Explaining physics to a TV camera
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.dial-a-scientistWhen 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. Sonic_CupShape
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. (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.)
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How long until we see Mythbusters doing a demonstration of this?
Too...many...imperial...measurements...brain...breaking... It doesn't help me that she switches to grams and calories at the end, though I guess BTU would just add to the confusion. It's got to hurt your mental arithmetic converting from mph to ft/s and fl.oz to lb just to get started.
She asks "Did any of you ever consider a problem like this in any physics class you took?" - yes, our BSc finals always included a paper which was full of 'real world' questions like this, where you have to ballpark estimate everything. Fun stuff.
Also: they don't sell more than 44oz of coke, since 45oz is the equivalent of 88mph in a DeLorean. At that point the coke would come back...to the future! and all down your shirt.
waiting for the "1 windshield, 1 cup" mashup.
Hmm, for a ~3000-pound car at 86 MPH, the kinetic energy would be 0.5 * m * v*v = 0.5 * 1400 * 38 * 38 = about 1 MJ, or only 240 kcal.
So you wouldn't even have to drink the whole Coke to get that much energy.
For mental exercise, try using speed in attoparsecs per microfortnight. (Almost exactly one inch per second.)
Actually, I'm quite fond of attoparsecs, because they give things an eerie kind of perspective. One attoparsec is about 3 cm (a leftponder would call 10 attoparsec about one foot).
And you need a bit more than 1,000,000,000,000,000,000 attoparsecs (= 1 parsec) to reach the nearest star. For the nearest, reasonably sized, galaxy you need 1,000,000 parsecs. Just four zeros more get you to the edge of the universe.
I'm still trying to get my mind around the concept of a 2-pound cup of soda. Assuming soda has approximately the same density as water, that would be almost a whole liter in a cup!
@2 Fair point, its a cultural unit error. I'd assumed when she said a passenger car she meant what it means here in the UK - something like a Ford Focus, which weighs nearly the same as a DeLorean. To get her figures you need something more like an SUV, which I guess are more common in the states.
There's a website - http://www.simonkelk.co.uk/sizeofwales.html - which converts units to multiples of everyday things for the media, maybe they could add coke as the new energy standard.
@#5 Jackie31337 - "Liter-O-Cola, do we make liter-o-cola?"
@bazzargh - Imperial units make my head spin as well; however, the media over here will simply not use things if you use meters or Newtons. I had to retrain myself when I did a project on NASCAR (www.science360.gov) where even the Toyotas are in Imperial units.
Here's another good energy analogy: A NASCAR race car going 180 mph has the same kinetic energy as a kilogram of TNT -- or four candy bars - stores.
My favorite unit is the jelly donut, which (in the US at least), is about a Megajoule's worth of energy. DLP
Seems to me there has been one important factor left out of the equation, the force of the wind. There was no mention of how fast either vehicle was traveling, but for the sake of argument lets just say both vehicles were traveling at the same speed, regardless of what speed that was. As soon as the cup filled (or partially filled) with soda exits the window, it will be met by the force of the wind equal to the speed of the vehicle. Overall then, the force of the cup striking the oncoming vehicle's windshield would be roughly equal to the same cup being thrown from someone standing beside the road added to the speed of the oncoming vehicle. I guess it's possible that the cup could still shatter the windshield, but I think it's not likely.
oaw, sepptb stole my joke
@tp1024
http://www22.wolframalpha.com/input/?i=one+attoparsec+per+microfortnight+to+inch+per+second
awesome!
Hard to explain it all on camera. Ever notice that TV news just lets people say 3 sentences. If you can't communicate the whole concept in 3 sentences your soundbite it too long.
jackie31337 asked:
Yes, we do make one liter (or larger sodas) - Double Gulp
I tried explaining plate tectonics to a toaster oven once.
Those aren't cups, they're buckets.
@#5 Soda doesn't have the same density as water. The sugar/corn syrup makes it much denser, about 1.5x that of water IIRC.
To jackie31337, you are obviously not 'merkin. When I was in the US, I had a coworker who had a prized one gallon cup. She's fill it with coke (and ice! lots of ice!) at breakfast and work through it all morning while in front of her 'puter. I'll let you guess what she looked like.
I once bought a 64-ounce Dublin Dr. Pepper from a Chicken Express in Watauga, Texas. Apart from being equal parts god-damned delicious and disgustingly piggy, it was notable in that the cup was literally in the form of a bucket: it had a handle! The picture I took of myself with it is still the source of great mocking by my wife, and surely the doom of any political career I may have hoped for.
... explanation seems to rely on mass of the cup and contents. An end-strike, if perfect, might also trap compressed air between liquid tamper and windscreen glass. Assuming of course there is a "steal" in the cup bottom. Not unlike a shaped charge?
@zikman (#13)
I've seen this one before. Just noticed that the speed comparison wrong by a factor of 10. A garden snail moves at most 0.05 attoparsecs per microfortnight, not 0.5 apm, as stated.
