The Physics of Automobile Accidents

Each day in America millions of accidents occur, but how does one decide who¡¯s fault the accident really was, or who was speeding? This is where accident reconstructionists come in. ¡°Accident reconstructionists are people who devote their careers to using their knowledge of physics and motion along with remains from accident scenes to determine the cause of the accident and how it could have been avoided¡± (Borges, 2002).

The purpose of this experiment was to determine the speed of vehicle #1 at the point of impact. Vehicle #2 was making a left turn in front of vehicle #1 traveling at a high rate of speed. The operator of vehicle #2 states that he did not see vehicle #1 before starting to turn, and they end up crashing into each other. The results supported the hypothesis that vehicle #1 was speeding at the point of impact.

The Physics of Automobile Accidents
Two cars are traveling down a highway in opposite directions. Both drivers are tired from driving all day and cross over the yellow line and hit head on. Crash! The driver of car A has remained inside the car and has broken ribs due to hitting the steering wheel. The driver of car B however is on the hood of car A and is pronounced dead at the scene, cause of death, a severe case of disobeying the laws of physics. Although both cars were heading at the same velocity one driver ended up dead while another survived. This seems like a complicated and hard thing to explain, but using the knowledge of basic physics it is easy.

Sir Isaac Newton was the first man to explain what happens in a collision even before automobiles were invented. He proposed the idea that an object in motion will continue in motion with the same speed and direction unless acted upon by an outside, unbalanced force. His theory is better known as the Law of Inertia. The driver of car B was not wearing a seatbelt and as a result was not connected to the body of the car (Bryce, 2002).

According to Newton¡¯s first law if an object is at rest, it tends to stay at rest, and if an object is in motion, it tends to stay in motion at a constant velocity until an outside force affects the object’s state of inertia. Car B was moving until it hit an outside force, car A. When the collision occurred the car and passenger changed their motion and direction. However, because driver B wasn¡¯t attached to his car by his seatbelt he continued with the same speed and in the same direction as the car before the collision. Driver B flew through the windshield and onto the hood of car A. The windshield and car A acted as the necessary outside force needed to bring driver B to rest. Since the driver of car A was wearing his seatbelt he experienced the same state of motion and deceleration as the car and avoided major injury (Bryce, 2002).

Momentum can be defined as “mass in motion.” All objects have mass; so if an object is moving, then it has momentum; it has mass in motion. Momentum depends upon the variables mass and velocity. The momentum of an object is equal to the mass of the object times the velocity of the object. An object has a large momentum if either its mass or its velocity is large. A fast moving car has more momentum than a slow moving car, assuming they have the same mass. A heavy truck would have more momentum than a small car, assuming they have the same speed. So, the more momentum an object has, the harder it is to stop and the greater effect it will have if it is brought to rest by impact or collision (Novak, G., & Gavrin, R).

Newton¡¯s third law states that for every action there is an equal and opposite reaction force. This law helps explain why a collision at low speeds is less serious than one at high speeds. If a car exerts a small force on a brick wall because its speed was low then the car and its passengers will experience a force of equal magnitude but it will be in the opposite direction. If cars of unequal mass collide the more massive car will force the smaller vehicle backwards and the smaller car will experience more force. This is due to the conservation of momentum (Writ, 2000).

The Law of Conservation of Momentum states that in an isolated system the momentum before a collision is equal to the momentum after the collision, if we disregard friction. If cars of unequal mass collide the more massive car will force the smaller vehicle backwards and the smaller car will experience more force. We can see that the momentum lost by the larger car was gained by the smaller car (Writ, 2000).

In automobile accidents there are two types of collisions: elastic and inelastic. Collisions in which objects rebound with the same speed, (having the same momentum and kinetic energy) as they had prior to the collision are known as elastic collisions. Elastic collisions are characterized by a large velocity change, a large momentum change, a large impulse, and a large force.

An inelastic collision is a collision in which the kinetic energy of the system of objects is not conserved. In an inelastic collision, the kinetic energy of the colliding objects is transformed into other non-mechanical forms of energy such as heat energy and sound energy. Any collisions in which the two colliding objects ¡°stick together¡± and continue with the same final are said to be inelastic collisions (Borges, 2002).

For many decades people have used the laws of physics to explain the events of car crashes. ¡°Accident reconstructionists are people who devote their careers to using their knowledge of physics and motion along with remains from accident scenes to determine the cause of the accident and how it could have been avoided¡± (Borges, 2002). They also work with manufacturers to come up with ways to reduce injuries that occur from car accidents. Reconstructionists use formulas and what they know to determine masses of the vehicle, impact location, rest position, and post impact. A reconstructionist¡¯s conclusions are very useful for car engineers, manufacturers and consumers. By studying accidents they have been able to come up with new safety features to help keep a person safe in the event of a collision.

