Student Guide
SUV vs. Compact Car – A Traffic Accident
Olivier Tardif-Paradis
Cégep de Victoriaville
Stéphan Gaumont-Guay
Cégep Limoilou
Traffic Accident
Background
You are a police investigator and you have been asked to investigate a traffic accident involving two vehicles. You go to the site of the accident to gather testimony from the witnesses and the information required for the investigation.
According to the first witness, a pedestrian who saw it happen, the accident occurred at the end of the afternoon on a sunny day. Coming out of a curve, the driver of the sport utility vehicle (SUV) lost control of his vehicle and ended up in the wrong lane, in the path of an oncoming vehicle. Both drivers tried to brake, but they collided anyway.
The second witness, the driver of the compact vehicle, was still in shock. He told you that he was driving within the speed limit when he saw the SUV skid out of control as he came out of a curve and come into his lane.
The driver of the compact car said he could have avoided the collision by driving off the road, but he deliberately chose to collide with the SUV rather than risk smashing into the concrete wall at the side of the road. He felt it was safer to collide with another vehicle than to strike a concrete wall at full speed.
It does appear that both drivers tried to brake, because there are still braking marks on the road. The SUV driver is dead. When you check his driving record, you discover that he had been involved in another accident two years ago.
As an investigator, you must gather all the information required and determine the possible causes of the accident, which will be presented in the event of a court case.
This information will allow the crown prosecutor to decide whether one of the drivers can be charged under section 249 (3) of the Criminal Code, Dangerous driving causing bodily harm.
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Diagram of the Accident
Your findings are as follows:
• Debris (oil, glass, metal, etc.) was found 5 m from the final position of the two vehicles.
• The speed limit on this boulevard is 80 km/h on the straight and 40 km/h on the curve.
• The curve radius is 48m.
• The mass of the compact car driver is 100kg.
• The mass of the SUV driver is 95kg.
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Three-step Cycle
List all relevant information that you gathered about the problem. Based on this information, indicate what you need to find out to solve the problem. As you discover new information, you should summarize and update the relevant information that you have gathered and ask new questions.
List the Following:
What We Know / To Be Determined / SummaryPreliminary Questions (Part 1)
Black Box 1: What Are the Causes of a Traffic Accident?
Compare the effects of different physics parameters on the braking distance, using this website:
http://www.phy.ntnu.edu.tw/java/Reaction/reactionTime.html
1) Braking distance as a function of reaction time (t=1 s or 0.5 s and μc = 0.5).
Write your conclusions.
2) Braking distance as a function of type of braking (μc = 0.5 and μs = 0.8)
Write your conclusions.
3) Braking distance as a function of initial velocity (μc = 0.5 and μs = 0.8)
Write your conclusions.
Black Box 2: Force (Chap. 5 and 6)
4) Describe the forces affecting the vehicles at different moments (SUV, compact car, braking, curve, etc.) using a forces diagram.
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______forces diagram:
______forces diagram:
______forces diagram:
______forces diagram:
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5) How could the curve influence the accident conditions?
6) What data are needed to calculate the initial velocities of the vehicles?
(Hint: Find the list of useful equations.)
Black Box 3: Friction (chap. 6)
7) What type of friction is in play when the vehicle is driving, braking, skidding on the curve, etc.?
(Hint: You should describe the type of friction each vehicle is subject to in each stage of the accident.)
8) How can the braking marks or yaw marks help determine the causes of the accident?
Black Box 4: Momentum (Chap. 9)
9) What type of collision occurred?
10) What causes the momentum to change?
11) What remains constant before and after a collision?
Black Box 5: Energy (chap. 8)
12) What is the unit of energy?
13) Is the energy a scalar or a vector?
Explain your answer using an example.
14) What formula can be used to calculate the energy of the motion (kinetic energy)?
Identify each variable in the formula.
15) What happens to the change in kinetic energy of an object? What is the difference in kinetic energy?
