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wks3 [2019/08/13 16:48] (current)
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 +===== 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,​
 +  * 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
 +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.
  • wks3.txt
  • Last modified: 2019/08/13 16:48
  • by rachel