nascar driver vs. wiley coyote: a real-life seriously inelastic collision

I'd like to claim that no animals were injured in the making of this blog, but (insert Joe Flaherty from SCTV doing Kirk Douglas) I'd be lying.  I put the most graphic picture near the very end of the post so those of who, like me, have weak stomachs could avoid it.  It isn't pretty. Especially if you like coyotes.

Brad Coleman, a NASCAR driver for Joe Gibbs Racing, was testing (like doing homework for those of you unfamiliar with NASCAR) at Toyota Arizona Proving Grounds when he hit a coyote going about 190 mph.  (Clarification:  Brad's car was going 190 mph.  The coyote was just meandering around in the middle of the track.)  Natural selection works:  If you're dumb enough to wander onto a racetrack with 130 dB cars roaring past, we don't really want those genes propagating, do we?  This is a perfect example of a real-life collision.

Collisions come in two extremes.  In a perfectly elastic collision, two objects bounce off each other and lose no energy.  We like those problems because students must apply conservation of energy and conservation of momentum, and you can write the problem so that they have to use both. The other extreme is the perfectly inelastic collision, in which the two objects stick together after the collision.  We always use "two cars hit each other and their bumpers stick together".  You see that a lot in real life, don't you?  If you scroll down the page, you'll notice (perhaps with the exception of legs), the two objects really did stick together after the collision. 

An American coyote, according to the Phoenix Zoo, weighs between 50 and 75 lbs. (Lemma:  Coyote weight increases as you move North.  Mexican coyotes may weight as little as 25 lbs while those in the northernmost reaches of the US tend to be 60-75 lbs.)  For the sake of argument, let's assume the coyote is 50 lbs (22.7 kg mass).  A NASCAR Car of Tomorrow weighs 3450 lbs and this particular driver weighs about 185 lbs, for a total weight of 3635 lbs, or a mass of 1649 kg. 

Momentum is the product of mass times velocity and measures essentially how hard it is to stop a moving object.  The faster something moves, the harder it is to stop.  The more massive it is, the harder it is to stop. It is much easier to stop a speeding coyote than a speeding race car and much easier to stop a slow car than a fast car. Writing it as a formula (at left), momentum is symbolized by p because m was already being used for mass.  v is velocity, so p=m times v.  Yeah, I know it's technically a vector, but we'll assume that the car was coming down the straightaway and make it a one-dimensional problem. 

Conservation of momentum says that the amount of momentum the "system" (meaning the car and the coyote together) had prior to the collision is the same as the amount of momentum the car and coyote had after the collision. If you don't want to go through the math, go ahead and skip down to where the equations end and just look at the answer.  It's OK.  Really. 

For those of you still with us:

Here's where real life makes the problem easier.  The dumb ole coyote is sitting on the track.  Even if it was moving, it was moving really slowly compared to the 190-mph race car, so we'll approximate the coyote as having zero velocity before the collision -- which means the second term on the left-hand side of the equation becomes zero (yay!). 

After the collision, the coyote and the car are stuck together, which means that the coyote is going the same speed as the car because - well, look at the picture below.  It is basically glued to the front fender.  Our equation thus simplifies to:

Driver Brad Coleman - the only surviving eyewitness - said

"I see this thing, it must've been 100 feet in front of me, just jump out.  Right when I saw it come out from under the guardrail, I was like "that's a coyote"...  I didn't see anything in the mirror, so I was like 'I wonder where it went'..."

Don't you think you might know if you hit a coyote?  Let's look at how much hitting the coyote would slow down the race car.  As I constantly remind my students, solve for the unknown before you plug in any numbers.  We want to know how much the coyote slowed down the car, so we want to know how fast the car and coyote are going after the collision.

Using the fact that 190 mph is about 85 m/s, the car has a mass of 1649 kilograms and the coyote is about 50 lbs (corresponding to a mass of 23 kg), the speed of the car and the coyote would be:

 

which is about 187.5 mph, so the coyote only slowed him down by about 2.5 mph (1.3% of the initial speed).  If you hit the coyote doing 60 mph (26.8 m/s), your speed after would be 26.4 m/s, which is about 59 mph or 1.6% of the initial speed.  The slower you're going, the larger the percentage speed you lose.

How did Brad know he hit the coyote? 

"It (the car) just started smoking like crazy and it smelled terrible...I said, "Guys, I hit a coyote.  I'm going to come in because I think it screwed up the radiator.  I think it clogged up the grille a little bit."

You have to realize that NASCAR crews are really into practical jokes, so I'm sure the crew was sitting back in the garage wondering if this was a joke, or if Coleman had really hit an animal.  I bet they were surprised to see the car come in looking like this:

This is going just a little too far for a hood ornament.  I hope whomever had to clean up the car got some type of bonus, as they really deserved it.  Car-car and car-wall collisions are never quite this messy. 