#11, if a mostly-full (mass around one pound, give or take) cup is projected out of a car at dozens of miles per hour, the wind will NOT decelerate it to rest (i.e. to the same velocity as the air) very quickly. You'd need many seconds for that, which you would only get if the person threw the cup upwards in a very high arc, probably not the case. So I would say that air resistance is negligible (and I'm an aeronautical engineer!), it would shave a few or several mph off the cup's velocity-relative-to-the-air but probably not most of it.
#18, I find it very hard to believe that soda is anywhere near 1.5x as dense as water. That would make it go straight to the bottom if you poured some into a mostly-full (1/2 or 3/4 full) glass of water. I could believe 1.1x or something like that.
As for anyone who is amazed at how many calories are in soda and how much K.E. they translate into in terms of a moving car, remember that a car can go from zero to many dozens of mph using a TINY amount of fuel, about as much as your cupped hand would hold. (Yes, I was imprecise on purpose). Gasoline is VERY energetic. If soda is anywhere NEAR as energetic, a small amount would be enough to get a car going quite fast. Which reminds me: #10, I think you're over calculating how much energy that NASCAR car has, or under-calculating the energy content in a candy store or in a kg of TNT. But I could be wrong, I haven't done the calculations, I'm just saying that it sounds like a little too much energy for me.
I believe it was KFC that offered a half-gallon soda for a while. They may still offer it, but their online "menu" sucks.
A half-gallon is 1.9 liters. That is one seriously enormous drink. It has a handle.
If you get regular Coca Cola and assume 20% loss of volume to ice, that's 614 kcals. More than a healthy meal should contain.
isn't that kumquats and durians, Airshowfan? The soda/gas energy comparison is mixing simple kinetics in a gravity field with release of chemical bond energy.
Does this mean if I drink a 44-oz Coke I'll have the energy to stop an 86-mph passenger car?
I've been looking for any data on how much force it takes to break a car windshield, but I can't find any. That said, 20-120 lbs seems very small.
I weigh 170 lbs. I have sat on a windshield without breaking it. Granted, though, the pressure is much greater if it is over the surface of a cup than over the surface of my butt. But is it enough to break a windshield? I guess so, but you'd think this would be a rating that would be available.
A couple of not-great sources quote that the tensile strength of a windshield is in the order of 10,000 psi. [1], [2]
If the numbers are anywhere near accurate, then I wonder about this story. 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 her calculations, so it seems that the cup shouldn't have broken the window.
yet a man can punch through a windshield.
Coffee cups are not made of Styrofoam (which is a trademark of Dow Chemical) but of generic polystyrene foam.
The styrofoam soda-cup didn't smash anything, the soda did. The cup's main contribution is keeping the liquid in a tight little package, so it puts all the damage in one spot.
@#1:
I've been wondering for years how long it would be until the Mythbusters just get an in-house physicist. It'd solve a lot of their problems very quickly if they were any good.
That was hot!
#27: "A couple of not-great sources quote that the tensile strength of a windshield is in the order of 10,000 psi... The cup would probably instantly start flattening and absorbing the force, so ... That's only 240 psi max". Ok, but those are not the numbers you should be comparing. Don't confuse the inwards pressure of the cup with the sideways tension on the glass. The tension can be a lot greater. Imagine pinning a string horizontally to two pins, fairly taut, with a gap in between. Now imagine you hook your finger over the middle of the string and pull down, turning the string into a shallow V. The tension on the string will be much greater than your downwards pull. (In fact, just the vertical component of the tension on the string (which is a small fraction of the overall tension if the string was taut enough for the V to be really shallow) has to match the force of your pull).
#31: Sometimes while watching Mythbusters, I'll pause it and do some back-of-the envelope calculations, usually sticking only to high-school physics and freshman-level engineering equations (i.e. what I can remember without opening books). Of course I make some guesses and assumptions, but that's half the fun. Typically the outcome of the calculations is something like "To get that to work they'd need a speed (or pressure or whatever) in the order of such-and-such, which is not realistic in the myth, but could be pulled off with a well-designed setup". And then the trends in their experiment match the trends in my calculations. (Or sometimes it makes me go "Of COURSE their experiment is failing, because they're not stabilizing the rocket engine so the thrust is going all over the place rather than in the direction that would help" or "... because the drop in pressure due to Bernoulli doesn't come from accelerating air by moving the container, but by making air flow through a narrowing path"). And then I think that this would be a prime opportunity to introduce the audience to some basic concepts in physics, step through one or two simple equations, and thus show the amazing predictive power of the science and math known to a smarter-than-average 17-year-old. In other words, they could show people that you don't have to be a super-genius at CalTech (just a high schooler who pays attention) to be able to do enough physics and math to predict real-world phenomena (even real-world phenomena that people debate enough to get on Mythbusters).
This is going to look great when Mythbusters do it. Especially when they put the dynamite in the cup.
Because they can.