Introduction to the tools

During this semester, you will use the Pasco 850 Universal interface connected to a computer and several software packages to collect and analyze data and present your results.  Most of the time, when doing experiments, you will work as a team of two.  Each team will have one Pasco 850 interface and a laptop computer to work with. All students are required to participate in all activities and stay until the session is dismissed.

Laboratory exercises are not just about getting the right result, but about recognizing that fundamental physics principles shape our everyday experiences and underlie many of the devices that we use in our personal and professional lives.  Please do not treat the laboratories as cookbook exercises.  Permit yourself to think!   Thoughtful answers to the questions in blue will give you most of the laboratory credit.

Open a Microsoft Word document to keep a live journal of your experimental procedures and your results.  Include all deliverables, (data, graphs, analysis, outcome).  Write a 'mini-reflection' immediately after finishing each investigation, experiment or activity, while the logic is fresh in your mind.

What 'Deliverables' mean in a physics lab report

In a physics lab course, deliverables are the specific items you must submit to demonstrate what you did, what you measured, and what you learned. They are the products of the lab activity.

Grading scheme for all labs:

• 25% for completion
  In order to receive full credit, you have to complete the entire lab and answer all parts.  Use full sentences explaining your results, show your work, insert and properly label tables and plots, proofread, and use correct units.  Make comments if you are stuck or if your results seem to have errors.  Mention what could have caused these errors in your results and how the results could be improved.  The journal will help you think about the material.
  

• 25% for accuracy
  You do have to put effort into these labs.  This is a 4 credit-hour course with lab, so, just like for in-person labs, you have to set aside time to work on the labs.
  

• 50% for the mini reflections and a short summary reflection at the end of your journal, i.e. a personal account of your experience with the lab.  It should be written in the first person.  You can format it as a report to a friend or acquaintance.
  
  You should reflect on the material and mention how well you understood it. 
  Did you understand what you were doing during an exercise or activity, or did you just follow instructions?
  Do your results make sense to you, or do you expect them to be wrong?  Why?
  Do you have suggestions on how to improve the exercise or activities so students can learn more from them?
  ...

  Some of the phrases you may want to use are:

  • The most important thing was...

  • I learned that...

  • At the time I felt...

  • This was likely due to...

  • After thinking about it...

  • Later I realized...

  • This was because...

  • This was like...

  • I wonder what would happen if...

  • I'm still unsure about...

  • ...

Introduction to the tools

Today you will familiarize yourself with some of the software and hardware tools you will use in your studio sessions.

• Pasco Wireless Smart Cart
• Track
• Books or blocks to lift one end of the track.

Investigation 1:  Testing the Constant Velocity Hypothesis with simulated data

Your main tool for analyzing data will be the Microsoft Excel spreadsheet program.  Let us go ahead and start using it.

Assume you have performed an experiment, measuring the position of an object moving along a straight-line path as a function of time.  Your data are shown in the table below.  You suspect that the object moved with constant speed, covering equal distance in equal time intervals.  You want to verify this by producing a plot of position versus time and confirming that it is well-fitted by a straight line.  If yes, then the slope of the straight line is equal the speed of the object in units of m/s.

Basic instructions for producing the plot are given below.  Experiment with the various options Excel presents to you.

(a)  Open Excel and enter your data.

• Highlight the table in the browser, right click Copy, and paste the table into an Excel spreadsheet by putting your cursor into cell A1 and clicking the Paste button.

(b)  Produce a graph of position versus time.

• Highlight your data in Excel.
• On the Excel menu bar click Insert, Chart, XY (Scatter), and pick one of the subtypes.  Excel will plot the second column versus the first column.
• Highlight your graph, click the + sign next to it, and give the chart a title and label the axes. The label for the x-axis should be "Time (s)", and the label for the y-axis should be "Position (m)".

(c)  Study your graph.  The plot of position versus time should resemble a straight line.  The slope of the best fitting straight line should yield the average speed of the object.  You can find this slope by adding a trendline to your graph. 

• Right-click your data and choose "Add Trendline".  Choose "Linear", "Display equation on chart".  (You can also set the intercept at zero for this data set.)  An equation y = ax + b will appear on your graph, where the number a is the slope and the number b is the y-intercept.

(d)  The fit is not perfect.  The data you have collected contain experimental uncertainties.  To find the resulting uncertainty in the slope you must use the regression function.

• Position the cursor in an empty cell.  On the menu bar click Data, Data Analysis, Regression.  For the input y-range choose the entries in column B.  For the input x-range choose the entries in column A.  (Again, put your cursor in the appropriate textbox and highlight the chosen cells.)  Under output options check new worksheet, and under residuals choose residual plots and line fit plots.  Click OK.
  [If you do not find data analysis on the menu, then you have to add the Analysis ToolPak Add-In.  Click File, then click Excel Options and then click the Add-Ins.  Click the Go button while Excel Add-Ins is selected and check Analysis ToolPak.]
• The regression function finds the best fitting straight line for your data.  Under SUMMARY OUTPUT, X Variable, you will find the slope of this line.  It should be the same value you got from the trendline.  The cell to the right of the slope contains the standard error in this slope from the fit.  The slope of the position versus time graph is the velocity.  The residual plot and line fit plot give you visual feedback on how well a straight line can be fitted to your position versus time data.

