dial-a-scientist

I used to get the standard phone calls and emails that most physics professors get:  the one from the guy who claims to have refuted Einstein's theory of relativity, the one from the guy who is positive that we never landed on the moon and it was all done on the soundstage, and the one from the guy who is really upset that Physical Review Letters won't publish his paper on the perpetual motion machine he's invented only because he doesn't have a Ph.D. and would I please submit the paper with my name on it because it would surely get published then.  The last guy clearly hasn't seen my CV, or he'd know my success rate with PRL.

Jennifer wrote a great blog about mediagenicity a couple years ago that I recommend to everyone, and not just because she tagged me as 'a bit of a physics bombshell'.  Before elucidating five rules for improving your mediagenicity quotient, she wrote:

"Mediagenics" are insightful, articulate, and likeably approachable, with a good sense of humor and innate ability to connect in any number of different ways with various audiences.  It's making the connection that's so critical, because without that, communication is impossible.

If you're at all mediagenic - and in physics, the bar is pretty low -- the kinds of phone calls and emails you get change.  Which is why I was standing out in the parking lot at school Friday night at 6:00 p.m. in 100 degree heat wearing a sweater over my sleeveless top because I dinged myself while moving things from one lab to the other and have a gigantic bruise on my upper arm.  (Note added 6/28/09: You can see the results here.)

It all started Wednesday, when I got an email from Brandon Webb, who handles PR for the College of Natural Sciences and Mathematics at UT Dallas.  He wanted to know if I could talk to a reporter who wanted to know whether a Styrofoam cup could break a windshield.  (That's an advantage to being officially mediagenic - I don't get contacted directly now - they go through my 'people' a.k.a Brandon.)

C'mon - a Stryofoam cup break a windshield?  Not likely.  Then the reporter emailed me the photos.  The windshield looks like a rock went through it just above the inspection sticker.  For you non-Texans, that's a few inches from the bottom left side of the windshield. 

Marilyn Mackey, the driver of the car with the broken windshield, was traveling about 65 mph down a highway.  As a car passed her in the opposite direction, its driver threw a cup out his or her window.  We know it was a cup of soda because, in addition to poor Marilyn getting wet, there is sticky dried cola-colored liquid all over the inside of the car.  The police pulled part of the cup out of the windshield (which is how we know it came from Sonic) and found a shredded straw inside the car.  (Thanks to the family for permission to post the photo!)

This called for a little research and one of Oullette's rules of mediagenicity is to take the call when it comes and appreciate that reporters work on hard deadlines, so it had to be quick.  The Sonic website has a nutrition calculator, complete with masses.  A small Coke is about 3/4 of a pound, while a Route 44 (the giant size) is about 2 lbs. A regulation baseball is about 1/3 of a pound, and the ginormous sode weighs about as much as a bag of sugar, just to put things in perspective.  A gallon of water weighs 8.3 lbs. The weight of the cup is negligible compared to the soda.  Yes, I did check: A Diet Coke weighs only very slightly less.

The two cars were coming at each other and we'll approximate that they were both going about 65 mph, which means that the speed of the cup relative to the car it hit was about 130 mph.  (You never thought you'd need to use relative speed when you learned it in high school, did you?)  If the driver of the oncoming car threw the cup instead of just releasing it, the cup would have an even greater speed when it hit the other car.

This is where the physicist side of me started to get fidgety.  I get uncomfortable with numbers, because there's a lot we don't know. As you can see from the diagram, if we really wanted to do this right, we'd need to know how close the cars got to each other before the cup was thrown, how hard the cup was thrown, the angle the cup was thrown, the drag on the cup, how much of the drink was left in the cup...

Jennifer's second rule comes to mind - know your audience and tailor your message.  Newspapers and television don't really want to know about all those details because they have to tell the story in a minute or two and caveats like that tend to take a lot of time to explain.  And they DO want numbers.  I explained to the reporters all the unknowns so they'd know why I was giving them a big a range of numbers.  Take a conservative case: Let's assume that taking everything into account, the cup hit at a speed of 130 mph and came to a stop.  (Again, an approximation because the cup went through the windshield and kept going.)  Then the change in momentum (the difference between the momentum the cup had prior to hitting and the momentum the cup had after coming to a stop) would be:

where I've used that 130 mph=191 ft/s and made the distinction between weight (2.00 lb) and mass (weight divided by the acceleration due to gravity).   The change in the momentum isn't the most important thing.  The force is the change in momentum divided by the time it takes to change the momentum. 

