A lot of the discussion about the physics in the latest Mythbusters episode focused on the giant Newton’s cradle. But what about the other myth? While Adam and Jamie were playing around with their giant balls, Kari, Tory and Grant balanced a car on a cliff in order to test whether a bird landing on the hood would be able to send it falling over the edge. Unsurprisingly, it turns out there’s some interesting physics to be found there as well.

Potential Energy and Equilibrium

First of all, what does it take to balance a car on a cliff? The easiest way to think about this physically is in terms of gravitational potential energy. Let’s say that the top of the cliff, at the point where the car is resting on it, is at height zero. Then the potential energy of the car is \(U = mgh_\text{cm}\), where \(h_\text{cm}\) is the height of the car’s center of mass. As a rough rule of thumb, the car “seeks out” the configuration of lowest potential energy (there are a bunch of caveats to that statement but it’s good enough for now), which means its …

Yep, that’s right, a rocket-propelled grenade finally made its way on Mythbusters! Personally I’m surprised it took them so long…

Anyway, let’s not get distracted from the science by cool explosions just yet. On last week’s season premiere of Mythbusters, Kari, Tory, and Grant tested a myth based on a scene in RED in which two characters are facing off, one (the hero) with a revolver and the other (the villain) with an RPG launcher. In the movie, they both shoot at the same time, the bullet hits the RPG in midair and detonates it, and the resulting explosion kills the villain. Now, in the show, this myth was busted on several counts:

• RPGs don’t even arm until about 60 feet after launch, about \(\frac{3}{4}\) of the way to the target and long after this one would have been hit by the bullet
• When an RPG explodes, it sends balls of molten copper flying forward, which wouldn’t have been stopped by the bullet
• The distance at which the explosion would have taken place, 16 feet from the villain, is quite survivable

Unfortunately, they didn’t test what I thought was the most …

A rather interesting question came up on Physics Stack Exchange (semi-)recently: How do we know that \({}^{14}\mathrm{C}\) decay is exponential and not linear? This question addresses something that confuses a lot of people when they’re first learning about radioactivity, namely the use of a half-life to describe the different rates at which different kinds of radioactive atoms decay. When you first hear that, say, carbon-14 has a half life of 5700 years, you might wonder why we don’t just say that it has a lifetime of twice that, or 11400 years? If half the sample is gone in the first 5700 years, won’t the other half be gone after the next 5700 years?

The model suggested by that statement is called linear decay, because the number of atoms remaining decreases linearly with time. Of course, we know from experiments that radioactive decay is not linear, it’s exponential. But you can also use simple physical reasoning to convince yourself that radioactive decay wouldn’t be described with a half-life if it were linear. Here’s a little thought experiment to show that:

1. Take a billion radioactive carbon-14 atoms, put them in a box, and …

Last month I posted about the then-current results from the ATLAS and CMS detectors at the LHC hinting at a possible new particle around \(\unit{120-150}{\giga\electronvolt}\). But in light of new data presented at the 2011 Lepton-Photon conference in Mumbai, we’re not so sure about it anymore.

Take a look at these plots from the ATLAS and CMS experiments, respectively:

The solid line in each plot represents the observed data, and the dotted line represents the expected background, which is basically the theoretical prediction based only on the stuff we already know to exist. The yellow band shows the \(2\sigma\) confidence interval. In other words, if there is nothing left to discover within this energy range (in particular if the standard model Higgs does not exist), there’s a 95% chance that experimental data falls within the yellow band.

When I displayed the equivalent plots from EPS HEP-2011 in my post last month, I pointed out that the interesting features were a couple of small regions where the solid line rose above the yellow band. Looking at the newer plots, you can see that that’s no longer the case. The experimental results are starting to …

Only 3 weeks late (blame web server troubles), I figure it’s time for me to write a wrapup post about my experience at the CTEQ summer school. Of course, I’m not really sure what to write, other than that it was awesome. If you’re ever in a position to go, I highly recommend it.

As I mentioned in another post, the school is basically an opportunity to go listen to presentations on QCD from members of the CTEQ collaboration and guest speakers that they invite. This means that there are some pretty big names there. And there are plenty of chances to interact with them. We had four one-hour lectures each day (every speaker invariably begged to be interrupted with questions), plus mealtimes (everybody ate in the same dining hall), plus an evening “recitation” which was really just an open Q&A with the day’s speakers, plus a “night cap” a.k.a. the CTEQ Happy Hour ;-)

Of course, there was a lot of physics to be learned. Basically, the school was divided into two halves of four days each: the first half consisting of lectures covering the fundamentals of QCD and quantum field theory (the …