Note:  The trendline is the best fitting straight line to the data.  It is the same line you get from the regression function line fit plot.  The slope of this trendline is your best estimate of the average speed.
The statistical uncertainty in the average speed is the standard error in the slope you get from the regression function.  This uncertainty only includes the error due to the scatter in the data points, not any systematic error, such as a calibration error.

To practice entering and copying formulas, let us calculate the speed of the object for each small time interval from the raw data.

• Type Speed (m/s) into cell C1.

We want cell C2 to hold the speed of the object between t = 0 and t = 1 s.  Speed is distance covered divided by the time interval.  The distance covered is the difference between the entries in cells B3 and B2 and the time interval is the difference between the entries in cells A3 and A2.

• Type =(B3-B2)/(A3-A2) into cell C2.  This yields the average speed of the object in the small time interval between the first and the second measurement.
  (Formulas always start with an equal sign.  A formula can be a simple numeric expression such as =2*4, or it can include longer expressions involving other cells and statistical and mathematical functions.)
• Copy the formula into cells C3-C11.  To copy a formula, position your cursor in the cell that contains the formula, choose copy from the menu bar, highlight the cells that will receive the formula, and choose paste from the menu bar.  (Quickly copy/paste in Excel, Youtube video)

Construct a plot of speed versus time.  Let us use the a method that does not depend on the data occupying adjacent columns.

• Put your cursor in an empty cell.
• On the Excel menu bar, click Insert, Chart, XY (Scatter), and pick one of the subtypes.
• Right-click the chart and choose Select Data, Add.
• Position your cursor in the X-Values text box and highlight entries 2 through 11 in the time column.
• Now position your cursor in the Y-Values text box, erase any entries in this box, and highlight entries 2 through 11 in the speed column.
• Type "speed versus time" into the Name text box.
• Give the chart a title, and label the axes.
  The label for the x-axis should be "Time (s)", and the label for the y-axis should be "Speed (m/s)".

There is a huge scatter in the values, because of experimental uncertainties in the measurements of small distances and time intervals.  But if we make many measurements we expect the average of these uncertainties to decrease with the number of measurements.  (The fitting routine producing the trendline averages over all data points and therefore produces a speed value with a much smaller uncertainty.)

Let us find the average value of all entries in column C.

• Into Cell D1, type Average Speed (m/s).
• Into cell D2 type the formula =average(C2:C11).

Investigation 1 Deliverables: (to be included in the your journal)

• Visuals:  Labeled plots (including trendline if applicable) of position versus time and speed versus time.
• Analysis:  What the slope represents in this specific physical context.  Does the standard error suggest your model (e.g., a straight line) is actually a good fit for reality?
• Outcome:  Your final calculated value of the average speed with its uncertainty. 

Understanding Motion - Distance and Time

Investigation 2:  Testing the Constant Velocity Hypothesis with real data

Sometimes the best way to measure the position of a moving object as a function of time is to make a video recording and then analyze the video clip.  In this exercise, you will analyze a clip showing a cart moving on an air track.  You will determine the position of the cart as a function of time by stepping through the video clip frame-by-frame and by reading the time and the position coordinates of the cart off each frame.  You will construct a spreadsheet with columns for time and position, and a plot of position of the cart versus time.

To play the video clip or to step through it frame-by-frame click the "Begin" button.  The "Video Analysis" web page will open.  You can toggle between the current page and the "Video Analysis" page.

• "Play" the video clip.  When finished, "Step up" to frame 0.  In some browsers you have to click "Pause" first.
• In the setup window, choose to track the x-coordinate of an object.
  
  From now on make sure that the zoom level of your browser stays constant (100% is best) and while you are calibrating or taking data the video frame stays fixed in the browser window.
• Click "Calibrate".  Then click "Calibrate X".
  The video clip shows a track with a scale in centimeter.  Position the cursor over some marked position in the left part of the frame, for example, the 50 cm mark, and click the left mouse button.  Then position the cursor over some marked position in the right part of the frame, for example, the 70 cm mark, and click the left mouse button again.  This will record the x-coordinates of the chosen positions.  Enter the distance between those positions into the text box in units of meter.  For the example positions, you would enter 0.2 into the text box.  Click "Done".
• Click the button "Click when done calibrating".  A spreadsheet will open up.
  Pick the point on the cart whose position you will track, for example the tip of the white arrow on the cart.
• Click "Start taking data". 
  Position the cursor over your chosen point.  When you click the left mouse button, the time and the x-coordinate of your chosen point will be entered into the spreadsheet.  You will automatically step to the next frame of the video clip.
• Repeat for each frame in the video clip until the cart has traveled approximately 20 cm.  Then click "Stop Taking Data".
• Highlight and copy your table.  Open Microsoft Excel, and paste the table into an Excel spreadsheet.  Depending on your browser, you may have to use "Paste" (Edge) or "Paste Special, Unicode Text" (Chrome).
• Your spreadsheet will have two columns, time (s), and x (m).
  
