1. "The [maximum] force of [static] friction is directly proportional to the applied load."
2. "The [maximum] force of [static] friction is independent of the apparent area of contact."
3. "Kinetic friction [force] is independent of the sliding velocity."
Guillaume Amontons, "Amontons' Laws of Friction," late 17th century
Preparation
Due 12:00 PM before start of lab
Prelab assignment 5 (*.html)
Equipment
laboratory laptop, PASCO Capstone
PASCO economy force sensor
table clamp, rightangle clamp, rods (for hanging force sensor)
10 g1000 g mass set
electronic weight scales
"750 Interface" box, power and USB cables
Microsoft Excel
Big Ideas
The forces acting on a stationary (or constant motion) object must cancel each other (zero net force, due to Newton's first law). Force sensors can be used to measure weight and tension forces. The maximum static friction force is proportional to the normal force for an object on a horizontal surface (Amonton's first law of friction). Data subject to random experimental errors can be characterized statistically (average, standard deviation) and represented graphically using error bars.
Goals
Students work in (selfassigned?) groups to understand how to apply Newton's laws to analyze the behavior of Amonton's first law of friction.
Students learn how to use sensors to measure forces.
Students learn how to handle data subject to random experimental errors by using spreadsheets to calculate the average and standard deviation of repeated measurements, and to display these using error bars on graphs.
Students build upon previous knowledge of graphing and curvefitting software, and best practices for data collection and graphical analysis.
Tasks
(Record your lab partners' names on your worksheet for tasks 12, to be turned in at the end of today's lab for randomly selected grading for your group.)
1. Calibrating PASCO Force Sensor Plug the force sensor into the "A" port on the front of the interface box, and connect the USB cable from the back of the interface box to the laptop. Plug in the AC power into the interface box as well, and flip the switch in the back to "on."
 Run the PASCO Capstone software package. From "Tools" on the lefthand side of the screen, click on "Hardware Setup," and click on the Bluetooth button to stop it from looking for wireless devices. Click on the "A" port on the interface box, in the dropdown window, select "Force Sensor, Economy." The interface box window should now depict the "A" port connected to a force sensor icon. Click on "Hardware Setup" again to hide this display.
 From "Displays" on righthand side of screen, drag a "Digits" window and drag a "Graph" window onto the blank page. Click on "< Select Measurement >" on the digit display, and in the dropdown window, under "Force Sensor, Economy" select Force (N)." Click on "< Select Measurement >" on the horizontal axis of the graph, and in the dropdown window, under "Time" select "Time (s)." Click on "< Select Measurement >" on the vertical axis of the graph, and in the dropdown window, under "Force Sensor, Economy" select "Force (N)."
 Press the "Record" button at the bottom of the screen. You can keep this running continuously. Later press the "Stop" button to end the data run.
 Mount the force sensor with the hook pointing downwards, and press, hold and release the "Tare" button. There may be a nonzero force value displayed even after this process; note this value. (This process should be repeated before every data run, just to be sure.)
Tare offset: __________ N (note ± sign as well).
 Now hang a 500 g mass from the force sensor hook, and record the value of force value displayed, along with its ± sign. Explain why this value is expected when hanging this mass from the force sensor (you may need to account for a nonzero tare value, and whether you added or subtracted this correction).
Force value: __________ N (note ± sign as well).
Brief explanation:
 Look at the (+) and (−) labels on the force sensor, and discuss why all forces that pull on the hook are expected to have negative values.
Brief explanation:
 Note the maximum load (in N) for the force sensor. What is the maximum amount of mass (in kg) that can be hung from the force sensor?
Maximum load: __________ N.
Maximum hanging mass: __________ kg.
2. Overcoming Static Friction ("Stiction") Place a 100 g mass on the wood block, and attach a string such that the weighted wood block can be horizontally pulled by the force sensor across a table. Press the "Record" button at the bottom of the screen. You can keep this running continuously. Later press the "Stop" button to end the data run.
 While the string is still slack, press, hold and release the "Tare" button. There may be a nonzero force value displayed even after this process; note this value. (This process should be repeated before every data run, just to be sure.) Explain whether this value will need to be added or subtracted to the displayed force values to give the correct experimental force values.
Tare offset: __________ N (note ± sign as well).
Brief explanation:
 Starting with a slack string, use the force sensor to slowly pull the weighted wood block (you should see the force value increase on both the digital display and the graph), and as soon as the weighted wood block has just barely begun to slide, stop pulling such that the string goes slack again. You should see a (downwards) spike on the graph, which represents the force required to overcome the maximum static friction force. Repeat this process several times until you get (somewhat) consistent results, which may depend on one or more of these factors:
 cleanliness of surface;
 specific part of table used;
 sensitivity/reaction time of person pulling;
 practice, practice, practice?
 Press the "Stop" button to end the data run. At the top of the graph window, click on "Add a coordinates tool," and in the popup window, select "Add Coordinates/Delta Tool." Click on and drag the coordinates crosshair until a downwards peak is selected (where the static friction force was overcome at its maximum value). You can read off the force value that the crosshair momentarily "points to," or you can also release the crosshair such that it "jumps to" the point of interest. Use this to read off five fairly consistent values for the maximum static friction force and record these values below.
Maximum static friction force (tarecorrected) for wood block with 100 g load
Trial → 
1 
2 
3 
4 
5 
f_{s,max} (N): 





