1. 2010

    The Conifer Catapult

    The tree catapult is a staple of cartoon physics, and I think I’ve even seen it acted out in one or two live-action movies. But according to the Mythbusters, it may have been actually used by medieval armies laying siege to castles. I actually thought preconstructed wheeled catapults would have been the norm, but still, you have to wonder: does it work?

    The underlying concept behind a tree catapult is simple enough: trees are stiff. If you pull one down and let it spring back up, it stands to reason that you could potentially fling a dead body pretty far. But that very same stiffness that gives a tree its flinging power also makes it resist being pulled down in the first place. This is a pretty straightforward application of the principle of conservation of energy: whatever energy the tree is able to expend in flinging its cargo into the air has to come from the work you do while pulling it back in the first place.

    $$W = \int \vec{F}\cdot\udc\vec{s}$$

    I can make a rough calculation by treating the top of the tree as a spring, known in physics terms as a simple harmonic …

  2. 2010

    Bouncing Bullets

    Whenever Mythbusters meet bullets — no, not literally, though this week’s episode of Mythbusters does have Adam and Jamie trying to shoot cardboard cutouts of themselves — you know something wacky and interesting is about to ensue. The myth in question is that, with an unwisely aimed shot, it’s possible for a bullet to bounce off three steel beams and come back to hit the shooter.

    Seems straightforward enough, right? If the beams, or walls as the case may be, are lined up at right angles to each other, why shouldn’t a bullet just bounce off all three and come right back to where it started?

    As Adam and Jamie (re)discovered during the show, bullets don’t bounce, at least not when they’re moving as fast as, well, a speeding bullet. They shatter on contact with any hard enough surface, like steel, and the pieces spray out in what could be a completely different direction from what you’d naively predict.

    From a physics perspective, this highlights the difference between elastic and inelastic collisions. Elastic collisions are based on the idea of a ball bouncing off a wall; it goes in at some speed and bounces right …

  3. 2009

    How the Mythbusters skipped a car

    On the last episode before breaking for Christmas, the Mythbusters build team undertook the slightly ambitious project of skipping a car across a pond, as shown in the movie Cannonball Run. At first this probably seems like a ridiculous thing to try — of course, on Mythbusters, what isn’t? But this one actually worked. Here’s a look at the rather interesting physics behind it.

    As Jesse explained on the show, there are basically two physical principles that allow you to skip a stone (or a car) across water: the spin, and the reaction force of the water. This isn’t buoyant force, like they’ve dealt with on previous shows; if buoyancy alone were the only thing pushing up on the stone, it’d float. Stones don’t float. (Neither do cars.) The force that keeps a stone skipping across the water is related to its speed. Spin and speed, that’s the magic formula.

    First, the spin. Any spinning or rotating object has angular momentum, which is like a rotational equivalent of linear momentum: roughly speaking, it measures how difficult it is to change the object’s motion. Objects with a lot of momentum are either very massive …

  4. 2009

    Unarmed and unharmed

    This is one of those really cool things that I’ve often wondered about: can you really shoot a gun out of an outlaw’s hand? Last week on Mythbusters, Adam and Jamie decided to test it out. Sure, it’s not the kind of thing you’d think would be easy (or safe) — unless you have access to that classic Mythbusters creativity. Their first idea involved a Velcro-like gripping arm to hold the gun, and although it may not be clear just how exactly that compares to a real hand, they obtained some interesting results from comparing the different gripping positions.

    Anyone who’s ever tried to pry an object out of somebody’s hand knows that the easiest way to do it is to twist it to apply stress on the thumb, the weakest point of the grip — not just to hit it as hard as possible. And whenever an object is twisting or rotating, the operational physical principle is torque, the rotational analogue of force. Torque can be calculated from the formula

    $$\vec{\tau} = \vec{r}\times\vec{F}$$

    but in most simple cases, we can identify an axis of rotation and then calculate the torque around …

  5. 2009

    Bus Jump

    It’s finally time to analyze the latest Mythbusters episode again. This one has Grant, Tory, and Jessie testing another myth about that bus from the movie Speed. According to the Mythbusters, in the movie the bus, traveling at 70 miles per hour, was able to jump over a 50 foot gap in the highway, land safely, and continue on its way.

