The image in question
I’d like to begin a series where I pick apart physics in certain media. I found this gif on Facebook, and I feel like it’s a pretty good place to start. The image is from a cartoon called Totally Spies and I remember that it used to air on Cartoon Network. I don’t know the details too much except that it’s supposed to be some female spy show. You could read the Wikipedia article I linked for details.
So before we go into what’s wrong with this picture, let’s go into what’s right. The resolution is pretty poor, but you can see that the middle of the burned door is yellow while the edges are fading shades of red. Because the door is presumably melting, it means that the door is getting rather hot. Lasers are just light beams and the reason they can melt things is because they deposit energy into what they strike. When the door receives that energy, it heats up at the area of contact. Heat then flows from warmer areas to colder areas via thermodynamics. Got a warm spot in the center, cooler areas nearby, the heat will flow. So why do the colours matter? Because hotter materials are different colors. Red hot is colder than yellow hot which is colder than white hot. The middle is the warmest, so it should be the colour that corresponds to highest temperatures. There’s also a small case to be made with how the door melts in that there are two “large” areas with let’s say a “medium” region and “smaller” regions that melt. Two lasers striking the door at different points, those spots should be the hottest, and should melt first. The region between them should reach melting temperature shortly after the striking regions do, so it melts next.
However that’s where the physics stops working. There are two major things that I would like to focus on in the way of bad physics. The laser and the melting door. I’ll start with the melting the door.
When I gave the show props for the colours of the melting door being okay, perhaps I should’ve given them half credit. So remember that when things get warm they change colors? Now obviously, the metal must be yellow-hot before melting. That much is apparent from how the metal was yellow hot before it started melting. But if you watch the melting animation, you’ll see that the edges of the yellow-hot region remain red-hot BUT they start to melt! Bad physics!
The reason this is important is because we view the door as melting from the ‘out-side’ but the laser strikes it on the ‘in-side’! So if anything, the side of the door facing into the room should melt first. That’s why I didn’t dock it points for the melting in the first section. Because we only see the door melting from the outside, we can’t tell too well the order in which it melts.
Now when I looked at the door, I had wondered as to whether or not it may have been easier to simply melt the glass. It’s probably some kind of laminated glass from what I’ve read on sound booth creation. The problem with glass is that it’s hard to really pin down its melting temperature without knowing what type of glass it is. For the sake of argument, let’s just take a high end estimate of 1700 degrees celsius. Many other sources talk about when glass becomes malleable which would be around 1300 degrees celsius but I’m going with melting because it’s easier to equate melting for steel.
(I suppose technically I should go with vaporization because the door doesn’t seem to show where there melt-steel is…) Anyway, the melting point of steel is also tricky because it also depends on the steel’s composition. But according to this source the melting point of steel could be as high as 1500 degrees celsius. This seemed odd to me because I always thought that glassblowing came before metalworking. The Iron Age, at the very least, came around 1200 B.C. The earliest glassblowing was apparently 1500 B.C. So glassblowing came before iron, which I would infer means that the temperatures necessary to melt glass were easier to achieve than that of iron. So the glass we’re talking about for windows is probably not the same type of glass that was used in early glassblowing.
Why am I talking about all of this melting business? Well, I’d like to talk about how much energy is being delivered to the materials (since it’s easy to talk about lasers in terms of Watts). There’s a material property called specific heat. Specific heat is how much energy is required to raise the temperature of a material. The Watt is a unit of power, and it is defined as a Joule per second. The specific heat of water is 4186 Joules per kilogram-kelvin. You have a 5kW laser, you can raise the temperature of one kilogram of water one degree celsius every second (you actually do a little more but I’m rounding here). Let’s look at the specific heats of glass and steel. DISCLAIMER: To be perfectly honest, I don’t really know if the glass we want is technically on the glass table. I’m going to assume it is, but I don’t know. I could be wrong. So we’re going to use the pyrex glass (753 J/kg*k) and the carbon steel value (120 J/kg*k). Obviously there are different masses of glass, so let’s compare how much glass that we need to melt and how much steel that we need to melt. When comparing densities, I will be using pyrex glass’ density because I’m using pyrex glass’ specific heat. The density of pyrex glass is 2.23 g/cm^3 (though looking at that page, we also see that the melting point is about 1500 degrees celsius, which helps narrow down our calculations). The density of carbon steel is 7.83 g/cm^3. So if we need to melt some mass M of steel to make an exit, we would need to melt about 1/3 M of glass to make an exit. Let’s do some math. We want to know how much energy would we would have to deliver to each material to melt some volume of it, let’s say 1000 cm^3. And we’ll be raising the temperature from room temperature to 1500 degrees celsius. So 1500 °C – 20 °C (room temperature) = a change in 1480 degrees celsius.
