"DeltaV (Δv) is commonplace notation used in mathematics and particularly in physics to denote a change or difference in velocity. In the context of a motor vehicle crash, Δv specifically refers to the change in velocity between precollision and postcollision trajectories of a vehicle:
Δv = v_{f} − v_{0}.
DeltaV emerged in the 1970s in the context of crash reconstruction analysis, and is considered by some researchers to be the best single predictor of crash severity..."
Steven G. Shelby, "DeltaV as a Measure of Traffic Conflict Severity,"
Transportation Research Board 90th Annual Meeting, issue 114199 (2011).
Preparation
Due 12:00 PM before start of lab
Prelab assignment 8 (*.html)
laboratory laptop, PASCO Capstone
wooden blocks, rubber band (for launcher)
collision track, carts, "cargo blocks"
masking tape
10 g1000 g mass set
PASCO Motion Sensor II
"750 Interface" box, power and USB cables
Microsoft Excel
Big Ideas
Collisions can be categorized as elastic (no kinetic energy lost in "rebounding"), partially inelastic (some kinetic energy lost in "rebounding"), or completely inelastic (much kinetic energy lost in "sticking").
The change in velocity of a car in an accident is a measure of physical damage incurred, and/or the probability of injury to the occupant.
Ultrasound sensors can be used to track the motion of objects.
Two measured values can be compared by calculating percent differences.
Goals
Students work in (selfassigned?) groups build upon previous experience with ultrasound sensors to track the motion of objects during collisions, classify collision types, interpret a collision process modeled with a simple velocity profile (the characteristic "¯\_" shape), and to assess crash severity from Δv calculations.
Students are introduced to calculations of percent differences.
Students execute a research task by taking and analyzing data, and write a conclusion and finally a descriptive abstract in a group lab report.
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. Cart Check and Launcher Setup Make sure you have two carts (one red, one blue) that will either repel each other magnetically, or stick to each other with velcro depending on which ends bump into each other. Turn the carts over, and test the wheels by spinning them (if they don't freely spin, or noticeably slow down right away, the axles will need to be replaced).
 Place the motion sensor at one end of the track, and set up a rubberband launcher just in front of the motion sensor, such that the cart can be given a consistent starting speed after being held and released. (The launcher should be located less than 10 cm away from the motion sensor, which will only pick up motion outside of this range.) Level the track such that it does not wobble, and the cart appears to roll without slowing down or speeding up after being launched. (The track does not have to be absolutely level, just enough that the cart has an approximately constant speed while traveling in the middle section of the track, where collisions will take place.)
 Select the narrow beam setting (the cart symbol on the "person/cart" switch") on top of the motion sensor. Plug the yellow and black motion sensor plugs into the "1" and "2" ports 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." Make sure that the motion sensor is angled to look horizontally along the track (or a slightly downwards angle may also work).
 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 "1" port on the interface box, in the dropdown window, select "Motion Sensor II." The interface box window should now depict both "1" and "2" ports connected to a motion sensor icon. Click on "Hardware Setup" again to hide this display. (At the bottom border of the screen, you may need to increase the sampling frequency from "20.00 Hz" to "40.00 Hz" to get better results.)
 From "Displays" on righthand side of screen, drag a "Graph" window onto the blank page. Click on "< Select Measurement >" on the horizontal axis of the graph, and in the popup window, under "Time" select "Time (s)." Click on "< Select Measurement >" on the vertical axis of the graph, and in the popup window, under "Motion Sensor II" select "Velocity (m/s)."
(At this point, and at other critical points, be sure save this workspace as a file to the desktop. PASCO Capstone may freeze or crash, but you can then exit the program completely, and click on the saved file on the desktop to start where you left off.)
 Press the "Record" button at the bottom of the screen, push the cart against the rubber band by a fixed amount, and release the cart from rest. Make sure to catch the cart before it runs off the track, and then press the "Stop" button to end the data run. Verify that the cart has an approximately constant speed while traveling in the middle section of the track, where collisions will take place; if necessary relevel the track.
 Launch the cart five times, and verify that it has an approximate consistent speed for consecutive launches; if necessary adjust and retape the rubber band and wooden blocks.
Cart launcher test
Trial → 
1 
2 
3 
4 
5 
v_{launch} (m/s): 