Seatbelts are the single most effective safety feature in reducing car fatalities. The seatbelt allows a person to be connected to the vehicle which allows for the momentum of a person’s body to be slowed down at same speed as the car. Seatbelts allow the passenger to take advantage of the cars energy absorbing design. A seatbelt’s job is to spread the stopping force across sturdier parts of your body in order to minimize damage.
A recent innovation called pretensioners tightens up any slack in the seatbelt in the event of a crash. The pretensioner pulls in on the belt. This force helps move the passenger into the best possible crash position in his or her seat. While the seatbelt helps in most cases sometimes it is not good enough and the driver is injured by the steering wheel. After careful research engineers came up with airbags, which in combination with a seatbelt can increase a passenger¡¯s safety in a frontal collision (Car Collision Testing, n.d.).

Airbags work by sensors on the car that detect a high rate of deceleration inside the passenger compartment and cause the airbag to go off. While the airbag is inflated it prevents the head and chest of front seat occupants from striking the steering column, dashboard, and windshield. Airbags greatly reduce the fatality from a collision for a person who is wearing a seatbelt and is involved in a head on collision.

Another safety feature that is less obvious to many people is crumple zones. Crumple zones are areas in the front and rear of a car that collapse fairly easily. Instead of the entire car coming to an abrupt stop when it hits an obstacle, it absorbs some of the impact force by flattening, like an empty soda can. The car’s cabin is much sturdier, so it does not crumple around the passengers. This redirects the energy in the collision and reduces injury.

Without a crumple zone the vehicle rebounds in an elastic manner regaining nearly all of its kinetic energy. The occupants of the vehicle will experience a force of equal and opposite direction which is very large. With a crumple zone much of the kinetic energy is transferred into heat and sound energy following in a much smaller force being applied to the car and its passengers.

Other safety devices being devised are break away poles, collapsing steering wheel columns, and side airbags. Each of theses new items is being created to improve the safety of passengers by looking carefully at the physics of collisions and using Newton¡¯s three laws of motion (Bryce, 2002).

An accident reconstruction was conducted using police report case #920801 ¨C 01 to determine the speed of vehicle #1 at the point of impact. It is hypothesized that vehicle #1 will be speeding at the point of impact.
The first thing that needed to be done was a measuring of the scene of the accident. This was done using a roll distance measurer. Next, a drag sled was used to find the drag factors. Finally, using distances and skid marks, the speeds of each vehicle during different times in the accident were found.
Below are some of the formulas and factors used:

s = speed f = drag factor F = force m = mass
d = distance w = weight ∆t = change in time
s = 5.47 ¡Ì df F∆t = m∆v ∆v = change in velocity
sc = ¡Ì sp2 + s12
S1W1 + S2W2 = S3W1 + S4W2

Speed Determinations
Variable Description Results

dp vehicle #1 skid marks prior to impact 62 ft 8 in
d2 vehicle #2 traveled from start to impact 55 ft
d3 vehicle #1 skid marks past point of impact 105 ft
d4 vehicle #2 skid marks past point of impact 35 ft 2 in
w1 weight of vehicle #1 3,653 lbs
w2 weight of vehicle #2 3,278 lbs
f1 drag factor of moving vehicle .15
f2 drag factor of stopping vehicle .72
fadjusted adjusted drag factor if front tires pinched .43
sp speed vehicle #1 pre-impact 37 mph
s1 speed vehicle #1 pre-impact 47 mph
sc combined pre-impact speeds (actual impact speed) 60 mph
s2 speed vehicle #2 from start to impact 16 mph
s3 vehicle #1 post impact speed 37 mph
s4 vehicle #2 post impact speed 28 mph


Police Traffic

Traffic Investigation Report
Town of Gladstone Police
Case # 920801 – 01

Doe v. Smith
Operator #1 John Doe
1234 Delta Avenue
Gladstone, MI
Date of birth: 4/27/78
Injuries: visible injuries, including cuts, bruised forehead

Vehicle #1 2003 Volvo S80 T6
front end damaged

Operator #2 George Smith
278 Main Street
Gladstone, MI
Date of Birth: 2/16/69
Injuries: visible injuries, including distorted left arm, cuts

Vehicle #2 2000 Chevy Malibu
driver side damage

Witnesses: none

Scene: North 29th Street and M-35
Gladstone, MI
number of lanes: 2
posted speed limit 40 mph
vehicle #1 going straight ahead
vehicle #2 making left turn
road condition: dry
time of collision: 2:17
date of collision: 1/5/03
no traffic controls present
weather condition: clear