We have no idea how long the cup took to come to a stop, plus it hit the windshield, slowed down, and then part of it continued moving into the car.  So let's just arbitrarily take a range from a tenth of a second to a half second.  At a half second, the force would be about 24 pounds and at a tenth of a second, the force would be about 120 pounds.  And that's the range I felt comfortable being quoted on in the newspaper article.

 

The reporter for Channel 8 asked me what the force actually meant.  The best way to describe it would be that a scale placed on the windshield would register between 20 and 120 lbs when the cup hit.  That quick calculation convinced me that it wasn't beyond the realm of possibility that a drink cup could actually break a windshield. If the cup were thrown, even a pretty bad arm could give it an additional 30-40 mph, so the force could have been much larger.  

When we taped my interview for Channel 8, the reporter asked if it mattered how the cup was oriented when it hit.  It does.  Brandon - who is just a joy to work with - had pitched them the idea of taping the segment in front of a car using a Sonic cup as a prop, so I had the cup right there.  This was a question that just came up, so I hadn't had a lot of time to think about it.  That always makes me nervous because the last think you want is to be captured on tape saying something wrong.   

It does make a difference.  Compare what happens when a cup hits bottom first or side first, as I've tried to illustrate to the right.  The bottom of the cup is really rigid, so there isn't going to be a lot of give.  If it hits side first, the cup is going to give.  If you've ever grabbed a flimsy drink cup and it squished and the lid came off, that's exactly what would happen.  This is the exact same principle the SAFER barriers use for racetracks.  Deforming the wall increases the time it takes for a car to come to a stop, and that decreases the force the driver feels.  If the cup hit side first, it wouldn't create as much force as if it hit end first.

And, of course, I wasn't mentally or numerically agile enough to think to calculate the kinetic energy during the taping.  A 2 lb cup of soda going 130 mph would have the same kinetic energy as a baseball thrown at 150 mph, or the same energy you get from exploding a half gram of TNT.  I've spent the last year doing nothing but trying to get my lab up and running again.  I apparently have lost the ability to do even simple math.  

So I was only off by a factor of 2 or so. 

(Total tangent: A 44 oz Coke contains 371 kilocalories of energy, which is equal to the kinetic energy of a passenger car going 86 mph.)

There are two important things you should take away from all of this.  First, don't throw stuff out the window of your car.  Ms. Mackey was wearing glasses and that's a really fortunate coincidence.  The glasses were pitted from where pieces of windshield glass hit them. If she hadn't been wearing glasses, she might have had very serious injuries to her eyes.  She could have lost control of the car and crashed and been killed.  We are fortunate that this is a "what the...?" story and not a tragedy.

That leads to my second point.  Did any of you ever consider a problem like this in any physics class you took?  If not, why not?  I spent about half a day answering questions about this situation from the media, from random people who emailed with follow up querstions.  It's clearly something people are interested in.  I mentioned this to one of my less free-thinking colleagues and was told that a problem like this is "simply too hard for beginning physics students".  Balderdash.  Doing calculations without friction when you like in a world where you can't escape friction is hard because nothing you calculate has any connection to real life.  Figuring out whether a drink can go through a windshield and kill someone is complicated, but I didn't use anything you don't learn in first semester high school physics.  I keep wanting to teach a course called 'Physics You'll Actually Use', but I haven't gotten anyone to approve such a title.  Yet.

A couple of weeks back, a producer from Good Morning America left a voicemail on my phone wondering whether it would be possible for LeBron James to jump over a taxicab.  We shot a segment and it ultimately never aired because the dumb ol' Cavs got themselves bumped out of the championship race.  I'm counting on Shaq to get them there next year so that I can finally reveal the answer.

Comments

[Skip]

When I took physics in the engineering honors program at the University of Texas about 20 years ago, the professor would do questions like that all of the time. It was one of the reasons I really enjoyed the class.

In high school physics about the closest thing we ever had was a problem that went something like this. Teacher says "A pickup truck is parked on a frictionless surface. Driver of the pickup truck grabs a gun off of the gun rack and fires it. How fast will the truck be moving in the opposite direction?"

One of the students raises his hand and says "how do you park a truck on a frictionless surface?"

At which point the teacher switched the question to be "Pickup truck is moving on a frictionless surface. All you have to park it is a gun. What direction(s) must the gun be fired to park the truck?"

