in order” (in this case, note in the table that t = 100 and t = 200 are in the “wrong” places.)

• You can manually change the scale of the graph: click and drag the top end of the vertical axis until the plot is squeezed to the bottom third of the graph. In general, presenting a graph like this is a bad practice! • Then, click on Autoscale . Most of the time, this provides the optimal display. • Auto Arrange On the top toolbar, select Page and Auto Arrange. • Data analysis tools • Use the Slope or Tangent tool to find the slope at different points on the graph. • Use the Examine tool to easily read the coordinates of a data point. Note that the position of the mouse is displayed in the bottom left corner of the screen. • Linear Fits are by far one of the most commonly used data analysis tools. Of course, they only make sense if the data shows a linear trend to begin with! For this purpose, let us graph the two columns we created, x2 and t2. On the top toolbar, select Insert and Graph. An x2 vs . t graph will appear. But this is the wrong time! Click on the label of the horizontal axis (“Time”) and select the desired quantity (“Time 2”) This new graph ( x2 vs . t2 ) should look more or less linear (we included that sine function in the definition precisely because we do not want a perfectly linear dependency for this exercise!), so we will use it to practice the Linear Fit tool. Select on the graph the data to be included (or just click on the graph, if all the data is to be included), and click on Linear Fit . A linear fit finds the values of m and b so the equation y = mx + b is the closest approximation to a given set of data. It also determines the correlation r . A good linear fit should have . Unfortunately, Logger Pro does not by default display the associated standard uncertainty in the parameters. To correct this, right click on the fit box, and select Show Uncertainty . Use the Snipping Tool to insert below the Linear Fit box. Are the parameters of the linear fit consistent with the formula used to generate the x2 column? Explain. Yes because the m and b values give the best linear average of the data sets • Inserting Logger Pro tables and graphs onto the notebook The Snipping Tool is once again the easiest way. Insert below a capture of the two graphs together. It should look nice if you have been following all the steps!

• Saving your work Each member should take home a copy of all the material produced during the lab (not just the notebook!) . You can use CyBox, your Google drive, a flashdrive, or email yourself the files. “My partner was supposed to send me the data but it never happened” will not be accepted as an excuse. • Submit lab notebook At the end of each session and before leaving the lab, each student must submit the notebook (.docx or PDF) as it is at that moment to the corresponding “First draft” Canvas assignment. This is an individual process. It is NOT acceptable to do one submission per group. Submit your records for this lab now. This is the end of the introduction to the Digital Lab Tools. This notebook contains another activity below (Lab FES) that you must also complete before your submission. Lab FES - Fundamentals of experimental science: • Metrology In the prelab, you watched the minilecture video Metrology .

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• Resolution, range, best estimate, error In experiment B in the Metrology slides, we used a mechanical balance with 0.1-g calibrated masses to measure the mass of a sample. Assuming that the balance works properly and that the scale masses are very well calibrated, write below the result of this experiment with 100% probability: • As a range • As a best estimate error. • As a best estimate percentage error. (2.2, 2.3) 2.25 ± 0.05 2.25 ± 2.22% As a rule of thumb, the uncertainty can be taken as half of the resolution of the equipment . • Other scales Digital scale We instead place our sample on a digital scale and obtain the reading shown to the right. Would this scale allow you to differentiate between samples with masses 2.241 g and 2.2386 g? Explain. No because the scale only reports to 3 sig figs and both 2.241g and 2.2386g would be rounded to 2.24g. How far below 2.24 g could the value be (with this reading on the display)? The lowest value it could be is 0.005g below (2.235g) for the scale to still round it to 2.24g. How far above 2.24 g could the value be? The highest value it could be is 0.005g above (2.245g) at which point the scale would start to round to 2.25g. Using these two limits above and below, write the measurement as a range, and then as a best estimate ± uncertainty. (2.235, 2.245) 2.24 ± 0.005 Dial scale The figure to the right shows what the reading would look like if we used a dial scale. What is the smallest amount you can discern on the dial: 0.2 g? 0.1 g? Maybe even 0.05 g? In this case, resolution depends on the ability of each experimenter! And that means that experimenters will also produce a slightly different uncertainty (which is half of the resolution, remember the rule of thumb defined at the end of section 1.1). Let’s settle for a resolution of 0.1 g. Write the reading above as best estimate ± uncertainty.

