wks3

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 — wks3 [2019/08/13 16:48] (current)rachel created 2019/08/13 16:48 rachel created 2019/08/13 16:48 rachel created Line 1: Line 1: + ~~NOTOC~~ + ===== Analyzing Experimental Data ===== + + Last week we looked into how uncertainty arises when taking + measurements. This week we will investigate how uncertainty arises + within a set of data and how to analyze your results using tools such as + plots and lines of best fit. + + Tools such as Excel or Google Sheets are a great asset to scientists to + help make calculations using an entire data set and these tools also + provide easy access to plotting. In this course, using a spreadsheet can + help to decrease the number of calculations that your group needs to do + for each data point. You can use them to calculate the mean across + multiple columns or to use the cell as a variable in any equation you + define. Plotting is another tool that can save your group from multiple + calculations,​ and it uses all of the data points in your set to create + the result. With enough data points, using a plot to find your result + can yield more precise conclusions than any one measurement. + + In this workshop, you are tasked with obtaining the spring constant of + the spring you are given using various masses as your data points. You + will need to use your plot as a tool to obtain this. This will require + you to discuss which equations will be helpful when you plot. You and + your group will discuss the value of considering many data points within + a measurement and why we look at a set of data to draw conclusions. This + workshop emphasizes uncertainty analysis, again, as understanding + uncertainty is a major learning goal of this course. However, this time + your group will be considering a data set rather than a single + measurement. It also adds to that understanding by further exploring the + concept of uncertainty as it relates to a known model. + + ==== Research Concepts ==== + + In order to be productive in class, it would be helpful to research + before class: + * Force diagrams + * Lines of best fit for linear data sets and the generic equation for these lines + * Ways of representing this kind of data in graphs + * How to construct a scatter plot in Excel or Google Sheets ([[http://​sheets.google.com]]) + * How to add error bars to plots in Excel or Google Sheets + * The difference between precision and accuracy + + ;#; + **Potentially Useful Equations**\\ ​ + $F_{spring}=kx$ and $PE_{spring}=\frac{1}{2}kx^2$\\ ​ + where k is the spring constant and x is the displacement from the spring'​s resting position + ;#; + + ==== Data Analysis ==== + + **Part 1 -- Discussion of Model** + + Your goal will be to find the spring constant of the spring that your + group is given using a ruler and set of masses. But first, you should + discuss how you will accomplish this by using the equipment and the + physics knowledge that you have. To help guide your discussions,​ + consider: + * What is the force diagram for this system? + * Using those equations, what variables do you already know? + * What variables can you measure with the given equipment? + * What variables do you need to find with equations? + + These questions are important to consider before deciding your + procedure. These can help your group create a plan for your experiment, + since the overall goal of the experiment (finding the spring constant in + this case) may not be possible by direct measurement. + + **Part 2 -- Take Your Measurements** + + Now that your group has discussed what measurements to make, you should + conduct your experiment. Record your data in a spreadsheet. Don't worry + about any calculations you need to make just yet. Focus on recording the + data that you can measure directly first. Some questions to consider + before taking your measurements:​ + * What is the precision of your measuring tools? + * How did you choose to measure the displacement?​ + * Is there another way in which you could measure the displacement that would make your results have less uncertainty?​ + + **Part 3 -- Calculations and Plotting** + + Plot your data as a scatter plot. Talk with your group about which + variable should be on the x-axis and which variable should be on the + y-axis. If your results are linear, add a line of best fit to your + results. What is the equation for your line of best fit? + + Recall the equation you found using your force diagram. Can you + rearrange this equation to look like your line of best fit? If so, + consider the questions below: + * What does your slope represent? + * What does your y-intercept represent? + * Do these results make sense? + * Can you find the spring constant from your plot? + + **Part 4 -- Representing Uncertainty in Plots** + + We have discussed uncertainty in Workshop 1, but how does the + uncertainty in our measurements translate to a plot? Error bars are the + graphical representation of the uncertainty value that we assign to + measurements. + + Discuss with your group the uncertainty on your x-axis and y-axis + variables. Then, add error bars to your plot. + + **Part 5 -- Taking More Data** + + As we've discussed, the precision of your measurement often depends on + the measurement device and how the measurement was taken. In some cases, + the measurement you take will be the same each time it is taken, while + others will show some variation between data points. If you find that + the variations between points are larger than the precision of your + instrument, you can increase the precision of your data by taking + multiple measurements. + + Repeat the measurement done in //Part 2//, two more times**.** Now you + will have a total of three datasets. Plot a line for each new dataset on + the same graph as before (so that you will have three lines on one + plot). Is there a trend between your lines? + + Calculate the mean for each data point. On a new plot, create a line + that uses the mean values from all three of your measurements (remember + to use your tools in Excel/​Sheets for this!). Use this to find your + final conclusion for the spring constant. Your group should discuss what + the equation for the line of best fit means and if it makes sense. Be + sure to also consider if the size of your error bars should change now + that you are using the mean value instead of a single measurement. + + At the end of the day, you will be turning in your notebooks. Tutors + will put particular emphasis this week on your figures, your discussion + of the plan for your measurements,​ and the discussion of the + equation/​model to find your results.
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