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.
The car driver, Mike Rokar, claims: a) to have made a full stop at the light before entering the intersection b) that Mr. Hawk did not slow down prior to the collision.
The truck driver, Lincoln Hawk, claims: a) to have been braking before the collision b) that Mr. Rokar did not stop at the flashing red light.
Your Task: The court has asked your accident investigation agency to provide a comprehensive analysis collision from a physics perspective. Your team must put together a formal report for the court that assesses the claims of both drivers and determines if one, or both, of the drivers is at fault.
What do we know? What can we figure out?
CRASH DETAILS
The police department determined that the force required to drag a 130N (29lb) car tire across the pavement at a constant velocity is 100N (23 lb). Specifications from the truck's manufacturer claim that (for technical reasons) the effective coefficient for truck tires is only 70% that of car tires.
After collision, the truck and car skidded at the angles shown in the attached diagram. The car skidded a distance of 8.2m (27ft) before stopping while the truck skidded 11m (37ft) before stopping.
The weight of the car is 13600N (3050lb) and the weight of the truck is 69700N (15695lb).
The pre-crash angle between the velocities of the truck and car was 90°.
The truck driver claims to have begun braking in anticipation of a collision; traveling at only 6.7 m/s (15 mph) at the moment of impact.
Police measurements show that the distance for the car from the traffic light to the collision point was 13.0m (42.5ft)
Ford Motor Corporation specifications indicate that the maximum acceleration of a comparably loaded Ford Escort is about 3.0m/s/s.
With the given information, we should evaluate both stories by backtracking the incident and finding out the truth with the details given. To evaluate their speeds, we can find the values of momentum. With this collision, they have momentum in the x and y directions respectively. Since this is obviously an inelastic collision with a loss of kinetic energy and deformation, momentum is conserved in this situation. Therefore, the final momentum of both vehicles will be equal to the sum of the momentum of vehicles before the crash. It is equal in both the x and y directions. It is important to find the acceleration of both vehicles after the collision in order to evaluate the results of the crash. To do this, we must find the coefficient of friction between the tires and the asphalt.
CALCULATIONS
Car: Force of Friction = Coefficient of Friction * Normal Force
100N = μ * 130N
μ = 0.769
Truck:
The coefficient of friction for the truck is only 70% of the car's.
0.7 * 0.769 = 0.538
μ = 0.538
Linking Newton's Second Law and Forces, we can determine:
Force of Friction = Coefficient of Friction * Normal Force
Car
Fƒ= 13600N * 0.769
Fƒ = 10458.4N
Truck
Fƒ = 69700N * 0.538
Fƒ = 37498.6
F=ma
The net force values are negative because the vehicles are traveling in their negative directions, in the x and y respectively.
Car
-10458.4 = 1360 kg * a
a = -7.69 m/s/s
Truck
-37498.6 = 6970 kg * a
a = -5.38 m/s/s
Next, we can determine the velocity of each vehicle by using kinematics:
These velocities were at specific angle measures, 33° for the car and 7° for the truck, so using sine and cosine we can find the x and y components of the velocities.
Car
Vy = 11.23sin(33°) = 6.12 m/s
Vx = 11.23cos(33°) = 9.42 m/s
Truck
Vy = 10.88sin(7°) = 1.33 m/s
Vx = 10.88cos(7°) = 10.80 m/s
With these specific direction velocities, we can determine the momentum of the vehicles as momentum is the direct product of mass and velocity.
Car
Py = 1387.7kg * 6.12 m/s = 8492.72 kgm/s
Px = 1387.7kg * 9.42 m/s = 13072.13 kgm/s
Truck
Py = 7112.2kg * 1.33 m/s = 9459.23 kgm/s
Px = 7112.2kg * 10.80 m/s = 76811.76 kgm/s
While we calculated the momentum in both directions for each vehicles, it is only necessary to calculate the momentum in the direction the vehicle was traveling. The car was traveling in the y direction, so we will only record the momentum of the car in the y direction. As for the truck, it was traveling in the x direction so we will only record the momentum of the truck in the x direction. Since the momentum is conserved, the sum of the momentum in the y direction is the car's momentum, and the sum of the momentum in the x direction is the truck's momentum.
Car
8492.72 kgm/s + 9459.23 kgm/s = 17951.95 kgm/s
Truck
13072.13 kgm/s + 76811.76 kgm/s = 89883.89 kgm/s
Finally, with these values, we can find the velocities before the collision happened using the equation of momentum
Car
17951.95 kgm/s = 1387.7kg * v
v = 12.94 m/s
Truck
89883.89 kgm/s = 7112.2kg * v
v = 12.64 m/s
With this finding, it extremely evident that Mr. Hawk was definitely NOT telling the truth, as he drove twice his claimed driving speed at the collision. In addition, to test if the car driver was telling the honest truth, we can use kinematic equations with the values we found with these calculations.
Both drivers lied in their stories about the crash. The car driver claimed he came to a full stop at the light, when in reality, he was traveling at 9.46m/s prior to the collision. The truck driver claimed he started braking before the collision and that he traveled at 6.7m/s, when in reality, he was going 12.94m/s. While they both lied in their statements, the person at fault was the person who broke the law. That driver was the car driver because he had a flashing red light. A flashing red light means that the driver must come to a full stop and proceed only when safe. The truck driver had a flashing yellow light which meant he could proceed with caution. Therefore, the car driver is at fault because he did not come to a complete stop. Mr. Rokar is at fault for the collision.