Picturediagram of the accident
Case Introduction
On January 17,2018, an automobile accident occurred at the intersection of Furiosa Dr. and Fury Rd. in Joule, VA between a compact car (driven by Mike Rokar) and a tractor-trailer (driven by Lincoln Hawk). At this intersection the truck driver had a flashing yellow light while the car driver had a flashing red light. Neither driver claims responsibility for the accident. 

Mike Rokar claims: 
  1. to have made a full stop at the light before entering the intersection
  2. Mr.Hawk did not slow down prior to the collision
Lincoln Hawk claims: 
  1. to have been braking before the collision
  2. that Mr.Rokar did not stop at the flashing red light
  3. to have begun braking in anticipation of a collision, traveling at only 6.7m/s at the moment of impact
Background Information
In physics, all friction, motion, forces, kinematics, and momentum of the objects are tightly connected to each other. In this case, in order to figure out whose fault it is, we will have to do calculation in the following steps: 
  1. Using forces to determine the coefficient of kinetic friction between the tires and the road for both the car and the truck
  2. Using friction and net forces to determine the speed of both vehicles right after the collision
  3. Using the conservation of momentum to determine the speed of the vehicles right before the collision
  4. Using the kinematics relations to determine the speed of the vehicles at the traffic light and compare the result to the statements they claimed
Calculations


Step 1 - Coefficient of Kinetic Friction
  • given that the force required to drag a 130N car tire across the pavement at a constant velocity is 100N; the effective coefficient of friction fro truck tires is only 70% that of car tires. 

​Step 2 - Speed After the Collision
  • given that the truck and car skidded at the after collision; the car skidded a distance of 8.2m before stopping while the truck skidded 11m before stopping
Using...... 
  • Coefficients of kinetic friction we just found
  • Newton's 2nd Law of Motion
  • Kinematic equations
Variables...
  • mc = mass of the car
  • mt = mass of the truck
Picture
Step 3 - Speed Before the Collision
  • Momentum is conserved in a closed system with no external impulse, which is the situation for this case
  • Horizontal and Vertical momentum are both conserved but independent from each other
  • The total initial momentum in the x-direction is just the initial momentum of the truck
    • the car is traveling only in the y-direction with no momentum in the x-direction
  • The total initial momentum in the y-direction is just the initial momentum of the car
    • the truck is traveling only in the x-direction with no momentum in the y-direction
Variables...
  • pix = the momentum of the system before the collision in the x-direction
  • piy = the momentum of the system before the collision in the y-direction
  • Vci = the speed of the car before the collision
  • Vti = the speed of the truck before the collision
Picture



​Step 4 - Speed of the Car at the Traffic Light
  • given that police measurements show that the distance for the car from the traffic light to the collision point was 13.0m
  • given that the maximum acceleration of a loaded Ford Escort is about 3 m/s/s
Conclusion
Both of the drivers lied in their claims...
  • The car driver did not come to a complete stop at the traffic light
  • The truck driver did not start braking and was only traveling at 6.7m/s at the moment of impact
Therefore, both drivers are at fault. 
However, since the car driver had a flashing red light while the truck driver had a flashing yellow light, the car driver was supposed to come to a full stop for the light, but as a matter of fact, he was still traveling with a speed of 9.24m/s. Thus, to sum up, the car driver severely broke the law by still moving at the moment when the traffic light was red, so Mike Rokar should be taking greater responsibility for this accident. 
Testimony
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