PHY 099 Problem-Based Learning Experience: Car Crash Reconstruction

Danny and Janet were on their way to a drive-in picture show....

You are a member of one of two investigative teams hired by two insurance company to determine the circumstances and who was at fault for a fatal accident taking the lives of three individuals. Each company represents the driver of one car. Your task will be to defend your insurance company from having to pay out a huge amount of money should your driver prove to be at fault. You are to use every LEGITIMATE means necessary to defend your insurance company. The approach will be either to prove that your driver was not a fault or to fault the car crash reconstruction of the other team to cast doubt on their conclusion. We will hold a bench trial (a single judge will make the decision) to determine the innocent or guilt of each driver.

There are general and specific questions that must be answered as you solve this problem. The general questions are as follows; these should be addressed in your report summary:

Specific requirements will be found in the appropriate section below. These requirements - to a large extent - drive the analysis of the problem.

Realize that as you work to find answers for the various general and specific questions, you MIGHT have to make use of the work-energy theorem, the impulse-momentum theorem, kinematic relationships, definitions, conversion factors, friction, conservation of momentum, conservation of energy, and more.

Start by reading the disclaimer followed by the newspaper clipping and the police report, and then view the aerial and land-based photographs of the crash site and information about the cars involved. After this, continue by following the specific requirements below the readings section as you prepare your final report.

Readings:

Disclaimer

Newspaper Clipping

Police Report

Aerial Photograph of Crash Site

Land-based Photograph of Crash Site

The cars:

1965 Ford Mustang

1969 Mercury Cougar

The victims:

Danny and Janet Other
Danny Quigley (68kg) and Janet Stupinka (55kg)

Johnny Revet (84kg)

Resources:

Crash reconstruction basics

Drag sled (drag tire) information

US Naval Observatory sun position calculator

Definition of terms:

Please use these variables in the analysis of the collision to help clarify the situation and make scoring easier.

v1 (v subscript 1) = north-bound velocity of car #1 prior to collision
v2 (v subscript 2) = east-bound velocity of car #2 prior to collision
vx (v subscript x) = east-bound component of velocity of combined cars following collision
vy (v subscript y) = north-bound component of velocity of combined cars following collision
dx (d subscript x) = east-bound component of distance of combined cars following collision
dy (d subscript y) = north-bound component of distance of combined cars following collision
"g" force = acceleration in terms of 9.8m/s/s (a 2-g acceleration is 19.6m/s/s; under 2 "g"s, a body would weigh twice as much as under 1 "g")
m1 (m subscript 1) = mass of car #1 including mass of two passengers (Quigley and Stupinka)
m2 (m subscript 2) = mass of car #2 including one passenger (Revet)

Specific Requirements (presented here in no particular order):

  1. Determine v1, the collision speed of car #1 immediately before impact.
  2. Determine v2, the collision speed of car #2 immediately before impact.
  3. Determine the x- and y-velocities of the "welded" cars immediately after impact (vx and vy).
  4. Estimate the time involved in the actual collision process (not to be confused with time of post-collision skidding which is irrelevant to the problem) and road width (used to determine south-to-north distance post collision).
  5. Find the force of impact of car #2 on car #1.
  6. Determine the magnitude of the "g" force of impact on the passengers in both vehicles being mindful that 1g = 9.8m/s/s.
  7. Search the Internet to find out how many "g's" of acceleration can a person can survive during a collision such as this.

Guidelines:

  1. You will work as part of a group. Your group will produce a single report that will be turned in as evidence to the judge at least on week prior to the hearing.
  2. Hand-written reports are not acceptable. The report must be word processed and have a professional appearance as would be expected for a formal investigation.
  3. All equations used must first be shown in variable form, and then solved for the one variable needed (e.g., if solving F = ma for a, then write a = F/m).
  4. Equations must be inserted into the report using an equation editor of some sort.
  5. Values and their units must be accurately inserted into equations but only after they have been solved in algebraic form (e.g., a = F/m = 20N/4kg = 5N/kg = 5m/s/s).
  6. When more complex equations are used such as with a square root, be certain to use an equation editor that is commonly part of word processing programs today.
  7. Please realize that you might have to search the internet for important information regarding each car, aspects of the natural environment (e.g.,weather, road conditions, sun), and the effects of acceleration on the human body (e.g., "g"s).
  8. If you refer to outside sources, you must cite them in your report's references section.
  9. IF YOU MAKE ASSUMPTIONS, clearing indicate what they are and fully justify them. Assumptions will necessarily include duration of impact (found from d=vt where v is the average velocity) and width of roadway for instance.
  10. Your final report must include one or more drawings including vector representations of motion.
  11. Your final report must address all specific questions in the body of the report and the general questions in the conclusion of the report.

As you work with your group, please keep the following points in mind:

Hints:

  1. Take your time and do it right.
  2. Consider this a 2-phase crash: For the collision, use conservation of momentum; post collision, use conservation of energy, F=μN, and kinematics as necessary.
  3. Begin your work by using the work-energy principle (FΔx=ΔE) to find the post-collision initial velocity. Recall that W=FΔx, and this work of stopping the cars is done entirely by friction.
  4. Using the above result, work backward to find the pre-collision speed of car #2 moving from west to east.
  5. For finding the forces, consider using FΔt=mΔv and ΣF=ma and F=μN as necessary
  6. Treat N-S and E-W components separately.
  7. Make use of the fact that car #1 is going due east and car #2 going due north prior to the collision.
  8. When doing the blunt-force calculations, you may consider only east-west motion.
  9. Include body masses in calculations.
  10. Develop a detailed drawing using the above definitions of variables.
  11. Work in metric units only; easy conversion via Internet – search “convert meters to feet” and similar.
  12. Use units in all calculation and watch the units carefully, especially the subscripts.
  13. The use of trigonometry is NOT needed.
  14. Work in teams to maximum effect.
  15. Use the rubric carefully to maximize your score.
  16. Follow all submission requirements (no group projects, no "identical" projects, hard copy, typed report, deadline, etc.)

Scoring rubric:

This project will be scored using a FORMAL RUBRIC. To maximize your score, be certain to review the rubric prior to beginning your work, during your work, and at the conclusion of your work prior to the submission of the final project.

(Last updated February 13, 2015, cjw)