    There’s an obvious physics question in here: could the bus even make the jump? Well, while it’s in the air, the bus is basically just a projectile, and projectile motion is one of the most basic topics in physics. This shouldn’t be hard to calculate. The equation for uniformly accelerated motion in one dimension is

    $$x = x_0 + v_{0x} t + \frac{1}{2}a_x t^2$$

    In a two-dimensional system, like a flying bus (up and forward: two dimensions, assuming it doesn’t move sideways), we use two of these equations, one for each dimensions. And if we ignore icky things like air resistance, it’s easy to determine each of the individual factors in the equation:

    • Let’s choose coordinates such that \(x_0 = 0\) and \(y_0 = 0\), setting the edge of the road where …
  6. 2009

    Buoyancy, part 2

    Following up on my calculation of the lifting power of helium balloons, it’s time to see how the same argument applies to ping-pong balls being used to raise a sunken ship.

    Raising a ship with ping-pong balls is, in fact, nearly the same situation as raising a child with helium balloons. All you have to do is replace the air with water, the helium with air, the rubber balloons with plastic balls, and the child and harness with a boat (though preferably not in that order). The physical principle at work (Archimedes’ Principle) is exactly the same, and so the same equation I used last time is equally applicable here: the buoyant force on an object (ping-pong ball) immersed in a fluid (water) is equal to the weight of the water displaced by the fluid,

    $$F = \rho g V$$

    Let’s see what this says about how many ping-pong balls it would take to raise the Mythtanic II, which weighs about \(\unit{3500}{\pound}\) according to the show. We can start by figuring out how much mass it takes to balance out the buoyant force on a single ping-pong ball, using \(-m_\text{load} - m_\text{ball} + \rho V …

  7. 2009

    Buoyancy, part 1

    Finally, time to get back to covering some old (by now) Mythbusters episodes. I’ll start with the bonus episode aired a few weeks ago, “Ping-Pong Rescue” — an oldie but a goodie in which the Mythbusters try to raise a boat with ping-pong balls and lift a child off the ground with balloons.

    This episode was all about buoyancy, the physical description of how stuff floats. Buoyancy goes all the way back to one of the scientific world’s earliest experts, Archimedes. According to legend, he had been tasked with figuring out whether a crown, given as a gift to the king of Athens, was composed of pure gold or of other, less valuable materials with merely a gold coating. The straightforward way would have been to melt the crown down in order to make an accurate measurement of its volume and thus determine its density, but the king, for some reason, didn’t want his crown damaged and so melting it was out of the question.

    The bright idea that Archimedes eventually came up with was — we think — based on a principle that now bears his name (Archimedes’ Principle): that the buoyant force on an object immersed in water …

  8. 2009

    Exploding a microwave oven with C-4

    Exploding grease, exploding microwave ovens, exploding cheese — it’s a Mythbusters fan’s dream episode :-) Of course, where there are explosions, there’s physics, and the latest episode of Mythbusters is no exception.

    Here’s one: you can’t blow up C-4 by microwaving it. Kari explained in the show that this is because C-4 is a plastic explosive, and microwaves are designed to pass through plastics (as well as metal and glass). So how exactly does that work?

    Microwaves heat food by a process called dielectric heating, which generally refers to the ability of many materials to absorb energy from electromagnetic radiation passing through them. Physically, an electromagnetic wave consists of rapidly oscillating electric and magnetic fields. These fields (well, primarily the electric field) exert forces on the charged particles that make up all matter — since the fields are oscillating, so do the forces. Essentially, an electromagnetic wave makes atoms and molecules rapidly jiggle back and forth, and as they do so, they bump into other nearby atoms and molecules, transferring kinetic energy to them and raising their temperature. Of course, if the atoms and molecules are gaining energy, that energy must be coming from somewhere, and the electromagnetic …

