A Question of Physics (I Think)
Ok, I am not a physics professor, so I have a question for the FU News crowd who might know something about the matter. Tom and I were having a discussion about morality, beginning with the premise that speeding is "more" immoral than modifying the Boggle ini file so that I can continue to play it on the computer for free. This discussion rapidly progressed to geekier topics, ranging from how much we personally drive over/above the speed limit all the way to the question I would like to pose.
Here it is:
Does a car going 90 mph that hits a stationary car have the same effect as two cars going 45mph that hit each other? By "effect," I mean in regard to the people involved and in regard to vehicular damage. Assume that all drivers are wearing seat belts and have standard air bags. Tom posits that the effect would be the same, but to my convoluted mind, I think that adding the speed of the two moving cars to get 90 and saying they would have the same effect as the single car going 90 is too simplistic.
So which is worse: Hitting a stationary object at 90mph, or hitting an oncoming car with both cars going 45mph? Or is there absolutely no difference?
The acceleration on the drivers is the same in both cases, assuming that the cars are not traveling at a significant fraction of the speed of light.
ReplyDeleteAssume: both drivers weigh about the same and are driving cars with about the same mass.
Case 1, Car A traveling at 45mph, Car B traveling at 45mph in the opposite direction.
NB: 45mph ~= 20 meters/sec.
Both Drivers A and B go from 45mph to 0mph in a short time (let us say .1 seconds). Their deceleration can be measured as 20m/s in .1 seconds, or 20m/s / .1sec = 200m/s^2. Since the force of gravity (at sea level) is 9.8m/s^2, we can measure the decelerational force on each driver as 200/9.8 or 20.4G's (20.4 times the force of the Earth's gravity).
Case 2, Car A is stationary, Car B is traveling at 90mph at time of impact.
Assuming they have the same mass, when Car B hits Car A, Car B will transfer some of its kinetic energy to Car A. Remember, an object has the same inertia regardless of its speed (for v << c), so the amount of energy it takes to move Car A from 0mph to 45mph backwards is exactly the same as the amount of energy it takes to slow Car B from 90mph to 45mph. Essentially, half of Car B's kinetic energy is transfered to Car A. Again, assuming the same time for the acceleration to take place (0.1 seconds), Driver A will have his velocity changed from 0 to 45mph (backwards) for a deceleration of 45mph/.1s = 20m/s/.1s = 20.4G and Driver B will have his velocity change from 90 to 45mph, for a deceleration of 90-45/mph/.1s = 45mi/h/.1s = 20m/s/.1s = 20.4G. So the decelerational effects are the same on each driver in each case.
Notes and Assumptions:
Firstly, we are assuming that all the force of the impact is absorbed by the cars here. In reality, metal is sort of springy and tends to return to its natural shape after being bent. This will cause the cars to absorb the impact when the metal compresses, and then the natural spring will release some of the energy back and push the cars apart. However, most of the energy of impact is absorbed by the metal. Note that the effect will still be the same in both cases. In Case 1, both cars will absorb some impact, then push off against each, giving each car some backwards velocity. In Case 2, the spring would push Car A away from Car B, so it would end up traveling a little faster. But in each case, the accelerations on each car would be the same. Rather than being 45mph/.1s, it would probably be closer to 50mph/.1s.
What about that speed of light thing?
You'll note in my answer I say "assuming that the cars are not traveling at a significant fraction of the speed of light." This is because the faster an object is moving, the higher its inertial mass, thus making it take more energy to accelerate the object. Assume now that the cars are traveling not at 90mph but 90,000,000mph (about 13% the speed of light). In this case, the amount of energy it takes to accelerate Car A from 0mph to 45,000,000mph is significantly less than the amount of energy it takes to decelerate Car B from 90,000,000mph to 45,000,000mph, so in reality, both cars would end up moving at a speed higher than 45,000,000mph, resulting in a greater acceleration than in Case 1. Note that if you smashed two cars together at these speeds, you would most likely induce nuclear fusion between the atoms of the two cars.
But what about pool and cue balls?