2.5 ± 0.1 As you can see, the determination of uncertainty can be a complicated issue –and it will get worse in a while once we start talking about probabilities. For the purpose of this class, we want you to be able to obtain some estimate of the uncertainty that you can reasonably justify. Our main goal is that you understand why uncertainty must always be part of the result. • Significant figures Let us imagine that we want to estimate the thickness of a sheet of paper. So we take a pile of paper, we count the number of sheets, and obtain 226. Then, we measure how tall the pile is with a ruler: 24.0 mm. As discussed in section 1, we could have a long argument about how much exactly should the uncertainty of this measurement be. Let’s settle to ± 0.5 mm Then, the thickness of one sheet is… this? Explain what is wrong with this result. Rewrite it with a meaningful number of significant figures, and explain your reasoning. 0.106 ± 0.002 In the example above, there was a neglect to pay attention to the significant figures. 24.0 ± 0.05 will have three sig figs making your final answer rounded to three sig figs as well because when using sig figs in multiplication you always round to the least number of sig figs and we can ignore the ± 0.5 because when added or subtracted to 24.0 (23.5, 24.5) the number of sig figs will still be three. • Statistics A simple pendulum If we hang a small weight at the end of a light string, we obtain a so-called simple pendulum. This is an example of an oscillatory system. The time the weight takes to move back and forth once ( i.e., to go through an entire cycle) is called the period T of the system. Let us assume that we repeat the following experiment 20 times: we displace the pendulum from its equilibrium position until the string forms an angle of 15° with the vertical, and release the system from rest. Using a stopwatch with a resolution of 1/100 th of a second, we measure the period of the oscillations in each repetition. The results are shown below. Event Period (s)

1 2.02 2 1.94 3 1.94 4 1.92 5 1.73 6 1.73 7 1.41 8 2.18 9 1.84 10 2.11 11 1.84 12 1.53 13 1.80 14 1.87 15 1.68 16 2.02 17 1.99 18 1.99 19 2.02 20 1.56 Since the variations between measurements are much more important than the resolution of the stopwatch, we will not worry about the error associated to the apparatus. This data is in the file Pendulum statistics.cmbl , but we just copied the numbers. Download and open the file on Logger Pro. Then, relabel X and Y to “Event” and “Period”, and include the proper units. In the graph, select all the points and click on the Stat icon in the tool bar. The software will then calculate the average and standard deviation of this data. You can use this to calculate the standard error. Enter your table, calculations and results below. (Remember to save the .cmbl file for your records.) The standard deviation is a measurement of the variations within the sample. It should not depend much on whether we repeat the test 10, 20 or 100 times. However, notice that the standard error has a in its denominator, where n is the number of measurements. In general, what happens to the standard error when n is very large? The standard error will continue to get significantly smaller.

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This is one of the reasons why repetition is a crucial element of reliable measurements! Can you suggest another? Another crucial element of experimenting is repeating your trials and or your experiment in the exact same manner. If you change something from your last repetition, then there is a new variable that you have to consider. For consistent results to give the best average, you need a consistent procedure. Later in the semester, you will learn that the period of a simple pendulum for small oscillations is given by: where L is the length of the string and g is the acceleration of gravity ( g = 9.81 m/s 2 ) Let us imagine that we measure the length of the string of our pendulum and obtain 89 cm. Using this value and the formula above, what is the theoretical expected period for this pendulum? Using this formula, the theoretical expected period for this pendulum is 1.9 seconds. Is the experimental value of the period consistent with the theoretical value? Explain. The experimental value(s) is fairly consistent with the theoretical value and falls within the same general range.

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