  9. 2009

    Dirty vs. Clean Car

    Hot on the heels of their Bullet Fired vs. Bullet Dropped episode, the Mythbusters have another result that’s poised to shake up the world of science… well, maybe not. But this week’s main myth, Dirty vs. Clean Car, is the kind of neat idea that most of us would never think to test and yet turns out to be surprisingly close to practicality. The myth that Adam and Jamie are testing is that dirt on a car has the same kind of effect as golf ball dimples, increasing the fuel efficiency of the car. To sum up the results (SPOILER ALERT ;-), it doesn’t work, at least not with dirt — but putting an actual dimpled coating on a car does increase the fuel efficiency by 11%. (Only on Mythbusters would they dimple a car…)

    As with a lot of recent myths, this one deals with fluid dynamics — but not just the simple stuff like drag force, as in the bullet myths. The golf ball effect is based on turbulence, specifically the idea that the rough surface of the ball induces turbulence which disrupts the wake (pocket of still air) that trails behind the ball. That pocket of still …

  10. 2009

    Lifting a car with duct tape

    It’s Mythbusters day again, and this time Adam and Jamie are testing the strength of duct tape in some rather interesting ways. Like using it to lift up a car, for example. This is a pretty cool demo, but there’s one thing that irked me: on the show, there was quite a bit of speculation along the lines of “Can duct tape really hold up a car?” Yes, in fact, duct tape can hold up anything, if you use enough of it. As they suggested in the show, when you’re using strips of tape (or string etc.) to hold up an object, the total force required is split among all the different strips of tape, and if your strips are approximately evenly distributed (in some particular sense), the force is approximately evenly split. With 100 strips of duct tape lifting a 5000 pound car, that’s an average of about 50 pounds per strip, which is reasonably within the limit that Adam and Jamie found (albeit somewhat unscientifically) — even accounting for the fact that some strips are carrying more weight than others.

  11. 2009

    Bullet Fired vs. Bullet Dropped

    With their season premiere this week, the Mythbusters are testing a classic physics story, so of course I had to comment on it. The myth in question is that if you fire a bullet from a gun held horizontally, it will hit the ground at the exact same time as a bullet dropped without any horizontal motion at all.

    Of course, in the mind of any physicist, this is no myth at all — the laws of physics that tell us this should happen are so well established that they’re almost beyond question. Specifically, it’s the linear independence of orthogonal vectors, which means that components of motion that are perpendicular to each other, like gravity (vertical) and constant velocity (horizontal), don’t get in each other’s way. You can split the motion of the bullet into two perpendicular components and analyze each one separately. This is, in fact, one of the first things students learn in an introductory physics class: analyzing the motion of a fallen or thrown object. The equations \(x = v_{0x}t\) and \(y = -\frac{1}{2}gt^2\) work for both the fallen bullet and the dropped bullet, just with \(v_{0x} = 0\) in …

  12. 2009

    Keeping your Convertible Dry

    No new episode of Mythbusters this week, unfortunately, but in its absence I get to write about Car vs. Rain, the episode originally aired three weeks ago. It focuses on a fantastic physics-based myth: when driving a convertible in the rain, does less rain get in the car if you step on the gas, as opposed to pulling over and putting the top up?

  13. 2009

    Curving bullets

    This week the Mythbusters tackled the question of whether you can make a bullet follow a curved flight path, as in the movie Wanted. The characters in the movie are able to do this using some fancy flick of the wrist as they fire the gun, but is it really possible? Apparently a lot of people were wondering.

    The short, simple answer is no. It’s an obvious application of Newton’s first law of motion: objects moving in a straight line will continue moving in a straight line at constant speed, unless subject to an external force. But there are only a couple of external forces that can act on a bullet: air resistance and gravity. Gravity certainly isn’t going to make the bullet curve sideways as we see in the movie, and all air resistance will do is slow it down, not change its direction.

    Then again, Kari, Grant, and Tory hit on an important point: bullets are highly symmetric and are typically ejected from the gun barrel with high spin. All this is optimized for motion in a straight line toward whatever you’re aiming the gun at. What happens if you use asymmetric, oddly shaped …