  
• Check if the cart moved with constant speed, covering equal distances in equal time intervals.  Produce a plot of position versus time as in exercise 1.  Add a trendline.

Investigation 2 Deliverables: (to be included in the your journal)

• Visuals:  Labeled plot of x(m) versus time (s) (including trendline).
• Analysis:  Is the cart moving with approximately constant speed, or is its speed increasing or decreasing?  Justify your answer.  How would your results change if the camera was not perfectly level?  Identify one possible systematic error in your video analysis and explain how it would influenced your final speed calculation.
• Outcome:  Your  calculated value of the average speed of the cart with its uncertainty. 

Vectors

Investigation 3:  Comparing graphical and algebraic vector addition

Use an on-line simulation from the University of Colorado PhET group to explore vector addition.
Click HERE to open the simulation.

Click the "Lab" image.  Explore the interface

• You can move the origin of the coordinate system.
• If you click a vector, you can display its values in the boxes on top.
• Checking "Sum" draws the vector sum of all vectors of a given color.
• This simulation only allows integer values for the x- and y-components of a selected vector.  Consequently, you cannot always exactly set the values of magnitude and direction.  Choose the closest values.
• The vectors can be easily translated, which is an important learning goal for this simulation.

Use the simulation to solve the following problems:

(a)  You walk 22.4 m in a direction 10.3^o North of East.
Use the simulation to represent your displacement vector.

• How far did you move in the North direction?
• How far did you move in the East direction?
• How would you calculate the North and East components of your displacement vector if you could not use the simulation?  Check that you get the same results.

(b) To get to a restaurant, you leave home and drive 12 miles South and then 10 miles West.
Use the simulation to represent your displacement vector.

• If a bird flew from your house to the restaurant in a straight line, what distance would it cover?
• In what direction would it fly?
• How would you calculate the magnitude and direction of the bird's displacement vector if you could not use the simulation?  Check that you get the same results.

(c) Suppose you and a friend are test-driving a new car.  You drive out of the car dealership and go 12 miles East, and then 5 miles South.  Then, your friend drives 8 miles East, and 2 miles South.

• Before using the simulation, ask an AI to solve the problem. Then, use the PhET simulation to find the the magnitude and direction of the car's displacement vector.  Compare the two answers.  If the AI was wrong, can you identify the specific physics mistake it made?
  (e.g., did it fail to treat the vectors as a sum?  Did it use the wrong trig function?)"
• Describe how you use the simulation to add vectors.

(d)  An airplane is flying North with a velocity of 150 m/s with respect to the air.  A strong wind is blowing East at 15 m/s with respect to the ground.

• What is the airplane's resultant velocity (magnitude and direction) with respect to the ground?  (In the simulation, scale your vectors appropriately.)

Investigation 3 Deliverables: (to be included in the your journal)

• Analysis:  Answer the questions posed in sections (a) through (d).

Experiment

In the studio sessions, you will also collect data using Pasco 850 interface and the Capstone software.  The Pasco 850 interface is a data acquisition system connected to the computer.  It can collect information from various analog and digital sensors, and generate seven different output signals.  This exercise will familiarize you with this data acquisition system.

The instrument you will use today is the Pasco Wireless Smart Cart.  The Smart Cart is a cart equipped with a position decoder.  Encoder wheel measure how far it has moved.  You will measure the position of the Smart Cart on an inclined plane as a function of time.

• Set up a track with one end elevated, by placing it on a thick book.
• Watch the video  "Getting started with the Pasco software", and use your experimental setup to perform the same experiments.  To lift the track, use a second book.  Pause the video when needed, so that you can follow the procedure step by step and learn about the capabilities of the data acquisition system.

Experiment Deliverables: (to be included in the your journal)

• Visuals:  your final graph in Capstone.  Click Edit, Copy, and then paste it into your journal. Do not copy the graph of another group.  The graphs of different groups will not look exactly the same, since the books and launch speeds are different.
• Analysis:  Do you think you are now familiar enough to acquire data using the Pasco software?  Please comment.

Convert your journal into a lab report.

Name:
E-mail address:

Laboratory 1 Report

• Make sure you completed the entire lab and answered all parts.  Make sure you show your work and inserted and properly labeled relevant tables and plots in your journal.
• Add a summary reflection at the end of your report in a short essay format.

Save your Word document (your name_lab1.docx), go to Canvas, Assignments, Lab 1, and submit your document.