[Annette]

"Physics You'll Actually Use" would probably pull in a lot more kids who don't realize how fun and interesting physics is. Your colleague does science a disservice with the attitude that what you propose is 'simply too hard'. My guess is that it would be "simply too hard" (difficult and inconvenient) for this person to change their curriculum.

[Jennifer Ouellette]

Wow, actual equations come to the cocktail party! Kudos! :) And phooey to your rigid colleague who thinks first year physics students -- or anyone else for that matter -- can't handle that type of problem. You'd need to walk them through it at certain points, but your explanation was crystal clear. I am tempted to find a place for your analysis in my calculus book... :)

@Skip: I would have loved your physics professor....

[Diandra Leslie-Pelecky]

@Jennifer - I'm glad that you think equations are a good thing...Was it Sagan that said every equation decreases book sales by 50%? I hope the same thing doesn't apply for the web!

[Mr. Jody Bowie]

Great post. Enjoyed reading and thinking about the calculations. If you ever teach "Physics you will actually use" I would love to collaborate with you on developing the class! Or I would love to have an outline of the curriculum. This is a theme that I think about in my class constantly: "how do I make this relevant to students?" I think (based on feedback from students) that I do okay, but I know there are many who just want to cover the book or the assigned topics or whatever. Its great to read about physics folks getting our "agenda" out there in the mainstream.

Also, I know what you mean about "the last think you want is to be captured on tape saying something wrong". I was interviewed by our local CBS affiliate about "skinny mirrors". Remember Elaine in "Seinfeld"? :-) Anyway, I was terrified that I might have said something wrong so far no backlash.

Great blog and I love reading all of ya'lls posts! Keep it up!

[Paul]

This was certainly one of the more enjoyable post I've read recently. It is so true to live and if you live close to a freeway, you will note poeple trowing stuff out their vehicles all the time. It's about time someone (like you) makes an interesting note of the danger of this habit. Nice going and send it to your local newspaper. Maybe they will post it.
PLO

[Philip Bliss]

Hey, really cool post. I'm confused about one thing--when I was in first year engineering, I went to a panel question-and-answer session with the profs. Someone asked "what is energy?" and there was a moment of silence before one of them answered, it's just a model. My question is this: isn't it misapplying to say that "44 oz Coke contains 371 kilocalories of energy, which is equal to the kinetic energy of a passenger car going 86 mph"? Numerically they're equal, but doesn't a dimensional analysis mean that the model of energy does not extend to that comparison? Or am I missing something?

[misterfricative]

I saw this on Youtube and was impressed by your clear, efficient explanation of the physics and how the orientation of the cup is a critical factor. It's great to see physics being applied helpfully and correctly on the news! Kudos.

But I think there must be something wrong with your claim that 'a 2 lb cup of soda going 130 mph would have the same kinetic energy as a baseball thrown at 150 mph'. Surely that would only be true if the baseball weighed about 1.5 pounds?

[Mikael]

Just some thoughts: your force analysis is quite sensitive (inversely proportional) to the time it takes to change the momentum.

You set 1/10th of a second as lower bound, but I think it could be much faster? For instance, say the cup did not loose significant speed - and that after hitting the windshield, it would travel 1 cm before breaking it (the windshield would very likely break before it was pushed 1 cm). This gives a contact time of: 1 cm / (130 miles per hour) ~ 0.2 milliseconds. Notice that even if the cup lost 80% of its speed during collision, it will still take less than a millisecond to move 1 cm. The impact could last longer if the cup+water deformed, but since water does not compress easily, it is probably not very elastic.

Also, the pressure might be more important than the force here. A bullet (say, moving at Mach 1 and with a weight of 5 gram) would have no problem breaking a windshield, despite having both lower momentum and kinetic energy (than a 1kg object at 130 mph).

As always lots of rough approximations are necessary to handle these annoying real-world problems :-)

[Diandra Leslie-Pelecky]

Hey Philip - great idea for a future post. The short answer is that is is a valid comparison and you can actually show that the units are the same! I will do that in an upcoming post. Thanks for the idea! DLP

[Diandra Leslie-Pelecky]

The folks over at boingboing turned me on to a great website: http://www.simonkelk.co.uk/sizeofwales.html, which allows you to input a length, area, etc. and will give you somethign that your value is roughtly comparable to. Way cool site.

