The Hyneman has a new line to add to his resume:

I kid, of course. Still, the Mythbusters’ demonstration of a motorcycle riding on water in last week’s episode was seriously cool. I have to admit, I didn’t expect it to work! But physics says otherwise — both the experiment, as we saw last week, and as I’m about to show you, the theory.

Underneath all the complicated fluid dynamical effects, a motorcycle can ride on water for much the same reason a speedboat does: it presents an upward slanted surface for water to bounce off of. For a speedboat, that surface is the hull; for a motorcycle, it’s the bottom of the wheels, especially the front wheel. But wheels are complicated. It’ll make things easier to start by examining the behavior of a speedboat-like slanted flat surface as it moves through water.

Conveniently, I’ve already done that calculation. It comes from another episode of Mythbusters a few years back, when they tried skipping a car across a lake. The calculation went like this: water molecules hit the lower surface of the car with a horizontal momentum \(-mv \unitx\) and bounce off in a downward …

As you might be able to tell by the lack of activity on the blog, I’ve been pretty busy the past couple weeks. Which makes it kind of hard to write about Mythbusters at my usual level of detail.

Fortunately, Rhett Allain has already done it for me. He analyzed last week’s episode to figure out whether air pressure is enough to pick up a manhole cover. And it is: an air pressure of \(\SI{101325}{Pa}\), normal atmospheric pressure, applied to a manhole’s surface area of \(\SI{0.369}{m^2}\) (seriously, click the link), gives a force of \(\SI{37400}{N}\) — over eight thousand pounds! That’s way more than enough to pick up a 300-pound manhole cover.

Of course, that would only happen if the manhole cover had a near-perfect vacuum above it. Perhaps if it were a manhole on a spaceship. But that’s not the situation on Mythbusters. (How cool would that be? Mythbusters in space… but I digress.) The manhole cover under an Indy car has air on both sides; the pressure of the air above is reduced, though, due to Bernoulli’s principle.

I know, I know, this blog post is very late! If I’m going to post about a Mythbusters episode, I usually try to do it before the next one airs. But this topic — calculating the circumstances under which a rope will pull a person’s leg — turned out to be pretty complicated. Which of course made it impossible to give up on.

And after days of toil, I think I finally figured it out! If you’re the kind of person who finds complicated physical interactions fascinating, you’re going to love this post. The math isn’t too complicated; if you know what a differential equation is, you’ll be fine, but the physical reasoning is something you could probably spend a while wrapping your head around.

The setup

On the Deadliest Catch-themed Mythbusters episode which came out last week, one of the myths being tested was that if a person steps in a coil of rope, and that rope is attached to a crab pot (trap) that gets dropped over the side of the ship, the rope will be pulled tight enough around the person’s leg that it will drag them overboard, and down to the …

It’s that time again: Mythbusters is back! And they sure know how to kick things off with a bang — or better yet, a prolonged burn!

For the 10th anniversary of the show, the Mythbusters revisited the very first myth they ever tested, the JATO rocket car. Wikipedia has the story in what appears to be its most common form:

The Arizona Highway Patrol came upon a pile of smoldering metal embedded into the side of a cliff rising above the road at the apex of a curve. the wreckage resembled the site of an airplane crash, but it was a car. The type of car was unidentifiable at the scene. The lab finally figured out what it was and what had happened.

It seems that a guy had somehow gotten hold of a JATO unit (Jet Assisted Take Off - actually a solid fuel rocket) that is used to give heavy military transport planes an extra ‘push’ for taking off from short airfields. He had driven his Chevy Impala out into the desert and found a long, straight stretch of road. Then he attached the JATO unit to his car, jumped in, got up some speed and fired off the …

It’s time to write about Mythbusters again! Last night on the show, the team tested a myth that balloons can take the place of an air bag in the front seat of your car, and if you have the right configuration of balloons, you’ll be protected from the damaging effects of a crash.

If you watched the show, you’ll know that this myth was thoroughly busted. The maximum acceleration a human body can take and still survive is \(100g = \SI{980}{m/s^2}\), and no matter what configuration of balloons they tried, they were unable to reduce the acceleration to any less than about \(120g\). This got me thinking about why that might be the case. Physically, keeping a body’s acceleration below a certain threshold is just a matter of spreading that acceleration out over a long enough distance. It’s easy to see that by looking at the relevant equation:

For a car crash, you’d be given \(v_0\), the initial speed, and \(v = 0\), the final speed, and so if you want \(a\) to be small, you have to make \(\Delta x\) large. Specifically,

It hasn’t escaped my notice that Mythbusters is back with a new season! Actually, it’s not really that new, since we’re now three (well, now four) weeks in, but I missed the first two episodes since I was out of the country. But it works out because this (actually last) week’s myth is full of interesting physics to analyze!

This past Sunday, Adam and Jamie tested the myth that if you’re driving fast enough, square wheels can actually provide a surprisingly smooth ride. At first, the idea of square wheels working at all, much less actually being smooth, can seem a little wacky, but with a bit of physical intuition, it’s not hard to convince yourself that it’s actually pretty plausible. As they explained in the show, the reason a square wheel is expected to bounce you up and down is that the distance from the axle to the bottom of the wheel changes as it turns. If you’re going slowly, every time the wheel tips over another corner, it’s going to fall down until its side is resting against the ground, taking you with it. But if you speed up …

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 …

While catching up on some old Mythbusters episodes, I ran across an interesting myth about spinning bullets. Apparently when you shoot a bullet into the surface of a frozen lake, it bounces backward, bounces over the ice a little way, and keeps spinning even after it comes to rest.

This is a very curious result. At first, it kind of seems to make sense. A bullet comes out of the gun spinning at 80000 revolutions per minute, according to the show, which is pretty fast. So it makes sense that it has a sizable amount of angular momentum, which in turn means it’ll take quite a bit of torque to stop it. Colliding with the ice conceivably might not be able to exert enough torque to do that, so the bullet would keep spinning.

But if that were the case, the bullet should maintain its orientation — it’d keep pointing in the same direction that it came out of the gun, because angular momentum is a vector quantity and it won’t change in either magnitude or direction without an external torque. That clearly wasn’t the case; the bullets the Mythbusters shot skittered across the ice, spinning in …

The latest episode of Mythbusters tested a slightly controversial and very physics-related myth: that you can propel a boat forward by putting a fan on the boat and pointing it forward, into the sail. What’s going on here?

First of all, why wouldn’t you expect this to work? Actually, first of all, why would you expect this to work? Think about the naive explanation for why a sailboat moves: the wind pushes forward on the sail, and the sail pushes forward on the boat. So someone who had never heard of physics might think that putting a fan on the boat and pointing it into the sail just gives you a convenient, portable source of wind. Presto, instant speedboat!

But, as explained on the show, that reasoning doesn’t work, because of Newton’s laws of motion. There are actually a couple of different ways to apply Newton’s laws to this scenario:

• Newton’s first and second laws (which are kind of the same thing) say that an object maintains its state of motion unless subject to an external force. The key word there is “external”: if you want your boat to move, you need something outside …