lab #01 the physics laboratory

Picket fence

Figure 1. Experimental setup showing picket fence just before passing through the photogate. Source: Vernier

H Y S I C S L A B O R A T O R Y M A N U A L

Welcome to the Physics Laboratory at Temple University. In this experiment, you are introduced to equipment and methods that will be used throughout the semester, so take an active role in familiarizing yourself with all of the components of the setup and how they work. The computer will be used for both data acquisition and analysis. Data is first acquired by a probe or sensor that connects with the computer via an interface. This data will then be analyzed with Excel. If you are not already familiar with the basic functions of Excel, especially calculations and plotting data, it is important that you gain proficiency in these areas quickly as Excel will be used for most of the experiments in this course.

computer with LabPro interface and LoggerPro software, photogate on a stand, picket fence

Part I. Experimenting with Logger ProThe photogate is essentially a stopwatch that uses a beam of infrared light to record the time. The photogate signals the computer to record the whenever the light beam that passes between its arms is broken by an object.

1. Setup the photogate and stand as in Figure 1 with the photogate extending beyond the edge of the table. To avoid damaging the picket fence, make sure it has a soft surface (e.g. foam pad) to land on.

2. Connect the photogate to the DIG/SONIC 1 input of the LabPro interface. Notice other ports on the interface; you will be using them for future experiments.

3. Open the LoggerPro file “Lab #1 The Physics Laboratory.”

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The Physics Laboratory

Lab

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A P P A R A T U S


4. To test whether the photogate is working properly, check whether the Gate

State reading in the status bar at the top left of the screen shows “blocked” and “unblocked.” Another way of testing the photogate is to see whether the red indicator light on the back of the photogate blinks as you pass your hand through it. If it does not seem to be working properly, look back over these steps and the settings in the software to try to figure out why on your own. Only after you’ve done this should you ask for help.

5. Click Collect to start data collection. Hold the picket fence above the photogate and release it vertically such that it falls through the photogate beam; be sure to fully release the picket fence before it enters the photogate so that it is truly in free fall.

6. Click Stop to end data collection. Copy and paste the velocity and time data into Excel.

7. To establish whether your measurements are reliable and reproducible, repeat Steps 5 and 6 until you have data for 6 runs in all. Exclude data from trials in which the picket fence does not pass cleanly through the photogate. Part II describes plotting the data for further analysis.

8. For your last run, also copy the distance vs. time data into Excel. We will make a plot of one of these runs to compare and contrast it to velocity vs. time.

Part II. Plotting Data in ExcelWe know that the picket fence is experiencing a constant acceleration due to gravity, so we can apply the kinematic equations to analyze its behavior. We have measured velocity and time, so it makes sense to use this equation to calculate acceleration:

v=vo+at. (1)

1. Open Excel and make a coordinate plot of velocity vs. time (Insert Scatter

chart type) for your first trial. Then right click on the plot and choose Select Data Add to add your other runs. In this way you have all 6 runs plotted on the same graph, but as individual data series.

2. Which variable, velocity or time, goes on the x-axis? Why?

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3. For each trial, fit your data to a line by adding a trendline to the plot by selecting Layout Trendline More Trendline Options from the Chart Tools menu. Choose the linear fit and select the option to display the equation of the trendline. This procedure fits your data to a line y=mx+b where m is the slope and bis the y-intercept. Record the slope in a data table. Add all appropriate titles and labels (with units!) to your graphs. These same plotting methods will be used throughout the semester.

4. Describe in words the shape of the velocity vs. time graph. What is the meaning if the slope?

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5. Also, use the data from your last run to make a plot of vertical distance vs. time. Again, add all appropriate titles and labels to your graph.

6. Describe in words the shape of the distance vs. time graph for the free fall. How should this look (linear, quadratic, etc.)?

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Part III. Further Data Analysis: Reproducibility and DistributionsThe purpose of performing an experiment is to gain knowledge about an unknown quantity (the value of g, for example) but before we go around claiming that we know g, we must confirm our result and, even better, make an estimate as to how reliable our result is. The first step in determining the reliability is to do multiple identical trials, or replicates of our experiment. After recording all the data, we will use Excel to calculate the average, and standard

deviation of our results.

1. Referring to Equation 1, extract the values for vo and a from the equation of your trendline for each run. Record these in a new data table with three columns: one column each for the Run #, vo (m/s), and a (m/s2).

