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.
The car driver, Mike Rokar, claims:
The truck driver, Lincoln Hawk, claims:
Crash Details
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:
- to have made a full stop at the light before entering the intersection
- that Mr. Hawk did not slow down prior to the collision
The truck driver, Lincoln Hawk, claims:
- to have been braking before the collision
- that Mr. Rokar did not stop at the flashing red light
Crash Details
- The police department determined that the force required to drag a 130 N (29 lb) car tire across the pavement at a constant velocity is 100 N (23 lb). Specifications from the truck's manufacturer claim that (for technical reasons) the effective coefficient of friction for the 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 8.2 m (27 ft) before stopping while the truck skidded 11 m (37 ft) before stopping.
- The weight o the car is 13,600 N (3050 lb) and the weight of the truck is 69,700 N (15,695 lb).
- The pre-crash angle between the velocities of the truck and car was 90 degrees.
- 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 13.0 m (42.5 ft)
- Ford Motor Corporation specifications indicate that the maximum acceleration of a comparably loaded Ford Escort is about 3.0 m/s^2.
Calculations
In order to determine the drivers' actual speeds and who was more at fault for the crash we need to use Kinematics, Momentum, Forces, Motion, Friction, and Conservation Laws. These physics concepts will help us figure out variables such as velocities before and after the collision, momentum in both the x and y direction, the friction coefficient of the car and truck against the road, and the acceleration of both vehicles after the collision.
First we will find the friction coefficient using the formula, Ff = Fn * µk.
Frictional Force = Normal Force * Friction Coefficient
100 N = 130 N * µk
µk for car = 0.769
The friction coefficient for the truck is 70% that of the car so
µk for truck = 0.538
Now that we have our friction coefficient we can plug that into our friction formula to find the friction forces for the car and truck
Frictional Force = Normal Force * Friction Coefficient
Ff = 13600 N * 0.769
Ff for car = 10458.4 N
Ff = 69700 N * 0.538
Ff for truck = 37498.6 N
With these frictional forces we can find acceleration through Newton's Second Law, Force = Mass * Acceleration
-10458.4 = 1360 kg * a
Acceleration for car = 7.69 m/s/s
-37498.6 = 6970 kg * a
Acceleration for truck = -5.38 m/s/s
Using one of our Kinematic equations, we are able to figure out the velocity of the vehicles after the collision
(Final Velocity)^2 = (Initial Velocity)^2 + 2 * Acceleration * Change In Position
0 m/s = Vi^2 + 2 * -7.69 m/s/s * 8.2 m
126.1 = Vi^2
Vi for car = 11.23 m/s
0 m/s = Vi^2 + 2 * -5.38 * 11
118.36 = Vi^2
Vi for truck = 10.88 m/s
We are given angles at which these vehicles skidded for the crash, so we can use trigonometric function to find the x-y components for the velocities
Y=11.23sin(33)
Y for car = 6.12 m/s
X=11.23cos(33)
X for car = 9.42 m/s
Truck: Y=10.88sin(7)
Y for truck = 1.33 m/s
X=10.88cos(7)
X for truck = 10.80 m/s
Since we have the final velocities of both vehicles after the crash, we can use the momentum equation, p = mv, and since momentum is conserved, pi = pf, in order to find the original velocities of the vehicles prior the crash
P= 1360*6.12
P for Car Y: 8323.3 kg*m/s
P=1360*9.42
P for Car X = 12811.2 kg*m/s
P=6970*1.33
P for Truck Y = 9270.1 kg*m/s
P=6970*10.80
P for Truck X = 75276 kg*m/s
Pi=Py+Py
Pi = 8323.3 + 9270.1
Pi for Car = 17593.4 kg*m/s
17593.4 = 1360*v
Vi for Car = 12.94 m/s
Pi=Px+Px
Pi=12811.2+75276
Pi for Truck = -88087.2 kg*m/s
88087.2=6970*v
Vi for Truck = -12.64 m/s
Mike Rokar additionally made the claim that he came to a full stop at the intersection, however we can prove this wrong by using the distance between the light and the collision point
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
In order to determine the drivers' actual speeds and who was more at fault for the crash we need to use Kinematics, Momentum, Forces, Motion, Friction, and Conservation Laws. These physics concepts will help us figure out variables such as velocities before and after the collision, momentum in both the x and y direction, the friction coefficient of the car and truck against the road, and the acceleration of both vehicles after the collision.