2. Preliminary Collision Readout Set up two carts (one red, one blue) such that their velcro ends will stick to each other after they collide. The striking cart "1" will be launched from the rubber band, and collide (and stick) to the stationary cart "2" that is initially located halfway down the track (note this position for the stationary cart, for consistent runs). Place the loading blocks and tape enough additional masses such that the total mass of the stationary block is approximately 10× the mass of the striking cart (this should the maximum load that the stationary cart can bear before the wheels "bottomout"). Test the launcher to make sure that the striking cart is not moving too fast (such that it will fail to stick to the stationary cart), or too slow (such that after the collision, the stucktogether carts fail to move at all).
 Observe and classify this collision as elastic, partially inelastic, or completely inelastic, and how you know this.
Collision type: [ elastic  partially inelastic  completely inelastic ]
Brief explanation:
 Press the "Record" button at the bottom of the screen, push the cart against the rubber band, and release the cart from rest. Make sure to catch the stucktogether carts before they run off the track, and then press the "Stop" button to end the data run.
 The velocity graph of the striking cart will be modeled with a constant positive velocity (upper horizontal line) before the collision, a downward diagonal line while colliding, and a constant slower positive velocity (lower horizontal line) after the collision. To find the approximate values of the (assumed constant) velocities before and after the collision, 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, drag and release the coordinates crosshair to just before the collision started. Record the initial velocity value just before the start of the collision. Repeat, in order to find the final velocity value just after the end of the collision (don't worry about the stucktogether carts gradually slowing down well after the collision ends). Watch the ± signs of these velocities, and fill in the values below for the striking cart.
Striking cart colliding with stationary cart test run
Striking cart 
v_{01} (m/s) 
v_{f1} (m/s) 
Δv_{1} (m/s) 



When you calculate and fill in the crash severity Δv_{1} for the striking cart, watch your significant figures (due to the subtraction operation, mind the decimal places).
 From this same collision, fill in the values below for the stationary cart. Note that the motion sensor only measures the initial and final velocities of the striking cart, but you can still deduce the initial and final velocities of the stationary cart. Briefly explain how you already know the initial velocity of the stationary cart, and how the final velocity of the stationary cart is related to the final velocity of the striking cart).
Striking cart colliding with stationary cart test run
Stationary cart 
v_{02} (m/s) 
v_{f2} (m/s) 
Δv_{2} (m/s) 



Brief explanation of deducing initial velocity value of stationary cart:
Brief explanation of deducing final velocity value of stationary cart:
When you calculate and fill in the crash severity Δv_{2} for the stationary cart, watch your significant figures (due to the subtraction operation, mind the decimal places).
 Compare the two crash severities Δv_{1} and Δv_{2} by calculating a percent difference between these two values (which compares one measured value with another measured value):
% difference = 100 × ( bigger − smaller )/(average of the two absolute values),
where the bigger value would be reported as "_____% greater" than the smaller value. Note that percent difference is not the same thing as percent error (comparing a measured value with an expected value), and not the same thing as percent change (comparing how a measurement increases or decreases from an older value to a newer value).
Crash severity Δv_{1} = __________ m/s.
Crash severity Δv_{2} = __________ m/s.
Percent difference = __________ for cart ___ larger than cart ___.
 Write a concluding statement discussing which cart (stationary or striking) experiences a greater crash severity, and by how much (which in realworld automobile accidents would be physical damage and/or injuries to the occupants). 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 Crash Severity for Completely Inelastic Collisions between Different Mass Cars
(Done on whiteboard only, to be worked on and presented as a group.)"In cartocar crashes, serious injuries are considerably more prevalent in crashes involving cars in the lightest weight classes and generally decline with increasing car weight."
B. J. Campbell and D. W. Reinfurt, "Relationship Between Driver Crash
Injury and Passenger Car Weight," University of North Carolina Highway
Safety Research Center (1973).
"Am I safer if I put bricks in my trunk?"
L. Evans, "Causal Influence of Car Mass and Size on Driver Fatality Risk,"
American Journal of Public Health, vol. 91 no. 7 (2001), pp. 10761081.  Consider a completely inelastic "rearend" collision between a striking cart and a stationary cart (with their velcro ends sticking to each other afterwards), where the stationary cart is initially empty, but can then be loaded with various amounts of "bricks in my trunk." Recall the definitions to be used:
m_{1} = mass of striking cart
v_{01} = initial velocity of striking cart
v_{f1} = final velocity of striking cart
Δv_{1} = v_{f1} − v_{01} = crash severity of striking cart
m_{2} = total mass of stationary cart (starting from empty)
v_{02} = initial velocity of stationary cart (this is always 0)
v_{f2} = final velocity of stationary cart (this is always the same as v_{f1})
Δv_{2} = v_{f2} − v_{02} = crash severity of stationary cart (not the same as Δv_{1})
Develop experimental trendline equations relating:
 the crash severity experienced by the striking cart (dependent variable) and the total mass of the stationary cart (independent variable); and
 the crash severity experienced by the stationary cart (dependent variable) and the total mass of the stationary cart (independent variable).
You should follow the suggested bestpractice guidelines for data collection and graphical analysis (slightly modified due to practical issues with this experiment):
 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 graphs.
Variable data points should be an average of repeated measurements (35 maximum), with a standard deviation reported in the data tables, and represented with vertical error bars on the graphs.
 Outlying data points should be replaced/removed.
 Proper choice of trendline fit types.
You do not need to take repeated measurements for each independent variable, as taking a large amount of different independent variable data points (ii) over a wide span (i), while being vigilant for outliers (iv) should be sufficient.
Because of the availability and combination of specific masses that can be taped to the stationary cart, it is not necessary to have every data point absolutely equallyspaced.
Refer to the example table below to organize the data to generate your two graphs. (Do not enter the "A..." column headings and "1..." row headings, as those are just Excel spreadsheet "coordinates.") Sample cell formulas to be entered below are highlighted in yellow.
Striking cart mass m_{1} = __________ kg (keep constant).
Striking cart colliding with stationary cart (initially empty)
 A  B  C  D  E  F  G 
1  Striking cart 
Stationary cart 
2 
v_{01} (m/s) 
v_{f1} (m/s) 
Δv_{1} (m/s) 
m_{2} (kg) 
v_{02} (m/s) 
v_{f2} (m/s) 
Δv_{2} (m/s) 
3 


