1. 2010

    Death rays and thermal radiation

    It’s been far too long since I did a Mythbusters writeup, but I think it’s time to stop stalling and bring this series back. On this week’s episode, Adam and Jamie tested the myth of Archimedes’ heat ray for a third time — that has to be some kind of record — at the request of President Obama.

    The gist of the myth is this: by focusing enough of the sun’s rays, using a large number of mirrors, on an enemy ship, the Greeks hoped to heat it up enough to make it catch on fire. So far (spoiler alert), there’s no evidence that this thing ever could have worked. All three of the Mythbusters’ tests have failed.

    But I think I can shed some light (no pun intended) on why. As it happens, I taught a lab on thermal radiation transfer this week, and that (along with an interesting perspective on gravitationally baking a turkey) reminded me that it’s fairly straightforward to calculate, at least in a simple model, the amount of radiation it takes to heat something up to a particular temperature. It all stems from the Stefan-Boltzmann equation,

    $$P = \sigma\epsilon AT^4 …
  2. 2010

    Experimental Design

    Mythbusters is back as of last week with new episodes! Although the season premeire about throwing dogs off the scent isn’t directly physics-related, I do have one issue to point out.

    Tory, Kari, and Grant did an experiment in which they tried to hide some “contraband” from a dog by sticking it in a container with a strong-smelling material, like coffee or peanut butter. They hid the container somewhere in a 17,000 square-foot warehouse and set the dog loose to find it — which he always did. So the conclusion was that strong scents can’t distract a sniffer dog.

    But what if the dog was actually following the distraction? I wouldn’t be surprised if the scent of e.g. peanut butter itself was a dead giveaway to the location of the container, even if did mask the smell of the fake drugs. It was probably the strongest smell in that warehouse. A better experiment would have entailed filling several containers with the smelly substance, distributing them around the building, and only hiding the fake contraband in one of them, then seeing if the dog identifies the right one.

    Of course, they did basically that later in the …

  3. 2010

    Decapitation: Energy or momentum?


    Took the words right out of my mouth. Or right off my keyboard. Whatever. I’m just happy to see other people are considering the same questions.

    But I’ve got a couple of things to add. First of all, kinetic energy can be easily related to momentum using the formula

    $$K = \frac{p^2}{2m}$$

    which tells you directly that an object with the same energy but larger mass will have a larger momentum.

    Also, the big question: is it energy or momentum that gives a collision its decapitating power? My thought is that it actually depends on force. Think about this from the point of view of a particle in the neck. This particle doesn’t “know” (as if a particle could “know” anything) how big the sheet of glass hitting it is; it doesn’t “know” how much energy or momentum the glass has. The reason is that energy and momentum are what I’m going to call global properties, basically meaning that the total amount of them possessed by some object comes from contributions from all different pieces of the object. To measure a global property of the …

  4. 2010

    Firework Man

    More Mythbusters! Yayyy!

    Just kidding, I am not that incessantly perky. But I did have an interesting thought while watching last week’s episode of Mythbusters. Kari, Tory, and Grant were testing the myth that a man in Germany launched himself 150 feet high using 400 firecrackers and splashed down safely in a lake. First of all, how dumb is this guy? Darwin Award anyone? (I guess he’d technically be ineligible since in the myth, he survived unharmed, but it was certainly a noble effort)

    Anyway, here’s my physics thought of the week for last week: \(v = \sqrt{2gh}\). That’s the formula for the vertical velocity you need to reach a certain height as a ballistic projectile. To get 150 feet of altitude requires \(\unit{47}{\mileperhour}\), and that’s if you launch straight up. Coming off an angled ramp, as they did in the show, you’d have to be going even faster. Of course, the guy in the myth isn’t quite a ballistic projectile; he gets an extended boost from the rockets. But still, \(\unit{150}{\foot}\) of altitude is pushing it, so I would have been inclined (pun? intended? nah) to dismiss this …

  5. 2010

    Waterslide Wipeout

    Like everyone else, I feel a need to analyze the giant water slide in the latest Mythbusters episode. But honestly, there isn’t much left to say. The original video has been around for a while and everybody else who does this kind of analysis has already had the chance to do it. Example 1; example 2 (okay, so I’m only linking to one blog, but there must be more).

    I guess I might as well do the obvious calculation, but I’ll use the Mythbusters’ parameters instead of those from the original video (which are unknown). The slide starts with a downward ramp \(\unit{165}{\foot}\) long at a \(\unit{24}{\degree}\) slope, which then curves upward to a \(\unit{30}{\degree}\) launch ramp that terminates \(\unit{12}{\foot}\) above the surface of the lake. They didn’t say how long the launch ramp is, but I can work without that information. I’ll be trying to calculate two quantities mentioned on the show: how far each Mythbuster flies from the end of the ramp, and his maximum speed.