Let’s plug in our numbers. First for the steel.
So about 1.4 mega Joules or 1.4 MJ for short (Billie Jean, is not my lover….) The assumption of 1000 cm^3 of material getting melted went into that… is that reasonable? Well… that’s about 61 cubic inches. That door looks to be maybe 2 inches thick? Look at that huge gap, it’s probably a great deal more than 61 cubic inches. So our estimate is low if anything. But going through the mess of trying to figure out with scaling how much material is actually melted is probably more complex than what readers care about. Also I’m eyeballing everything because I don’t have photoshop to pixel-perfect this stuff. Now let’s see how much energy we need to melt the glass.
I’ve defined pg and ps to be the densities of glass and steel, respectively. We see immediately that you need about half the required energy to melt the glass! (Lord knows what would’ve been required to burn away the sound-absorbing material that surrounds the room…) And before you say that they would’ve had to climb up to that little window door – LOOK AT THE GIANT FREAKING WINDOW TO THE RIGHT OF THE DOOR. Also, it takes like 2 seconds (being generous) to melt the door. That means that the laser used is delivering about 700,000 Joules per second to the door. That’s .7 Mega Watts. This was delivered FROM the lipstick ehh… to be frank I have no idea what they’re called. Let’s say lipstick pencil. This .7 MW were delivered from the lipstick pencil. Which worries me because I want to know how this .7 MW laser was generated in such a small device, and why the device doesn’t heat up in the woman’s hand as she fires it. And why doesn’t it destroy the compact mirror that was used to reflect it? We’re also neglecting the most obvious of questions – why did she not just point the laser at the door and melt it like that? Reflecting lasers does not increase the power of lasers. There’s no additional energy being pumped into the laser. If anything, the laser is losing energy.
That’s all of the door stuff. Now let’s focus on the laser – mirror thing. It is its own boatload of problems but it should be much easier to deal with. Let’s suppose that, (for some reason or another) the lipstick pencil doesn’t melt as it is being used. The compact mirrors are lying on the floor. The lipstick pencil is CLEARLY pointed towards the mirrors. By the Law of Reflection (and now we have to assume that for some reason this .7 MW laser doesn’t destroy the compact mirror in a second) the reflected beam should’ve gone into the floor, not to the other mirror. But let’s say the light beam bends towards the other mirror. Then, in fractions of a second the light beam would STILL go into the floor. See the picture below.
So how long would this take? Well, if each compact mirror is… say… about 7 cm tall (2.7 inches, 0.07 meters) and they’re placed… what looks to be a full tile apart. Those tiles look to about two female heads in length? What’s the average length of a female head? Well, a Google search led me here. Sure it’s circumferences, but we can work with that. About 53 cm to the circumference of a female head. These women appear to be teenagers from my point of view? But that’s fine, we’ll use the same value for an adult woman’s head. 53 cm divided by pi (which is pronounced ‘pee’ in Greek by the way) leads to about a 17 cm diameter head. We want two of those, so we’ll assume that the tiles are 34 cm (0.34 meters) apart.
(I keep putting things in meters because I can quickly recall the speed of light in meters per second)
Let’s do some math. Let’s say that the incoming angle is 1°. Completely unreasonable, but I’m using it to prove a point. Simple trigonometry shows that the first reflection, if the laser strikes the very top of the mirror, will travel 0.006 meters down. Okay, cool. So we can actually bounce a few times. We can bounce a lot of times, actually. How many bounces? We can bounce 11 times before hitting the floor. Almost 12 times but almost only counts in horseshoes and hand grenades. The total path length for those 11 reflections is 11 times is really close to 11 times .34 meters (this is actually somewhat expected due to the small angle approximation for tangent). So light would travel about 3.74 meters before it hit the ground. How long would that take? Well, c, the speed of light, is 3*10^8 meters per second. So, close to 1/1*10^8 of a second. The time of reflection in the gif is much longer than that, so bad physics.
So this has been a short excursion into the realm of cartoon physics. I hope you’ve learned a little something, as it has been a pleasure getting serious about silly little animations. That’ll be all for now.