Monday, 25 January 2016 14:01
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Low Speed Accidents - Conservation of Momentum: Where does it go, Part II

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**Conservation of Momentum: **

**Where does it go, Part II.**

By: Patrick Sundby, Accident Investigator

Specializing in Low Speed and Catastrophic Crashes

Mark Studin DC, FASBE(C), DAAPM, DAAMLP

In the previous writing we explored the standards for vehicle integrity during low speed collisions. In this writing we will expand on Conservation of Momentum. If you have not read the previous article you are encouraged to do so. While it’s not necessary to read it doing so will assist you as this writing will build on concepts contained within. If you do not have it, please contact us and we will make it available to you.

Expand on Conservation of Momentum.

Remember we previously said “The momentum going into a collision can be accounted for in the outcome” when we discussed the concept of Conservation of Momentum. Here we will introduce the formula and walk through its components; we will need to understand this in order to explore how different size vehicles affect each other in a collision.

The full formula:

Let’s walk through this, on the left side of the equation we have which is the weight of the first vehicle before the collision multiplied by which is the velocity (in feet per second) of the first vehicle before the collision. is the weight of the second vehicle before the collision times which is the velocity (in feet per second) of the second vehicle before the collision. On the right side of the equation we have which is the weight of the first vehicle after the collision multiplied by which is the velocity (in feet per second) of the first vehicle after the collision. is the weight of the second vehicle after the collision times which is the velocity (in feet per second) of the second vehicle after the collision.

Ok, I know this seems very complex and the explanation is not jumping off the page so let’s write with a little more ease of understanding. Let’s take the National Highway Transportation Safety Administration (NHTSA) standards for testing and put two of the same mass vehicles in this. Let’s use a 2012 Toyota Corolla, and because we need two of them we will say one is red and the other is blue.

Red Corolla * 5 mph + Blue Corolla * 0 mph = Red Corolla * 0 mph + Blue Corolla * 5 mph

The 2012 Toyota Corolla has a curb weight of 2,734 pounds, substituted in the formula it looks like this:

2,734 lbs * 5 mph + 2,734 lbs * 0 mph = 2,734 lbs * 0 mph + 2,734 lbs * 5 mph

We need the speeds in feet per second, to do this we will multiply by 1.47 times the miles per hour. This gives us 7.35 feet per second.

2,734 lbs * 7.35 fps + 2,734 lbs * 0 fps = 2,734 lbs * 0 fps + 2,734 lbs * 7.35 fps

Now when we do the math to show the conservation of momentum we end up with the following:

20,094.9 + 0 = 0 + 20,094.9

20,094.9 = 20,094.9

Momentum conserved.

Now we have proved the concept so we are going to apply it to a collision involving two different vehicles. We will substitute the 2012 red Toyota Corolla for a 2012 red Chevrolet Tahoe. The 2012 Chevrolet Tahoe weighs 5,448 lbs. Now the formula looks like this:

Red Tahoe * 5 mph + Blue Corolla * 0 mph = Red Tahoe * 0 mph + Blue Corolla * 9.96 mph

5,448 lbs * 5 mph + 2,734 lbs * 0 mph = 5,448 lbs * 0 mph + 2,734 lbs * 9.96 mph (speed after impact)

We need speeds in feet per second, to do this we will multiply by 1.47. This gives us 7.35 (5mph) and 14.64 (9.96mph).

5,448 lbs * 7.35 fps + 2,734 lbs * 0 fps = 5,448 lbs * 0 fps + 2,734 lbs * 14.64 fps

Now when we do the math to show the conservation of momentum we end up with the following:

40,042.8 + 0 = 0 + 40,042.8[1]

40,042.8 = 40,042.8

Momentum conserved.

Three important points can be observed in this demonstration.

First, when testing is done note the change in speed in the Tahoe is 5 mph (5 to 0). This is less than the speeds used by the Insurance Institute for Highway Safety which we have previously discussed and we would expect the Tahoe to have no structural deformation and minimal cosmetic damage.

The second point to note is the change in speed the Corolla experiences, 9.96 mph (0 to 9.96). This change in speed is four times the minimum needed to induce whiplash injury.

Finally, neither vehicle exceeds the speed of 10 mph, which the auto manufactures and insrunace institute for highway safety often consider threshold for injury. This confirms that cars can easily deform and occupants get injured in low speed crashes once you begin to look at the conservation of energy (momentum) and coefficient of forces transferred to the target car.

Should you want a further explanation or to discuss a case, please contact me 571-265-8076

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Edmunds.com. (2012). *2012 Chevrolet Tahoe Specifications*. Retrieved from Edmunds.com: www.edmunds.com

Edmunds.com. (2012). *2012 Toyota Corolla Sedan Specifications*. Retrieved from Edmunds.com: www.edmunds.com

Brault J., Wheeler J., Gunter S., Brault E., (1998) Clinical Response of Human Subjects to Rear End Automobile Collisions*. Archives of Physical Medicine and Rehabilitation*, 72-80.

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*Patrick Sundby**has decades of experience in the automotive industry including several years in law enforcement collision investigation. He has also been a driver training and firearms instructor in law enforcement and a police officer for 9 years before specializing in accident investigations. He has had the privilege of participating in both learning and teaching at Prince William County Criminal Justice Training Academy in Virginia and studied at the Federal Law Enforcement Training Center in Georgia. His specialty is low speed and catastrophic crashes and has testified over 500 times at various level. He can be reached at 571-265-8076 or patrick.sundby@gmail.com*

*Dr. Mark Studin**is an adjunct associate professor of chiropractic at the University of Bridgeport College of Chiropractic, an Adjunct Professor of Clinical Sciences at Texas Chiropractic College and a clinical presenter for the State of New York at Buffalo, School of Medicine and Biomedical Sciences for postdoctoral education, teaching MRI spine interpretation and triaging trauma cases. He is also the president of the Academy of Chiropractic, teaching doctors how to interface with the legal community (www.DoctorsPIProgram.com). He teaches MRI interpretation and triaging trauma cases to doctors of all disciplines nationally, and studies trends in health care on a national scale (www.TeachDoctors.com). He can be reached at DrMark@AcademyofChiropractic.com or at 631-786-4253.*

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[1] If the formula is completed with rounded numbers the answer is 40,025.76 not 40,042.8. The full numbers are not shown, but used, to ensure a match at the end of the equation.

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