You're probably saying, "but hey, when you hit a ball with the cue ball in pool, they don't continue moving at the same speed together; one ball stops and the other gains all its energy." Yes, but we don't drive pool balls, do we? This is because cue balls are almost completely rigid and almost none of the force of impact is absorbed by the ball. Cars would not exhibit this same physical property. Also, the acceleration of two pool balls smashed into each other would be the same regardless of which is moving. Smash two pool balls into each other at 45mph, and they'll end up moving away from each other at 45mph, for an acceleration of 90mph. Take a cue ball and smash it into the stationary 8 ball at 90mph and the cue ball will decelerate by 90mph and the 8 ball will accelerate to 90mph. Same acceleration in both cases.
So it comes out the same, right?
Well, not really. From a pure safety view, it's probably safer to be involved in Case 1 than Case 2. This is because, when all is said and done, in Case 1, the two cars are stopped (or very nearly so). In Case 2, you have the problem that even after impact, the cars are still moving at close to 45 mph, leaving them free to spin out of control, crash into other cars, fall of a cliff, etc.
As the only certified California Traffic Accident Investigator that trolls this blog, I have an opinion on this matter.
ReplyDeleteHowever, due to a heavy workload, I don't have time to explain.
~The Blue Fox
I just want to point out that contrary to popular old wives tales about human strength and car accidents, you can actually survive a 45 to 0 instant crash without a seat belt. I was in the back right seat of a humvee that went from 45 to 0 when it slammed into a ditch (nope, we didn't even touch the brakes, and it was head on). I ended up grabbing the back of the front seat and ending up in the lap of the guy in the front seat. So there. That's all I have to add to this discussion.
ReplyDeleteBut did the guy in the front seat survive?
ReplyDeleteThe difference in what happens after the initial point of contact varies greatly, depending upon direction of travel and mass of the vehicle. However,the energy at the point of contact (in the instant) is the same.
ReplyDeleteNo crash is instantaneous, they all happen over time and are typically measured from initial point of impact to final point of rest.
In general, the vehicle with the most lug nuts "wins". The amount you "lose" varies on how many lug nuts you have and how much you paid for your vehicle. It is possible to have a large number of lug nuts and only have paid $500 and you'll lose less than the other guy who paid more but had fewer lug nuts.
I general, if you are going to an object "head on" vehicles are much "safer" to hit than other objects that are more permanently attached to the ground, such as: walls, rocks, large trees, etc. These other objects are less likely to "absorb" the impact.
As for the "morality" of surpassing the speed limit, that is a grey area. In California, the "basic speed law" says you should not travel faster than what is reasonable for the time and conditions. Where the "maximum speed law" says you shall not travel faster than 65mph, unless otherwise posted with a faster speed limit. (so much for "maximum" :P) The "prima facie" speed limit is "posted" as the 80% speed driven on a given road, or 35mph in a business district, or 15mph at a blind intersection, or 25mph in a school zone when children are present.
Yes, the speed limit is purposefully set lower than what is safe and reasonable.
These speeds are not determined to establish a moral standard, they are designed to keep the city planning office from getting sued in the event of a vehicle accident.
Speeding is "immoral" when it is at a speed that is beyond reasonable. 85mph in a residential area with blind, uncontrolled intersections is immoral. 65mph in heavy fog on the freeway is immoral.
~the blue fox
No one was really hurt. We were all just bruised.
ReplyDeleteOh...
ReplyDeleteOne of the more interesting facts about car crashes.
Vehicle vs Pedestrian
Look for the shoes of the pedestrian's shoes. They will either be on the ground "attached" to where the pedestrian was hit or if they were firmly tied you can locate and measure the "skid marks" left by the shoes and calculate a minimum speed required to create the skids.
If the vehicle was not in a "locked 4 wheel skid" at the time of impact the skids from the shoes can be used to determine the minimum speed of the vehicle. If the determined speed of the vehicle was above the speed limit you can ex post facto cite the driver of the vehicle with a speeding ticket. (This is one of the few ways a an officer can cite a misdemeanor not committed in their presence.)
Another interesting fact:
All vehicles equipped with airbags have an EPROM recording a 30 second buffer of vehicle data. When the air bags are deployed the EPROM stops recording. The following information is captured: speed of the vehicle, engine speed, % of throttle applied, and % of brake applied.
This information is typically only retrieved in fatal accidents where the circumstances of the crash are needed.
If you get past the whole: injury, suffering, death and dismemberment part about traffic accident investigation it is probably one of the more fun fields of "applied physics" to get into.
~TBF