 Calculate the average of these five measurements (keep the raw result for now, to be truncated later).
Average f_{s,max} = __________ N.
 Calculate the standard deviation σ of these five measurements, which is a measure of the "spread" of these data points (assuming that the error is random in nature). Use WolframAlpha (*.html) to calculate the standard deviation, by replacing the example numbers in the text box with your data points from above (keep the raw result for now, to be truncated later).
Standard deviation σ_{fs,max} = __________ N.
 The standard deviation of the random experimental errors can be considered the uncertainty of the average. Truncate/round the average and standard deviation of f_{s,max} to one uncertain significant figure.
Data set f_{s,max} = __________ ± __________ N.
 Compare the uncertainty of an individual force measurement (0.1 N) with the standard deviation of your repeated force measurements. The general rule to determine if a measurement can just be done once, or needs to be repeated (to find an average and standard deviation) is:
If trial measurements seem to vary by more than twice the value of the measurement uncertainty, then a number of repeated measurements should be made to determine an average value, until the standard deviation is comparable in value to the measurement uncertainty. (Or due to time constraints in this course, up to a maximum of 35 repeated measurements, if necessary.) Write a concluding statement discussing whether repeating this measurement only five times was sufficient in this case, and specifically why. Include the specific relevant numbers in this statement, such that it can be read (and cited) on its own without referring to the above calculations and numbers.
Brief concluding statement:
3. Modeling Amonton's First Law of Friction
(Done on whiteboard only, to be worked on and presented as a group.) Develop an experimental trendline equation of how the maximum static friction force (dependent variable) on a weighted wood block is proportional to its total weight (block plus load mass(es), this is the independent variable), starting with a 100 g mass added to the mass of the wood block. Refer to the example data table below to create your spreadsheet; add more columns as necessary. (Do not enter the "A..." column headings and "1..." row headings, as those are just Excel spreadsheet "coordinates.")
(The first column is the total mass of the block plus the added weights on it (so you will need to add in the mass of the block itself); and your data points only need to have roughly spaced intervals, depending on the availability of your smaller masses.)
Maximum static friction force (tarecorrected?) vs. total mass
 A  B  C  ...  ...  ... 
1 
Block + load total mass (kg) 
f_{s,max} trial 1 (N) 
f_{s,max} trial 2 (N) 
... 
Average f_{s,max} (N) 
Std dev (N) 
2 






3 






4 






5 






6 






7 






8 






9 






10 






11 






(Refer to the previous week's lab for instructions on how to generate a graph with independent and dependent variables in nonadjacent columns, with error bars.)
(Due to the softwareintensive nature of today's lab, it is not necessary to write a procedure for your group whiteboard project other than to cite the motion sensor type and software package used.)
 Print out one copy of your data table, and print out one copy of your graph (with trendline equation and error bars); you do not need to record the data table or draw the graph on a whiteboard. Note that you should follow the suggested bestpractice guidelines for data collection and graphical analysis:
 Minimummaximum data range (spanning a factor of at least 5×, 10× is better).
 Has minimum number of data points (10).
 Concentrated data in rapidly changing portions of graph.
 Variable data points should be an average of repeated measurements (35 maximum), with a standard deviation reported in the data table, and represented with vertical error bars on the graph.
 Outlying data points should be replaced/removed.
 Proper choice of trendline fit type (in this case, linear, as you are testing a law of proportionality).
 Write out a concluding statement on the whiteboard regarding the validity of your mathematical modeltesting it by measuring the maximum static friction force using a total mass greater than your maximum experimental total mass for the loaded block, and comparing the percent discrepancies between the measured maximum static friction force, and predicted static friction force from your trendline equation. Include the specific relevant numbers in this statement, such that it can be read (and cited) on its own without referring to the above calculations and numbers.
 Bring up your whiteboards to the front of the class, to be presented to the instructor, which should include:
 A descriptive abstract: a brief summary of the purpose and methods used, but not of the data nor the conclusions. (Use the sample abstract below for today's lab.)
"We used a force sensor to measure the maximum static friction force to unstick a wooden block loaded with various masses as it just begins to slide on a horizontal table. We then constructed a mathematical model of how the maximum static friction force depends on the total mass of the block and load, and tested the validity of this model by predicting and measuring the maximum static friction force for block and load values outside the original data set." Stepbystep procedure.
 Data table, calculations and/or results.
 Evidencebased conclusion statement.
 Documentation Rubric (tasks 12)
(Graded from randomly selected group member)
Score  Description 
3  Explanations complete and calculations correct, or very nearly so. 
2  Essentially complete; few explanations/calculations missing or incorrect. 
1  Substandard effort; substantive amount of explanations/calculations missing or incorrect. 
0  Unacceptable or no significant effort. 
 Whiteboard Rubric (task 3)
(Graded as a group, evaluated by instructor during debrief session)
Score  Description 
3  Complete, thorough, understandable, with little or no clarification needed during verbal instructor critique (can be resubmitted and presented again with requested corrections/revisions made). 
2  Minor problems; some corrections/revisions requested by instructor still needed, but not completed. 
1  Minimally acceptable effort, essential/critical revisions still needed. 
0  Unacceptable or no significant effort beyond experimental work.  Followup
Complete this week's lpostlab assignment, next week's prelab assignment, and review lab instructions.
Due 12:00 PM before start of next lab
Postlab assignment 5 (*.html)