=B3A3 

0 
=B3 
=F3E3 
4 


=B4A4 

0 
=B4 
=F4E4 
5 


=B5A5 

0 
=B5 
=F5E5 
⋮ 
⋮ 
⋮ 
⋮ 
⋮ 
⋮ 
⋮ 
⋮ 
Refer to previous labs for instructions on how to generate a graph with independent and dependent variables in nonadjacent columns. (No error bars for the two graphs for this lab.)
 Due to the data collection nature of today's lab, it is not necessary to write a procedure for your group whiteboard project other than to cite the software and hardware used and what it was used for.
 Print out one copy of your data table, and print out one copy of each your two graphs (with trendline equations and error bars); you do not need to record these on a whiteboard.
 (No trendline validation is required for this lab.) Write out two concluding statements on the whiteboard comparing the crash severity for the two drivers in a completely inelastic "rearend" collision, in order to separately support or refute each of these claims:
 "Am I safer in a striking car if I hit a car or a truck?"
 "Am I safer in a stationary car if I put bricks in my trunk?"
Include the specific relevant numbers in these statements, such that they can be read (and cited) on its own without referring to the above graphs, calculations and numbers.
 After your procedure, data analysis, and concluding statement sections are complete, write out a descriptive abstract for your experiment. Note that you should follow the suggested bestpractice guidelines for content ((i)(iii)) and style ((iv)(viii)):
 Describes measurements/equipment/methods.
 Describes data analysis/modeling.
 Describes how model is
validated with experiment applied to make realworld predictions.
 Use of active voice, firstperson pronouns.
 Written in pasttense.
 No opinions, unnecessary facts.
 No abbreviations, equations, symbols.
 No specific numbers, conclusions, recommendations.
 Bring up your whiteboards to the front of the class, to be presented to the instructor, which should include:
 A descriptive abstract.
Stepbystep procedure. (Summary of data collection apparatus used, and what it was used for.)
 Data table, calculations and/or graphs.
 Evidencebased conclusion statements.
 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, and still receive full credit). 
2  Minor problems; some corrections/revisions requested by instructor still needed, but not completed during time remaining in lab. 
1  Minimally acceptable effort, essential/critical revisions still needed. 
0  Unacceptable or no significant effort beyond experimental work. 
Followup
Complete this week's postlab assignment, next week's prelab assignment, and review lab instructions.
Due 12:00 PM before start of next lab
Postlab assignment 8 (*.html)
