"The idea behind the airbag is to take advantage of the physics of a crash. In the case of a headon collision, a car usually stops fast. The body of the driver, of course, doesn't. It follows Newton's second law: its momentum continues until an outside force (usually the steering wheel, dashboard or windshield) brings it to a stop. An airbag doesn't just soften the blow. It actually lowers the impact by stretching it out over a longer period of time. It also spreads the impact over a larger area of the body. That way, no single area (forehead, chin, neck) bears the brunt of it. That's why airbags inflate and then quickly deflateto gradually bring the driver's momentum from 60 mph to zero."
"How Airbags Work, And How They Can Fail" (January 11, 2016),
popsci.com/howairbagsaresupposedtowork.
Preparation
Due 12:00 PM before start of lab
Prelab assignment 7 (*.html)
Equipment
whiteboards, markers
laboratory laptop, PASCO Capstone
Big Ideas
Collision damage and bodily injury in car accidents are due to the high accelerations experienced, which can be determined by modeling the velocity vs. time graph with a characteristic "¯\_" shape.
Goals
Students build upon previous experience with motion tracking software to analyze videos of objects during collisions.
Students understand how to interpret a collision process modeled with a simple velocity profile.
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 task 1, to be turned in at the end of today's lab for randomly selected grading for your group.)
1. Analysis of LowSpeed Bumper Tests Download these video resources to your desktop:
These are selected 5 mph bumper collision videos from the Insurance Institute for Highway Safety.
 Run the PASCO Capstone software package. From "Displays" on righthand side of screen, separately drag a "Movie" window and a "Graph" window onto the blank center page, such that they each take onehalf of the page.
 In the "Movie" window, select "Open Movie File," and open the first video for the 2007 Toyota Camry. Click on the "Enter video analysis mode" button. Resize the calibration tool bracket to the width of a tire. Set the width to be "0.43 m" (corresponding to a 17 inch diameter tire).
 Click on the movie window "Properties," select "Movie Playback" and change the "Playback Frame Rate to "150" (this was shot in slow motion, at 150 frames per second).
 Move the playback head to the start of the movie. Make sure that the "Automatically advance the frame after clicking the object" and "Magnify video around the cursor" option buttons are selected.
 For each frame, click on a specific part of the car that will remain visible throughout the collision (such as a corner of the headlamp, etc.; you can move the playback head back and forth to verify this). You can stop when the car has completely rebounded from the wall.
 On the vertical axes of the first graph window, click on "<Select Measurement>" and choose "Video Analysis > Object #1 > xvelocity, Object #1 (m/s)." Click on "Scale axes to show all data," and click on "Adjust scaling for data changes  select scaling behavior " and choose "Scale Both Axes (Keep All Data Visible)."
 At the top of the graph window, click on "Apply smoothing to active data  Select amount of smoothing," and in the popup window move the "Smoothing" slider all the way to the right to "51."
 The velocity graph of the 2007 Toyota Camry will be modeled with a constant positive velocity (upper horizontal line) before the collision, a downward diagonal line while in contact with the wall, and a constant negative 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, which should be around 2.8 m/s (corresponding to 10 km/h or 6.2 mph, according to the 2006 IIHS LowSpeed Crash Test protocol). Record the initial velocity value just before the collision. Repeat, in order to find the final velocity value after the collision (you may need to "eyeball" this value, as it may have fluctuated). (The data table for these entries is following the next step.) Watch the ± signs of these velocities.
 At the top of the graph window, click on "Determine slope of line between endpoints of interval surrounding data point," and a dashed line labeled with "m = ?" will appear. Click on, drag and release the dashed line such that the tangent slope will lie along the middle of the downward diagonal line, which will be the acceleration of the 2007 Toyota Camry during the collision process. Record this value below. Watch the ± sign of this acceleration.
2007 Toyota Camry low speed full frontal crash test
initial velocity v_{x,i}^{ } (m/s) 
final velocity v_{x,f}^{ } (m/s) 
acceleration a_{x} (m/s^{2}) 



