A car who had a flashing red light and a truck who had a flashing red light collided at the intersection of Furiosa Drive and Fury Road in Joule, Virginia. The car driver claims to have made a full stop at the intersection and the truck driver claims to have slowed down prior to the intersection. Both drivers claim the other is lying about slowing down or stopping at the intersection. To determine who was at fault in the situation I have to analyze the data provided and come to a conclusion. After the collision, both cars started skidding at different angles with only friction slowing them down.
The truck driver, Lincoln Hawk, claims to have yielded because of the flashing yellow light and said he was only traveling 6.7 m/s at the moment of impact. It is unknown how fast the car driver, Mike Rokar, was driving, but he claims to have stopped at the light and his car, a Ford Escort, according to Ford has a maximum acceleration of 3.0 m/s/s. Police measurements show that Mike Rokar's car had only traveled 13.0 m after the line at the light before the collision. If he truly was stopped completely at the light, using kinematics, I found that he would have only been able to get to about 8.83 m/s by the time of the collision. To determine both of the drivers true speeds, you can use momentum to calculate their true speeds.
Using momentum you can find their speeds before and after the collision. After the collision, the car and truck both have momentum in the x and y directions(y is upwards and x is sideways according to the diagram). Momentum is conserved in this collision in both directions, so the sum of the final momentum in the y direction for both vehicles is equal to the momentum of the car prior to the collision. The sum of the final momentums in the x direction for both vehicles is equal to the momentum of the truck prior to the collision.
In order to determine the acceleration of the vehicles after the collision, you need to find the coefficient of friction between the tires of both vehicles and the road. It is given that the force required to drag a 13 kg tire across the pavement is 100 N. It is also given that the coefficient of friction of the truck is 70% that of the car tires.
Calculations
Frictional Force = Normal Force * Coefficient of Friction 100N = 130N *μ μ = 100N/130N for the car μ = 0.769 .769*.7= μ for the truck .538= μ for the truck
Using the μ, we can find the acceleration using f=ma and the frictional force formula.
For car:Frictional Force = Normal Force * μ ƒ = 13600 N * .769 ƒ = 10458.4 N For truck:ƒ = 69700 N *. 538 ƒ = 37498.6
For car:Force = Mass * Acceleration -10458.4 = 1360 kg * Acceleration Acceleration of car = -7.69 m/s/s For Truck:-37498.6 = 6970 kg * Acceleration Acceleration of truck = -5.38 m/s/s
Using the acceleration and the given distances that each vehicle skidded, we can find the velocities of each vehicle after the collision
(Final Velocity)^2 = (Initial Velocity)^2 + 2 * Acceleration * Change In Position For car: 0 m/s = Vi^2 + 2 * -7.69 m/s/s * 8.2 m 126.1 = Vi^2 For car Vi = 11.23 m/s For truck: 0 m/s = Vi^2 + 2 * -5.38 * 11 118.36 = Vi^2 For truck Vi = 10.88 m/s
These velocities are at angles, so using sine and cosine we can find the x and y components of the velocities.
Car: Y=11.23sin(33) Y=6.12 m/s X=11.23cos(33) X=9.42 m/s Truck: Y=10.88sin(7) Y=1.33 m/s X=10.88cos(7) X=10.80 m/s
Using these velocities, we can find the momentum prior to and after the collision. The momentum in this collision is conserved so the final momentum in the y direction is equal to the momentum of the car prior to the collision and the final momentum in the X direction is equal to the momentum of the truck prior to the collision.
Car Y: P=mv P= 1360*6.12 P= 8323.3 kg*m/s Car X: P=mv P=1360*9.42 P=12811.2 kg*m/s
Car Initial Momentum: Pi=Py+Py Pi = 8323.3 + 9270.1 Pi=17593.4 kg*m/s Truck Initial Momentum: Pi=Px+Px Pi=12811.2+75276 Pi= -88087.2 kg*m/s
Using these momentums, we can find out both vehicles velocity prior to the crash to see whether or not they were lying and who was at fault.
Car: P=mv 17593.4=1360*v vi=12.94 m/s Truck: P=mv 88087.2=6970*v vi= -12.64 m/s
This data proves that both drivers were lying about their speeds prior to the collision. The truck driver, Lincoln Hawk, claimed to have been going only 6.7 m/s at the time of the collision, but he was actually going over twice that speed at 12.64 m/s. The car driver, Mike Rokar, claimed to have stopped at the light, but it would have been impossible for his car to accelerate to 12.94 m/s by the time of the collision. As I earlier stated, Mike Rokar would only have been able to accelerate to 8.83 m/s in the space between where he claimed to have stopped and the position of the collision. Using kinematics, we can find the minimum speed at which he traveled through the flashing red light.
Vf^2=Vi^2+2*a*X 12.94^2=Vi^2 + 2 * 3 m/s * 13 m 167.4=Vi^2+78 Vi = 9.46 m/s
This proves that the car was traveling at a minimum speed of 9.46 m/s through the red light and that he was lying.
Conclusion
Both the drivers lied about their speeds during the collision, but only the car driver, Mike Rokar, broke a law prior to the collision. He had a flashing red light, but still didn't stop and traveled through the light at a minimum speed of 9.46 m/s. The truck driver, Lincoln Hawk, also lied about his speed and was actually going twice the speed he claimed. Although he lied about his speed, he had a flashing yellow light which means yield, but it does not require you to slow down although it encourages it. Because of this, the car driver, Mike Rokar, was at fault in the accident.