[Diandra Leslie-Pelecky]

@misterfricative: You are right that pressure is definitely important, so the area of contact is indeed relevant. I like your analysis of the deformation of the windshield. The problem is that at some point you introduce such a range of variables that you come up with an error bar that borders on absurd. The points you raise would be too much for the media, but that is exactly what I sat around talking to friends about over a beer on Saturday.
Plus, I only had 1.5 hour lead time to get this ready and I had to deal with the really important stuff, i.e. my hair.

[misterfricative]

Hi Diandra -- I like that analysis too, but I can't take credit for it. That was Mikael. My post was the previous one which wondered about the KE equivalence of 2lb @ 130mph vs 5oz @ 150 mph

[misterfricative]

PS and yeah, hair *is* important! Mediagenicity definitely counts!

[Diandra Leslie-Pelecky]

I'm sorry Mikael for mis-awarding the credit!

@misterfrictive: Uh, yeah, I was just slightly off - like by a factor of 2+. I've inserted the math in the blog, which I should have done from the start. I blame it on a faulty envelope.

[Uncle Al]

Hve you ever been hit by a slushball rather than a snowball? Lumps of ice make a difference.

[Clay B]

You are right that the angle of the cup relative to the windshield would be critical. You could measure how much force is required to deform the cup in its most stable configuration (bottom hitting the glass directly) by stacking weights on the cup until it crumples. If this is less than the force needed to break the glass, the cup is going to deform before the glass breaks. Of course you still have that much mass hitting the window, but the liquid may splash out and spread over a larger area, reducing the pressure at any particular point.

Was there ice in the cup? As a thought experiment, consider the difference between hitting a solid chunk of ice, a liquid in a confined container (say a plastic bottle with the top on), a liquid in an open container, and an unconfined liquid.

[Brian Clapper]

The obvious joy you get out of explaining this kind of scenario makes me smile, for a whole bunch of reasons. Bravo! (and thanks).

[Alex Vincent]

This begs for a Mythbusters episode.

[Sam F]

Were you able to find out the rated strength of a windshield?

As you briefly mentioned in your comments, the important number isn't the exact force hitting the windshield, it's the pressure.

A couple of not-great sources quote that the tensile strength of a windshield is in the order of 10,000 psi, to keep using imperial units. [1], [2]

If the numbers are anywhere near accurate, then I wonder about this calculation. The cup would probably instantly start flattening and absorbing the force, so I would think that 1/2 inch square or more could easily be touching the window. That's only 240 psi max (according to your calculations that the max force might be around 120 lbs), so it seems that the cup shouldn't have broken the window.

Of course the question is how much the cup flattened on impact, but even if only 1/10th of a square inch were touching, this would still be well below the quoted strength of withstanding 10,000 psi.

[Chaos Motor]

"One of the students raises his hand and says "how do you park a truck on a frictionless surface?""

By dropping it along the Normal vector? It'll bounce a bit cut should stay in place if the surface isn't inclined, right? Or would there be motion due to the center of gravity if it isn't in the geometric center?

[Diandra Leslie-Pelecky]

@Chaos Motor: But you're assuming there's gravity! If there's no friction, perhaps there's no gravity, either!
Seriously, it would bounce a bit, but if you dropped it precisely straight (i.e. all four wheels hit perpindicular to the ground), it should be parked.

[Mikael]

@Sam F:

As I mentioned above I think the contact time may be less than 1ms, which means the impact force could be >100 times greater.

Also, the deformation/orientation of the cup is probably not relevant - it is the mass of the liquid that breaks the window, and liquids are quite imcompressible.

[Dave]

Deformation is entirely relevant: ask a mythbuster... which breaks more windows? A frozen chicken or a thawed one? The behavior of the material as it transfers it's energy to the target is key to the question of will it break, or will it just smoosh? Hardness vs. initial area of contact, the nature of the material to stick together as a mass or spread out quickly, even the very real effects of wind resistance on the projectile, the buffering/buffeting effects of the vortex around the moving car... Liquids are non-compressible, but their tensile strength is terrible and the spread out very quickly.

Now there's a question I'd like to see the Mythbusters test.... a blob of water vs a blob of ye-olde-favorite corn-starch'n water in impact tests...

[Ben Artin]

http://www.amazon.com/Flying-Circus-Physics-Jearl-Walker/dp/0471762733 is an entire book filled with real-world physics problems, ranging from easy to crazy hard. Highly recommended!