Here's a great problem for all the kids starting physics this fall.  Give them the same information that's available on the Internet:  the car was going 190 mph and the coyotes was pretty much 100 ft ahead of the car and just sitting there.  Have them calculate:

1. How fast the car was going after it hit the coyote?
2. How fast do you think you could move your foot from the gas to the brake?
3. How long would it take the car to go 100 feet at 190 mph? and
4. What approximations did you make and how would your answer change if your approximations weren't valid?

The last question is probably the most important. The picture suggests that coyote mass was not strictly conserved, so the mass of the coyote plus car is probably a little smaller than I estimated and the car didn't even slow down that much.  Real life almost always demands approximations.  The important thing is knowing how much error your approximations might introduce if they are wrong.

Partial solution:  190 mph converts to about 279 feet every second.  Brad estimated that the coyote was 100 feet ahead of him, so he would have traveled the entire distance in (100 ft/279 ft =) 0.36 seconds.  Go see if you can shift your foot from full out on the throttle to the brake in a third of a second.  And there are a lot of other possible questions.  How fast would Brad have had to decelerate to miss the coyote.  Why didn't he swerve around to miss the coyote (remember reaction time!)  Why is hitting a deer on the highway with a passenger car so much worse than this was?  (Deer are a lot heavier!)  Deer also have a higher center of gravity (longer legs) - how would that affect the collision?

This reminds me of a situation in which I'd written a problem that asked, "Texas Motor Speedway sells enough hot dogs each year to circle the track six times.  How many hot dogs do they sell?"  and I got told by someone from a federal funding agency that I had made a mistake because I hadn't given the length of a hot dog and said whether it included the bun. (Your tax dollars at work, folks...)

You get on the web and look up that Texas Motor Speedway is 1.5 miles long and estimate that a hot dog is about six inches long (with or without bun, doesn't change much).  This isn't rocket surgery, folks!  I don't know about you, but my real-life job rarely presents me with precisely the information I need to solve a problem. 

I'm about to undergo a lot of changes in my life.  Until I moved out of my office last week, I had a stuffed Wiley Coyote hanging on the wall.  He was there for a very important reason - Wiley is my totem animal. Have you ever noticed that Wiley never falls until he looks down?  Seriously - as long as he doesn't realize he's doing something he really shouldn't be able to do, he can do it.  Sometimes, we are our own worst impediments when we talk ourselves out of being able to do things.  My motto for the next few weeks is going to be "Don't look down". 

"Meep meep" indeed.

Comments

[Dr. Rob]

A friend gave me a link to this because we ran over an armadillo and ended up with an ornament to our car as well (not as gross as yours) - http://img200.yfrog.com/i/jmnl.jpg/ - We were going about 70 and the armadillo was dead already (so its velocity was nonexistent prior to the collision).

Since my dad is a PhD in physics, I have to say that this post gave me a smile despite the gruesomeness of the picture. Stuffed animals give me the willies.

[Thomas Joseph]

Poor coyote. :(

[Tim Gaede]

While visiting relatives while vacationing in rural Texas, I borrowed a car for a drive to visit other relatives a few hours away. The car's owners were an elderly couple who no longer drove that car anyway. In the predawn darkness a coyote, apparently not deterred by the glaring headlights, sprinted straight into the front bumper and grille causing slight damage. I was a bit rattled.

When I reported the incident to the car's owners they were elated that I got one of those buggers that cause nothing but trouble on their granddaughter's ranch.

[Rick Pikul]

You might want to check your math: Regardless of the initial velocity of the car, mcar/(mcar+mcoyote) is going to be the same, (0.986). This means that the loss of speed is always going to be 1.4%. The 1.3% and 1.6% values you get seem to be round-off error.

[tim]

man I can not get enough of looking at this awesome hit.
since coyotes plague our natural habits being such a ruthless killer
Thanks Brad for the excellent elimination of at least one, in such a fashionable manor.. 'that's real coyote hunting at it's finest'.

[TexasJim]

Too bad it didn't trash that stupid toyota...

[Account Deleted]

Good thing nothing happened to it's engine. If it was an average car, the coyote's carcass might end up damaging the engine, breaking the car. Imagine how a car costs nowadays in car dealerships.

Indianapolis once had a serious accident involving animals on the road. I was quite surprised, since I never even knew we had Opossums roaming around. They had to pay tons for car repair (Indianapolis's car repair fees are cheap though) and mortgage after they tried to avoid the little critter and ended up hitting a post.