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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?"

"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.

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....

@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!

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!

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.

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?

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?

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 :-)

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

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

@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.

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

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

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.

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

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.

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

This begs for a Mythbusters episode.

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.

"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?

@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.

@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.

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... is an entire book filled with real-world physics problems, ranging from easy to crazy hard. Highly recommended!

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    Physics Cocktails

    • Heavy G
      The perfect pick-me-up when gravity gets you down.
      2 oz Tequila
      2 oz Triple sec
      2 oz Rose's sweetened lime juice
      7-Up or Sprite
      Mix tequila, triple sec and lime juice in a shaker and pour into a margarita glass. (Salted rim and ice are optional.) Top off with 7-Up/Sprite and let the weight of the world lift off your shoulders.
    • Listening to the Drums of Feynman
      The perfect nightcap after a long day struggling with QED equations.
      1 oz dark rum
      1/2 oz light rum
      1 oz Tia Maria
      2 oz light cream
      Crushed ice
      1/8 tsp ground nutmeg
      In a shaker half-filled with ice, combine the dark and light rum, Tia Maria, and cream. Shake well. Strain into an old fashioned glass almost filled with crushed ice. Dust with the nutmeg, and serve. Bongos optional.
    • Combustible Edison
      Electrify your friends with amazing pyrotechnics!
      2 oz brandy
      1 oz Campari
      1 oz fresh lemon juice
      Combine Campari and lemon juice in shaker filled with cracked ice. Shake and strain into chilled cocktail glass. Heat brandy in chafing dish, then ignite and pour into glass. Cocktail Go BOOM! Plus, Fire = Pretty!
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      Dr. Strangelove's drink of choice.
      3/4 Triple sec
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      2-3 drops Grenadine
      Fill shot glass 3/4 with Triple Sec. Layer Bailey's on top. Drop Grenadine in center of shot; it should billow up like a mushroom cloud. Remember to "duck and cover."
    • Mad Scientist
      Any mad scientist will tell you that flames make drinking more fun. What good is science if no one gets hurt?
      1 oz Midori melon liqueur
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      1 splash soda water
      151 proof rum
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    • Laser Beam
      Warning: may result in amplified stimulated emission.
      1 oz Southern Comfort
      1/2 oz Amaretto
      1/2 oz sloe gin
      1/2 oz vodka
      1/2 oz Triple sec
      7 oz orange juice
      Combine all liquor in a full glass of ice. Shake well. Garnish with orange and cherry. Serve to attractive target of choice.
    • Quantum Theory
      Guaranteed to collapse your wave function:
      3/4 oz Rum
      1/2 oz Strega
      1/4 oz Grand Marnier
      2 oz Pineapple juice
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      Pour rum, strega and Grand Marnier into a collins glass. Add pineapple and fill with sweet and sour. Sip until all the day's super-positioned states disappear.
    • The Black Hole
      So called because after one of these, you have already passed the event horizon of inebriation.
      1 oz. Kahlua
      1 oz. vodka
      .5 oz. Cointreau or Triple Sec
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