Car Crash

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					                              CSI: Highway Traffic Act
                                    SPH4U Culminating Task
Internal Memo: Ontario Provincial Police Forensic Investigation

To: Forensic Science, Automotive, Toronto Police Services

Re: Automotive crash on Wednesday, July 7, 2010 at Highway 9 & Tottenham Road

Please analyze the diagram below and report to me by ______________________ giving your
opinion on the speed of the vehicles at the moment of impact. We believe that the red car has a
speed in excess of the limit (max. 60 km/hr) and wish to press charges accordingly. During the
collision the driver of the blue car was thrown horizontally from the window (from a height of
0.5m) and travelled 8m. All relevant details I’ve gathered are detailed on the diagram below. As
there were no other witnesses to the accident other than the two drivers, I hope that you are
able to provide an independent opinion, especially in view of conflicting reports. Once your
report is completed we can move forward with charges. Thank you for your assistance in this
manner,

James Ponorack
Detective, Road Safety Division


                   Red          Blue




                                                   To solve this problem you may need to
                                                   use:

                                                         Conservation of momentum
                                                         Projectile motion
                                                         Kinematics equations
                                                         Conservation of energy


Other Eyewitness and Background Information

Initial direction of blue car             [S]        Displacement of blue driver from collision    8m
Initial direction of red car              [S30E]
Direction of entangled cars               [S15E]     Height of blue car driver above ground when
Length of final skid                      18 m       thrown horizontally                      0.50 m
Coeff. of friction ashphalt/rubber
          Wet: 0.95           Dry: 1.07
Report Criteria

Your assignment is to prepare a two part official report to respond to the detective that can be
used in a court of law to bring criminal charges against one or both drivers. The information
required to press charges is detailed below. The first part of the report will contain all technical
aspects of the investigation; this must contain all calculations. The second part will be a non-
technical report that needs to be read and understood by non-physics students in court.

Part A: The first part of the report will be a technical analysis of the crash. This must contain all
calculations performed to determine relevant crash information. This should include:

   a) Calculate the velocity of both vehicles just after the crash when they lock together (speed
      and direction).
   b) Calculate the velocity of the driver of the blue car just before the crash.
   c) Calculate the final momentum of the system just after the crash.
   d) Calculate the momentum of each individual vehicle before the crash (using components).
   e) Calculate the velocity of both vehicles just before the crash.
   f) Calculate the kinetic energy lost during the collision?

Part B: The second part of the report will be a non-technical summary of all the relevant
physics principles that apply to the crash. This report should be 1-2 pages in length. This
summary should include the answers to the following questions:

   a) Both vehicles are found “locked” together – comment on this and how it affects the way in
      which you calculate your answers. How would it differ if they separated?
   b) Explain any assumptions that you have made and how they affected your results?
   c) Proper language and terminology must be used to communicate your results. Include the
      following terms in your report: elastic collision, inelastic collision, work-energy theorem,
      friction, conservation of energy and work.
   d) What happened to the kinetic energy lost in the collision? Does the collision still obey the
      Law of Conservation of Energy?
   e) Research two technologies that may have been used to minimize the effects of the
      accident. Relate these to the principles of energy and momentum.

Timelines
   1)   Review task & initial peer conversation (see hints below) (1/2 day)
   2)   Perform calculations (1 day)
   3)   Hand in Part A of Report to be marked (beginning of class on _____________________)
   4)   In class work period to prepare final report (1 day)
   5)   Hand in Part B of report (beginning of class on _____________________________)

Hints for Peer Conversation
   1) How fast were the coupled cars moving after the collision? What information can we use
      to find this?
   2) How fast was the driver of the blue car moving when they were thrown from her car?
      What information can we use to project(ile) her speed into the past?
   3) How can we use these speeds to find the initial momentum of the system?
   4) How can we use the initial momentum to find the original velocities of the cars?
   5) How will friction affect the results?
Group Names: Matt, Sean, Nate, Dale, Sandra

All highlighted words directly relate to the questions and topic of the culminating task.