    (here’s a full-size version)

    There are two parts to this problem:

    1. The slide
    2. The flight

    The first part …

  6. 2010

    The car crash

    The blogosphere has been abuzz with analysis of last week’s episode of Mythbusters, in which they tested Jamie’s assertion (from a previous episode) that two cars crashing into each other at 50 miles per hour is the same as one hitting a wall at 100 miles per hour. OK, well, that turned out to be wrong.

    I didn’t have the time to write about it just after the episode and there’s no point in me repeating what’s been said about it elsewhere, but I do want to point something out: the reason it was wrong is that in one case, a car crashes into another car, and in the other case, it crashes into a wall. The car and wall react differently in the collision — the car compresses, the wall doesn’t, so when there are two cars involved, the energy of the collision gets split between them. There isn’t any fundamental difference between two objects crashing together at 50 miles an hour and one object at 100 miles per hour crashing into a stationary one.

    I would have liked to see the Mythbusters test one car at 100 miles per hour crashing into …

  7. 2010

    Calculating terminal speed

    In the 22,000 Foot Fall episode of Mythbusters, Adam did a calculation of how long it should take for a falling person to reach terminal speed. It occurred to me that there’s a wrong (but simple) way and a right (but complicated) way to do this calculation — I wonder which one was used on the show to come up with 487 feet?

    First, the simple way. From numerous tests in previous episodes, the Mythbusters know that the terminal speed of a person falling through air is about 120 miles per hour. Based on that, you could try to figure out the fall height it takes to achieve that speed using the formula

    $$h_0 = \frac{v_T^2}{2g}$$

    (It’ll become clear later on why I’m calling the height \(h_0\)). This formula comes from the kinematic equation \(v^2 = v_0^2 + 2ad\) with initial velocity \(v_0 = 0\), final velocity \(v = v_T = \unit{120}{\mileperhour}\), and acceleration \(a = g = \unit{9.8}{\frac{\meter}{\second^2}}\). Plugging in the numbers and calculating gives

    $$h_0 = \unit{147}{\meter} = \unit{482}{\foot}$$

    That’s reasonably close to what Adam got on the show, so I’m guessing this is the method …

  8. 2010

    Velocity addition: a myth?

    On the episode of Mythbusters aired a couple weeks back, Kari, Grant, and Tory set out to test the myth that if you have a car driving forward at, say, 60 miles per hour, and you shoot a ball out the back at the same speed, it will fall straight down. Now, if you know anything about physics, your first thought upon hearing this might have been the same as mine: “huwhah?” The idea that velocities of equal magnitude and opposite direction cancel each other out in this way is a pretty fundamental result…

  9. 2010

    Shockwave reflection

    The latest episode of Mythbusters features a myth with a deep physical explanation… no pun intended! Well, maybe. Anyway, the myth is that by diving under the water, you can escape injury from an explosion occurring above the surface. Adam and Jamie tried to solve this puzzle by experiment (what else), and their results seemed to show that the myth might actually be true, but I want to look at it from the theoretical standpoint: why might being underwater protect you from an explosion?

    There is actually a not-too-obscure answer to this puzzle, and it has to do with refraction and reflection. These are phenomena that occur when a wave (of any sort — light, sound, or whatever) crosses a boundary between two media in which it has different speeds. Part of the wave bounces back (that’s reflection) and part of it continues through, but in a different direction (that’s refraction). Exactly how much of the wave’s power is reflected and how much is transmitted through, as well as the new direction of the transmitted part, depends on the angle of the incoming wave with respect to the surface, and also on the relative speed of the wave …

  10. 2010

    Soda Cup Killer

    The Mythbusters are back! In their first episode of the new season, Adam and Jamie tested the myth that a cup of soda casually thrown out a car on the highway can smash through a windshield and kill the person sitting behind it. (Technically busted, but still really dangerous!)

    One of the major factors that determines whether or not a projectile (like the cup of soda) will be able to smash a windshield is the force exerted by the cup on the glass. On the show, the Mythbusters used a piezoelectric force sensor to directly measure the force exerted when a cup of soda/ice/slush impacted on a steel plate, but we can also try to calculate the force using Newton’s second law,

    $$\vec{F} = \ud{\vec{p}}{t}$$

    First some simplifying assumptions are in order. I’m going to start by assuming that (1) each part of the cup and its contents continues to move at constant velocity up to the moment it impacts the plate, and that (2) after impacting the plate, the soda/ice/slush flies out in a direction perpendicular to its initial trajectory, along the plane of the plate. Of course, I wouldn …