In the prior writing we explored the criteria for vehicle integrity. In this writing we’ll expand on conservation of momentum. You’re encouraged to do so when you haven’t read the previous article.

Expanding on Conservation of Momentum

Remember we previously said, “The momentum moving into a collision could be accounted for at the outcome” when we discussed the concept of conservation of momentum. Here we will introduce the formula and walk through its parts; we have to comprehend this in order to explore each other influence.

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 looks very intricate and the explanation is not jumping off the page so let’s write with a bit more ease of comprehension. Let us take the National Highway Transportation Safety Administration (NHTSA) standards for testing and place two of the identical mass vehicles in this. Let us use a 2012 Toyota Corolla, and we will say the other is blue and one is red because we need two of them.

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 significant points can be observed in this protest.

First, when testing is done notice the change in rate at the Tahoe is 5 mph (5 to 0). This is less than the rates used by the Insurance Institute and we would expect the Tahoe to have minimal damage and no structural deformation.
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 original.

Conclusion

Finally, neither vehicle exceeds the speed of 10 mph, which the automobile manufactures and insurance institute for highway safety often consider threshold for injury. This confirms that cars can easily deform and residents become injured in low speed crashes once you begin to check out the conservation of energy (momentum) and coefficient of forces moved to the target car.

The scope of our information is limited to chiropractic and spinal injuries and conditions. To discuss options on the subject matter, please feel free to ask Dr. Jimenez or contact us at 915-850-0900 . 

References

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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