Appendix:
What You Need to Understand:
Chapter 6 in Benson: Particle dynamics
- Understand Newton’s laws in the problems about uniformly accelerated rectilinear motion (UARM), which requires producing separate force diagrams for each object.
- Under the importance of the notion of centripetal force, which allows for the creation of circular motion (uniform or otherwise).
Exercises: E5, E7, E11, E29, E40
Chapter 7 in Benson: Work and energy
- Understand the phenomena.
- Understand what the translational kinetic energy of an object represents physically.
- Understand that the change in kinetic energy of an object is the result of net mechanical work done on the object in question.
Exercises: E5, E22, E38
Chapter 9 in Benson: Momentum
- Understand the importance of the notion of (vectoral) momentum in physics problems, especially problems involving collisions or variable mass systems.
- Understand how a perfectly elastic collision differs from a perfectly inelastic collision.
Exercises: E2, E17, E18.
References:
1. ABS brakes:
http://www.tc.gc.ca/eng/roadsafety/tp-tp13082-abs1_e-214.htm
2. Mythbusters: Mythssion Control: Crash Force
Here is the first part of the video
http://www.youtube.com/watch?v=3GuqiAHGGT4
and here is the second part
http://www.youtube.com/watch?v=c-JGIYLZZUg&feature=related
3. Société de l’assurance automobile du Québec:
http://www.saaq.gouv.qc.ca/en/documents/pdf/prevention/road_slow_quiz.php
4. Game about driver reactiontime: http://www.phy.ntnu.edu.tw/java/Reaction/reactionTime.html
5. Criminal Code of Canada http://lois-laws.justice.gc.ca/eng/acts/C-46/FullText.html
Were the Road Conditions at Fault? (Part 2)
Now you have to take the routine measurements to determine the friction coefficient of the road in this location. You are not certain how to proceed. There is no point in asking advice from the investigators, as they are all very busy right now. You have to figure this out yourself.
You have a block of iron that weighs several kilograms, with a tire tread attached to one side.
16) What data can be obtained using this friction block and a dynamometer?
Diagram, parameters, variables, etc.
17) Based on this information about the method to use, find an equation that will determine the friction coefficient of the road.
Hint: Make a diagram of the forces.
18) Could the road design (construction, surface, speed limits, etc.) be at issue? Justify your answer using a diagram and calculations.
Hint: Analyze each section of the road. Analyze all possible road conditions.
Was the SUV Driver at Fault? (Part 3)
19) What information do we need to help determine whether or not the SUV driver was at fault?
Hint: Refer to your conclusions from the section on causes of a traffic accident.
20) Your approach: (diagram, forces diagram, calculations, etc.)
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Technical Data
Vehicles / Compact Car / SUVPhoto / /
Years of production / 1999 - 2006 / 2003 - 2010
Maximum horsepower / Thermal: 70 hp
Electric: 13hp / 325 hp at 5,200 RPM
Dimensions
L x W x H / 3.9m x 1.7 m x 1.4m / 4.8m x 2.1m x 2.0m
Brakes / ABS / ABS
Total mass / 838 kg / 2,909kg
CO2 emissions / 122 g/km / 468 g/km
Friction coefficients:
Tire / dry road: ms=0.8 and mc=0.5
Tire / wet road: ms=0.5 and mc=0.35
Tire / icy road: ms= between 0.3 and 0.1 depending on salt level and mc=0.1
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Was the Compact Car Driver at Fault? (Part 4)
21) What information do we need to help determine whether the compact car driver was at fault?
22) Your approach: (diagram, forces diagram, calculations, etc.)
23) The driver of the compact car could have avoided a head-on collision with the SUV but he did not. Is his statement justified?
Driver of compact car: “It’s far more dangerous to collide with a concrete wall than with a car coming in the other direction. I learned that on Mythbusters!!!”
Explain your point of view before doing the calculations:
______
24) What energy would the compact car have absorbed if it smashed into the concrete wall?
25) What energy did the compact car absorb in the collision with the SUV?
26) Validate your conclusion using the assembly in front of the class.
Do you arrive at the same conclusion as in 3)? Explain any differences.
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