Overall Expectations

C1. analyse, and propose ways to improve, technologies or procedures that apply principles related
to energy and momentum, and assess the social and environmental impact of these technologies
or procedures;
C2. investigate, in qualitative and quantitative terms, through laboratory inquiry or computer simulation,
the relationship between the laws of conservation of energy and conservation of momentum, and
solve related problems;
C3. demonstrate an understanding of work, energy, momentum, and the laws of conservation of energy
and conservation of momentum, in one and two dimensions.

Specific Expectations
C1.1 analyse, with reference to the principles of energy and momentum, and propose practical ways to improve, a
technology or procedure that applies these principles (e.g., fireworks, rocket propulsion, protective equipment,
forensic analysis of vehicle crashes, demolition of buildings) [AI, C]
        Question: Part A, all
C1.2 assess the impact on society and the environment of technologies or procedures that apply the principles of
energy and momentum (e.g., crumple zones, safety restraints, strategic building implosion) [AI, C]
        Question: Part B, c)

C2.1 use appropriate terminology related to energy and momentum, including, but not limited to: work, work–
energy theorem, kinetic energy,gravitational potential energy, elastic potential energy, thermal energy, impulse,
change in momentum–impulse theorem, elastic collision, and inelastic collision [C]
                 Question: Part B, c)
C2.2 analyse, in qualitative and quantitative terms, the relationship between work and energy, using the work–
energy theorem and the law of conservation of energy, and solve related problems in one and two dimensions [PR,
AI]
                 Question: Part A
C2.3 use an inquiry process to analyse, in qualitative and quantitative terms, situations involving work,
gravitational potential energy, kinetic energy, thermal energy, and elastic potential energy, in one and two
dimensions
                 Question: Part B, c)
C2.4 conduct a laboratory inquiry or computer simulation to test the law of conservation of energy during energy
transformations that involve gravitational potential energy, kinetic energy, thermal energy, and elastic potential
energy (e.g., using a bouncing ball, a simple pendulum, a computer simulation of a bungee jump) [PR, AI]
                 Question: N/A
C2.5 analyse, in qualitative and quantitative terms, the relationships between mass, velocity, kinetic energy,
momentum, and impulse for a system of objects moving in one and two dimensions (e.g., an off-centre collision of
two masses on an air table, two carts recoiling from opposite ends of a released spring), and solve problems
involving these concepts [PR, AI]
                 Question: Part A
C2.6 analyse, in qualitative and quantitative terms, elastic and inelastic collisions in one and two dimensions, using
the laws of conservation of momentum and conservation of energy, and solve related problems [PR, AI]
                 Question: Part A
C2.7 conduct laboratory inquiries or computer simulations involving collisions and explosions in one and two
dimensions (e.g., interactions between masses on an air track, the collision of two pucks on an air table, collisions
between spheres of similar and different masses) to test the laws of conservation of momentum and conservation of
energy [PR, AI]
                 Question: Similar topics but does not involve lab or computer simulation
C3.1 describe and explain Hooke’s law, and explain the relationships between that law, work, and elastic potential
energy in a system of objects
                Question: N/A
C3.2 describe and explain the simple harmonic motion (SHM) of an object, and explain the relationship between
SHM, Hooke’s law, and uniform circular motion
                Question: N/A
C3.3 distinguish between elastic and inelastic collisions
                Question: Part B, a)
C3.4 explain the implications of the laws of conservation of energy and conservation of momentum with reference
to mechanical systems (e.g., damped harmonic motion in shock absorbers, the impossibility of developing a
perpetual motion machine)
                Question: Part B – general, c)
C3.5 explain how the laws of conservation of energy and conservation of momentum were used to predict the
existence and properties of the neutrino
                Question: N/A

				
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