Violations: Operator #1 exceeding lawful speed

Operator #2 failure to grant right of way to another vehicle

Accident Description

Vehicle #2 making left turn in front of vehicle #1 traveling at high rate of speed. Vehicle #1 put down 62 ft 8 in skid mark prior to impact and vehicle #2 traveled 55 ft from stop to impact. Vehicle #1 left 105 ft of skid marks past the point of impact, while vehicle #2 left 35 ft 2 in. Operator of vehicle #2 states that he did not see vehicle #1 before starting to turn.

drag factor of road measured with sled = 0.72
weight of vehicle #1 = 3,653 lbs
weight of vehicle #2 = 3,278 lbs

Statement: Smith (Operator vehicle #2)
I was on my way to the grocery store to get some food. I stopped and put my turn signal on and then waited for some traffic to pass before I started my turn. I looked up the road but didn¡¯t see anything coming except a car and I figured that it was far enough away for me to turn safely. I started my turn and then heard breaks screeching and the guy just plowed into me. I never saw the car before it hit me. He must have been going really fast.

Statement: Doe (Operator vehicle #1)
I was riding behind a car and decided to pass. I got completely past it and then started to pull back into the right lane. I noticed a red car up ahead that looked like it wanted to turn left, and then all of a sudden it just jerked across in front of me. I hit my brakes really hard and tried to keep control of the car, but I couldn¡¯t stop in time and hit the car broadside. The guy in the red car just pulled right out in front of me and I didn¡¯t have time to stop.

Drag Sled Measurements

Calibrating the police drag sled:
1) Place the empty drag sled on a calibrated scale.
2) Add sand to plastic bags so the total weight of the sled is 20 lbs.
Using the police drag sled:
1) The scale must be pulled parallel to the road surface for accurate results.
2) The sled should be pulled slowly, with a steady pulling force, using the arms to absorb the jerky motion of the sled.
3) The sled should be pulled so there is a steady reading on the scale for a short distance (6¡± ¨C 8¡±)
4) The drag factor is determined by dividing the pulling force by the weight of the sled.
Sled weight (w): 20 lbs
Surface Pull Force (F) Drag Factor (F/w)
Traveled asphalt 13.5 lbs .675
Traveled asphalt 14.5 lbs .725
Traveled asphalt 15.0 lbs .750
Average .717

Drag factor = .72
Calculating Speeds
Vehicle #1 pre-impact speed:
dp = 62 ft 8 in
f2 = .72
sp = 5.47 ¡Ìdf
= 5.47 ¡Ì(62.67 ft)(.72)
= 36.74 mph

Vehicle #2 traveling speed from start to impact:
f1 = .15
d2 = 55 ft
s2 = 5.47 ¡Ìdf
= 5.47 ¡Ì(55 ft)(.15)
= 15.71 mph

Vehicle #1 post-impact speed:
d3 = 105 ft
fadjusted = f2 * 60%
= (.72)(.6)
= .43
s3 = 5.47 ¡Ìdf
= 5.47 ¡Ì(105 ft)(.43)
= 36.75 mph

Vehicle #2 post-impact speed:
d4 = 35 ft 2 in
f2 = .72
s4 = 5.47 ¡Ìdf
= 5.47 ¡Ì(35.17 ft)(.72)
= 27.53 mph

Vehicle #1 pre-impact speed:
w1 = 3,653 lbs s3 = 36.75 mph
w2 = 3,278 lbs s4 = 27.53 mph
s2 = 15.71 mph
S1W1 + S2W2 = S3W1 + S4W2
S1 = S3W1 + S4W2 – S2W2
= (36.75 mph)(3,653 lbs) + (27.53 mph)(3,278 lbs) ¨C (15.71 mph)(3,278 lbs)
3,653 lbs
= 47.36 mph

Vehicle #1 combined pre-impact speeds (actual impact speed):
sp = 36.74 mph
s1 = 47.36 mph
sc = ¡Ì sp2 + s12
= ¡Ì 36.742 + 47.362
= 59.94 mph

Using the laws of physics it was found that the operator of vehicle #1 was traveling 60 mph at the point of impact, which is 20 mph over the speed limit. The operator of vehicle #2 was charged with failure to grant right of way to another vehicle.

Sir Isaac Newton was the first man to explain the physics in crashes. His laws of motion and formulas are still used today by accident reconstructionists.

Seat belts are designed to stop occupants from continuing at the same speed as the vehicle was traveling before impact. Front air bags and side air bags help with stopping occupants in a vehicle from continuing forward and being ejected out of the vehicle. Crumple zones on cars allow the vehicle to absorb some of the initial impact and decrease the force applied.

Car accidents are physics in motion and each car accident is different. Understanding how physics work in collisions is something that everybody should know. According to the National Transportation Safety Board, the average driver will be in at least four car accidents throughout their lifetime, and of those four car crashes one will be severe enough to cause major bodily injuries or even death. When considering the momentum of each and every vehicle it is hard to imagine that every time we get into a car, we are getting into a metal bullet and just waiting or turn to put physics in motion.

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