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I’m alive! And I can still do derivatives! December 6, 2006

Posted by eric22222 in General, Math, Personal Favorites.
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Okay, because I’m going to have to tell people about a hundred times today, I decided to post about last night’s accident here:

David and Zach called me saying they needed a jump start. I drove down to Sonic and hooked up David’s car. Once he was able to start it, we disconnected the cables. David drove out of the parking lot and coasted into the parking lot next door. We hooked it up again, and David drove once around the parking lot. This time, we let the battery charge for about fifteen minutes. David drove off, and I followed close behind. Things were looking up. We hit mostly green lights. There was one we had to stop at, but the car kept running. It was the second light where things went downhill (figuratively. It was literally uphill). David’s car started jerking, and slowed to a stop in the middle of the road. I pulled up next to them and hooked the jumper cables back up. I turned my hazard lights on and let the battery charge. I was sitting in my car, Zach was holding David’s hood up (it didn’t stay up on its own), and David was there, too. I was watching the traffic merge over from my rear view mirror.

Then I saw it: the car that didn’t change lanes. I had a solid five seconds to contemplate the situation. I considered jumping out of the car, but decided on pushing my brakes in and holding on tight. I think I heard someone yell “Dobbs!” but I can’t be sure. I felt a quick jolt, and skidded about ten feet. Everyone was ok afterwards, but my car didn’t really survive. So… I’m getting to carpool home for Christmas.

Now let’s move on to the mathematical computations:

The weight of an SUV (Toyota Highlander) is 3784 lbs, which means a mass of 1716.393 kg, and my sedan (Chevy Malibu) ha(s/d) a weight of 3297 lbs, or a mass of1495.494 kg. The speed limit was 45 mph, or 20.1168 meters per second.

The initial momentum of the system was 1716.393 kg * 20.1168 = 34528.3347 kg*m/s.

This was an inelastic collision, that is, the cars stuck together after impact, leaving the new mass of the system as 1495.494 kg + 1716.393 kg = 3211.887 kg. After impact, the velocity of the system would be 34528.3347 kg*m/s / 3211.887 kg = 10.750 m/s (24 mph) due to the conservation of momentum. This was a near immediate change in velocity, which means a tremendous amount of force.

My car skidded about 15 feet, which is 4.572 meters. At the time f (final) and i (initial), v(f) = 0, v(i) = 10.75, x(f) = 4.572, and x(i) = 0. Change in x = initial velocity * change in time + 1/2 * acceleration * change in time squared.

After some figuring, I’ve found that the acceleration is 12.638 m/s/s. That’s compared to a 9.80 m/s/s from gravity. This means I underwent 1.290 times the acceleration of gravity. My brakes therefore applied a force of 12.638 m/s/s * 3211.887 kg = 40592 Newtons of force to the road. This was over a distance of 4.572 meters, meaning a total work of 185585 joules of energy. The power is work over time, so 218064 watts of power.

Errors:

  • Some energy would be lost due to heat and sound on impact and during the stop.
  • These calculations neglect air resistance.
  • This also assumes the other driver didn’t stop, but that may be true as there were no skid marks from her car.

So, for the summary:

  • Mass of my car: 1495.494 kg
  • Mass of her car: 1716.393 kg
  • My original velocity: 0 m/s
  • Her original velocity: 20.1168 m/s
  • Momentum of system: 34528.3347 kg*m/s
  • Combined mass: 3211.887 kg
  • Velocity after impact: 10.750 m/s
  • Time of skidding: 0.851 s
  • Displacement: 4.572 m
  • Acceleration: 12.638 m/s/s
  • Force: 40592 N
  • Work: 185585 J
  • Power: 218064 W
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Comments»

1. The Matt Luc - December 7, 2006

Where is the drawn-out diagram? I want to see the drawn-out diagram! Anyway, I’m glad that you are okay. If you weren’t then who else would go to my blog and check the cool video I posted? =D

2. tammy - December 8, 2006

You really are a genious, you know that? I’m glad you are alive and I’m sorry about your car. That does stink. I won’t be bringing my car with me because more often than not I think I’d be needing the jumpstart if I did. Are you coming back Home with AnCharlene? Just wanted to know. I’ll be up there in January so be ready for me!

3. Alex - March 3, 2007

Glad you’re okay, but as a distant observer I find the way you described the situation somewhat comical, particularly your acknowledgment of air-resistance-related discrepancies in your calculations.

Then again I got rear-ended a few years back, at rest facing downhill in a GMC Jimmy, where our partner in collision was going about 45MPH in a packed car with the sun in her face. I found it kinda funny how her car crumbled.

4. eric22222 - March 3, 2007

Yeah, I was going for comedy here. I find it easier to handle situations like this if I can laugh at them.


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