 Print out one copy of this page (with movie, v_{x}(t) graph, initial and final velocity coordinates, and acceleration parameters). On the printout graph, draw in horizontal lines to represent the initial velocity and final velocity values, and extend the diagonal slope line such that you have a simple "¯\_" shape (no curved corners) for an idealized collision process. Determine the time of the "\" portion of the graph, from the corner of the "¯\" to the "\_" corner; this is the total approximate time that the 2007 Toyota Camry was in contact with the wall. (Estimate your time to within onehalf of a grid square; if a grid square is 0.04 s, then estimate to the nearest 0.02 s.)
Collision contact time Δt = __________ s.
 Is the sign for the value of the initial velocity v_{x,i} of the 2007 Toyota Camry before the collision positive or negative (or zero)? Briefly explain how this is consistent with the placement of the origin in your video window.
Sign of v_{x,i}: [ + − 0 ]
Brief explanation:
 Is the sign for the value of the final velocity v_{x,f} of the 2007 Toyota Camry after the collision positive or negative (or zero)? Briefly explain how this is consistent with the placement of the origin in your video window.
Sign of v_{x,i}: [ + − 0 ]
Brief explanation:
 Is the sign for the value of the acceleration a_{x} of the 2007 Toyota Camry during the collision positive or negative (or zero)? Briefly explain how this is consistent with the placement of the origin in your video window.
Sign of a_{x}: [ + − 0 ]
Brief explanation:
 Repeat 1(b)(k) for the 2007 Volkswagen Passat. (You may either save the previous experiment and start over completely, or judiciously modify this file for this new vehicle. For scale calibration, the tire size is still 0.43 m (17inch wheels), but the frame rate for this clip should be changed to 180 fps. Record your values below, and print out one copy of this page (with movie, v_{x}(t) graph, initial and final velocity coordinates, and acceleration parameters).
2007 Volkswagen Passat low speed full frontal crash test
initial velocity v_{x,i}^{ } (m/s) 
final velocity v_{x,f}^{ } (m/s) 
acceleration a_{x} (m/s^{2}) 



Collision contact time Δt = __________ s.
 From Newton's second law:
ΣF_{x} = m⋅a_{x},
calculate the net external stopping force exerted on each car (due to the normal force of the wall) during their collisions.
2007 Toyota Camry
(mass 1.580×10^{3} kg)
ΣF_{x} = __________ N (proper sig figs).
2007 Volkswagen Passat
(mass 1.593×10^{3} kg)
ΣF_{x} = __________ N (proper sig figs).
 For these collisions, the 2007 Toyota Camry experienced damage that would take an estimated cost of $936 to repair, while the 2007 Volkswagen Passat experienced $4,594 in repair costs. Assuming that the degree of damage is only caused by the amount of net stopping force exerted on a car (and not due to the cost of different manufacturer parts), explain how prolonging the stopping time for the 2007 Volkswagen Passat would decrease the acceleration and the net stopping force (while the initial and final velocities remain the same), by describing how the velocity versus time graph would change as a result.
Brief explanation:
2. Crash Survivability
(Done on whiteboard only, to be worked on and presented as a group.)
An analysis of Indy Racing League car crashes from 19962003 concluded that the threshold for developing head injuries was an acceleration of 50g (50 times the acceleration due to gravity, or 490 m/s^{2}):"We analyzed 374 crashes. A driver in a crash with an impact of ≥ 50g developed a head injury 16.0% (30/188) versus 1.6% (3/186) in those of < 50g (P < 0.001). The mean peak gforce for those with head injury was 79.6 (SD 28.5) versus 50.6 (SD 28.0) in those with no head injury (P < 0.001)."
C. S. Weaver, B. K. Sloan, E. J. Brizendine, H. Bock, "An Analysis of Maximum Vehicle G Forces and Brain Injury in Motorsports Crashes," Medicine & Science in Sport & Exercise, vol. 38, no. 2 (2006), p. 246.  Download these video resources to your desktop:
These are selected "Front Full Width Rigid Barrier Test50 km/h" collision videos from the European New Car Assessment Program, with frame rates of 574 fps, and 18 cm wide circular reference stickers on the vehicle doors.
Choose any two of the above vehicles, and assess whether their drivers will experience accelerations above the 50g injury threshold. Review the above process 1(b)(k) that was used to find the acceleration of a vehicle, but instead track the acceleration of the driver crash test dummy head. (As a check, you should find from the video analysis that the initial speed should be approximately 50 km/h, or 14 m/s.)
Euro NCAP front full width rigid barrier test crashes

initial velocity v_{x,i}^{ } (m/s) 
final velocity v_{x,f}^{ } (m/s) 
acceleration a_{x} (m/s^{2}) 
Vehicle 1 driver 



Vehicle 2 driver 



(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 software package used and what it was used for.)
 Record your data on the whiteboard, and print out the graphs for your two vehicles.
 Write out a concluding statement on the whiteboard assessing the likelihood of injury for the driver in these two vehicles. 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.
 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 relates to other research findings.
 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 software package used, and what it was used for.)
 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 lab report and postlab assignment, next week's prelab assignment, and review lab instructions.
Due 12:00 PM before start of next lab
Postlab assignment 7 (*.html)