2. Look at your list of 6 slope values (i.e. acceleration values) and, in one or two qualitative sentences, report how reproducible your acceleration results appear (e.g. very similar values, widely varying from one trial to the next, etc.).

3. The first step in data analysis is usually to find the average of a set of values. The average is a simple way of removing random variation and

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errors in the data. Thus, we will call the average our best estimate of the true value of g. Note: one must be careful to only average together values from identical trials. To find the average click in the first empty cell below your column of values and type without quotes “ =average( ” Then highlight your 6 values and hit enter. The equation should calculate the average for you. You can also manually enter the equation by typing “=average(A1:A6)” when your data is in cells A1 through A6, for example. This is your best estimate of the value of g. Did you get close to the accepted value of 9.8 m/s2?

4. The second step in data analysis is to determine the standard deviation of the

mean for the 6 acceleration values. The standard deviation of the mean is a measure of how much difference there is between each data point and the average. Thus, standard deviation is high if there is a lot of spread in the data, and low if the data points are all very close. To calculate standard deviation, click in the cell just below your average and type “=stdevp(” and then highlight your 6 acceleration values and hit enter. Basically, you are doing the same steps as you did for the average, just replacing the command “average” with “stdevp.”

5. Is your standard deviation low when compared to the value of your average? As a rough guideline, a standard deviation less than 10% of your average is OK (but the lower the better!). Does this standard deviation seem reasonable with what you put for your quantitative description of reproducibility (item no. 2 above)? This shows how standard deviation is a measure of reproducibility.

6. The equation for standard deviation of the mean of a variable x is:

σ x=√∑ (x i−xavg)2

n

(2)

where x i are your individual values of g, and xavg is the average value of g, and the equation is summed from i = 1 to 6 in our case. Looking at this equation, what would the standard deviation be if all of your measured values were the same? Explain.

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In your lab report, write your best estimate of the value for g as the average ± the standard deviation: g±σg.

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7. Now look at how your values relate to the accepted value of 9.8 m/s2. Do all of your values fall higher or lower than 9.8? If so, there may be a systematic error in the experiment, such as inaccurate timing measurement by the photogates. Alternatively, there could be other forces at work besides gravity, meaning the assumption that the acceleration is only due to gravity is wrong. Include any sources of error here, and always be sure to mention them in your future lab reports.

8. Error propagation. So we have a value for g and an estimate of error in the form of the standard deviation. If we want to calculate the force F on the picket fence using the equation F=mg, we can simply multiply what we got for average g times the mass m of the picket fence. However, F will also have error associated with it, due to the fact that g was used to calculate it – thus the error propagates through from g to F.

To find F and its associated error, first measure the mass of the picket fence using the scales provided. For the error of the mass measurement, we will use a common technique of taking half of the smallest interval on the scale, which is 0.05 grams for most of our scales. Example: if your picket fence weighs 84.55 grams, you report the value (m±σm) as 84.55 ± 0.05 grams. Next, calculate F by multiplying your average g times 84.55 g. Finally, calculate σ F using the error propagation formula below for which you will need your values σ gand σ m.

Equation: Error Propagation Formula:

F=m∗g σ F=F√( σ mm )2

+( σ gg )2

(3)

Finally, report your calculated force as F±σ F.

Additional Questions:1. Looking at the data, you should notice that the time values are getting

smaller and smaller the farther the picket fence falls. Why is this?

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2. How does the computer know the velocity when all it is measuring is time? Hint: the other part of the equation for average velocity.

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3. It is very useful to understand the effects of errors, both to prevent them and to account for unexpected results. When you drop the picket fence, the markers are perpendicular with the photogate beam. How your results be affected if the picket fence was dropped at an angle through the photogate?

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How would your value for acceleration from your graph be affected if you let the photogate slide from your fingers rather than releasing it cleanly?

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4. Using calculus, how do you determine (1) velocity from position, and (2) acceleration from position?

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Include all graphs, data tables, and answers to questions in your lab report.

Enter here notes for use in writing your lab report. You will write your report outside of class, so if you look at the lab report grading rubric for what is to be included in your report, you’ll see that it will help you quite a lot to make notes on the procedure, sources of error, answers to discussion questions, and reminders to look up reference material from your text, etc.

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Notes:

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lab #01 the physics laboratory

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