First we will find the friction coefficient using the formula, Ff = Fn * µk.
Frictional Force = Normal Force * Friction Coefficient
100 N = 130 N * µk
µk for car = 0.769
The friction coefficient for the truck is 70% that of the car so
µk for truck = 0.538
Now that we have our friction coefficient we can plug that into our friction formula to find the friction forces for the car and truck
Frictional Force = Normal Force * Friction Coefficient
Ff = 13600 N * 0.769
Ff for car = 10458.4 N
Ff = 69700 N * 0.538
Ff for truck = 37498.6 N
With these frictional forces we can find acceleration through Newton's Second Law, Force = Mass * Acceleration
-10458.4 = 1360 kg * a
Acceleration for car = 7.69 m/s/s
-37498.6 = 6970 kg * a
Acceleration for truck = -5.38 m/s/s
Using one of our Kinematic equations, we are able to figure out the velocity of the vehicles after the collision
(Final Velocity)^2 = (Initial Velocity)^2 + 2 * Acceleration * Change In Position
0 m/s = Vi^2 + 2 * -7.69 m/s/s * 8.2 m
126.1 = Vi^2
Vi for car = 11.23 m/s
0 m/s = Vi^2 + 2 * -5.38 * 11
118.36 = Vi^2
Vi for truck = 10.88 m/s
We are given angles at which these vehicles skidded for the crash, so we can use trigonometric function to find the x-y components for the velocities
Y=11.23sin(33)
Y for car = 6.12 m/s
X=11.23cos(33)
X for car = 9.42 m/s
Truck: Y=10.88sin(7)
Y for truck = 1.33 m/s
X=10.88cos(7)
X for truck = 10.80 m/s
Since we have the final velocities of both vehicles after the crash, we can use the momentum equation, p = mv, and since momentum is conserved, pi = pf, in order to find the original velocities of the vehicles prior the crash
P= 1360*6.12
P for Car Y: 8323.3 kg*m/s
P=1360*9.42
P for Car X = 12811.2 kg*m/s
P=6970*1.33
P for Truck Y = 9270.1 kg*m/s
P=6970*10.80
P for Truck X = 75276 kg*m/s
Pi=Py+Py
Pi = 8323.3 + 9270.1
Pi for Car = 17593.4 kg*m/s
17593.4 = 1360*v
Vi for Car = 12.94 m/s
Pi=Px+Px
Pi=12811.2+75276
Pi for Truck = -88087.2 kg*m/s
88087.2=6970*v
Vi for Truck = -12.64 m/s
Mike Rokar additionally made the claim that he came to a full stop at the intersection, however we can prove this wrong by using the distance between the light and the collision point
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
Conclusion
After doing many calculations and solving for all the variables involved, we can safely say that both drivers lied during their testimonies. However, although both lied about details, one of their testimonies changed the perspective of the crash. Lincoln Hawk, did lie about his approximate speed while driving through the intersection, he stated his speed was about 6.7 m/s, while the calculations show it is around double that of Lincoln's testimony. Moving on to Mike Rokar, his statement was absurdly incorrect. He said that he broke at the light and then entered the intersection, which we found to be completely untrue as the distance to the collision from the light did not match up with the velocity and acceleration his car could have been going at the time. While both lied about aspects, Mike Rokar is at fault for the collision for failing to break while at the light and blatantly lying during his testimony.
After doing many calculations and solving for all the variables involved, we can safely say that both drivers lied during their testimonies. However, although both lied about details, one of their testimonies changed the perspective of the crash. Lincoln Hawk, did lie about his approximate speed while driving through the intersection, he stated his speed was about 6.7 m/s, while the calculations show it is around double that of Lincoln's testimony. Moving on to Mike Rokar, his statement was absurdly incorrect. He said that he broke at the light and then entered the intersection, which we found to be completely untrue as the distance to the collision from the light did not match up with the velocity and acceleration his car could have been going at the time. While both lied about aspects, Mike Rokar is at fault for the collision for failing to break while at the light and blatantly lying during his testimony.