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:
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
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
What am I to do?
I, as an agent of an accident investigation agency, am to provide a professional written report on the accident which covers; the background information about the principles that apply to the accident, calculations that determine the coefficient of friction, calculations that determine the speed of each vehicle after the collision, calculations that determine the speed of each vehicle before the collision, and a detailed opinion piece as to which driver was at fault for the accident justified by scientific evidence.
Prior to Calculations Information
In order to determine the calculations asked of the agency, a clear understanding of certain topics must be established.
Momentum: the impetus gained by a moving object, measured as the product of its mass and velocity
Conservation of Momentum: the total linear momentum of a system without external influence remains constant in magnitude and direction
Friction: the resistant force that one surface or object encounters when moving across another
Momentum: the impetus gained by a moving object, measured as the product of its mass and velocity
Conservation of Momentum: the total linear momentum of a system without external influence remains constant in magnitude and direction
Friction: the resistant force that one surface or object encounters when moving across another
Crash Details
1. 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 trucks manufacturer claim that, for technical reasons, the effective coefficient of friction for truck tires is only 70% that of car tires.
2. 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
3. The weight of the car is 13,600 N (3050 lb) and the weight of the truck is 69,700 N (15,695 lb).
4. The pre-crash angle between the velocities of the truck and car was 90 degrees.
5. 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.
6. Police measurements show that the distance for the car from the traffic light to the collision point was 13.0 m (42.5 ft)
7. Ford Motor Corporation specifications indicate that the maximum acceleration of a comparably loaded Ford Escort is about 3.0 m/s^2
2. 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
3. The weight of the car is 13,600 N (3050 lb) and the weight of the truck is 69,700 N (15,695 lb).
4. The pre-crash angle between the velocities of the truck and car was 90 degrees.
5. 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.
6. Police measurements show that the distance for the car from the traffic light to the collision point was 13.0 m (42.5 ft)
7. Ford Motor Corporation specifications indicate that the maximum acceleration of a comparably loaded Ford Escort is about 3.0 m/s^2
Calculations
COEFFICIENT OF FRICTION
Frictional force (Ff) = coefficient of friction (µ) * Normal Force (FN) Car 100 N = µ * 130 N 100 N / 130 N = µ µ = 0.76923 (for the car) Truck 100 N = µ * 130 N 100 N / 130 N = µ µ = 0.76923 µ * 0.7 (70%) = 0.53846 (for the truck) ACCELERATION
Force (Fnet) = Mass (m) * Acceleration (a) Car 10,429 N = 1383.457 kg * a a = 10,429 N / 1383.457 kg a = 7.5383 m/s^2 (Acceleration is negative because the vehicle is slowing down) a = -7.5383 m/s^2 Truck 37,567 N = 7119.1322 kg * a a = 37,567 N / 7119.1322 kg a = 5.2769 m/s^2 (Acceleration is negative because the vehicle is slowing down) a = -5.2769 m/s^2
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KINETIC FRICTIONAL FORCE
Force of Kinetic Friction (Fk) = Coefficient of Kinetic Friction (µk) * Mass (m) * Gravity (g) Car Force of Kinetic Friction (Fk) = 0.76923 * 1383.457 kg * 9.8 m/s Force of Kinetic Friction (Fk) = 10,429 N Truck Force of Kinetic Friction (Fk) = 0.53846 * 7119.1322 kg * 9.8 m/s Force of Kinetic Friction (Fk) = 37,567 N VELOCITY (POST COLLISION)
Final Velocity (Vf)^2 = Initial Velocity (Vi)^2 + 2 * Acceleration (a) * Change in position (Δx) Car (Vf)^2 = (Vi)^2 + 2 * -7.5383 * 8.2m 0 = (Vi)^2 + 2 * -7.5383 * 8.2m Vi = 11.118 Truck (Vf)^2 = (Vi)^2 + 2 * -5.2769 * 11m Vi = 10.774 DIRECTIONAL MOMENTUM
Momentum (p) = Mass (m) * Velocity (v) Car Y = 6.0552 m/s * 1,383.457 kg = 8,377.1088 kg m/s X = 9.3243 m/s * 1,383.457 kg = 12,899.7681 kg m/s Truck Y = 1.3130 m/s * 7119.1322kg = 9,347.4205 kg m/s X = 10.6936 m/s * 7119.1322kg = 76,129.1521 kg m/s |
VEHICLES MOMENTUM
Since momentum is conserved in this collision, the sum of all momentum in each direction will determine each vehicles momentum prior to the crash.
Car
8,377.1088 kg m/s + 9,347.4205 kg m/s = 17,724.5293 kg m/s
Truck
12,899.7681 kg m/s + 76,129.1521 kg m/s = 89,028.9202 kg m/s
Since momentum is conserved in this collision, the sum of all momentum in each direction will determine each vehicles momentum prior to the crash.
Car
8,377.1088 kg m/s + 9,347.4205 kg m/s = 17,724.5293 kg m/s
Truck
12,899.7681 kg m/s + 76,129.1521 kg m/s = 89,028.9202 kg m/s
VELOCITY PRIOR TO THE COLLISION
Momentum (p) = Mass (m) * Velocity (V)
Car
17,724.5293 kg m/s = 1383.457 kg * V
V = 12.811767 m/s
Truck
89,028.9202 kg m/s = 7119.1322 kg * (V)
V = 12.505586 m/s
Momentum (p) = Mass (m) * Velocity (V)
Car
17,724.5293 kg m/s = 1383.457 kg * V
V = 12.811767 m/s
Truck
89,028.9202 kg m/s = 7119.1322 kg * (V)
V = 12.505586 m/s
Looking back at the cars reported speed we can see that the driver, Lincoln Hawk, was not truthful in reporting his speed and was lying about the accident. Mr. Hawk is at fault for speeding.