Thursday, October 20, 2011

Physics with Phineas and Ferb

The post below is very different from its original form which was a fun exercise with gravity; however, midway through I realized it would be useful tool to teach some physics concepts to some students I tutor. Hopefully I didn't do an injustice to the ideas presented, but also it is hopefully easy to understand by an audience without a great deal of scientific understanding.

I have a confession to make, I love kid shows, mostly the stuff from my time in Elementary School, like Doug, Hey Arnold, Bill Nye the Science Guy, and Magic School Bus and I still watch those shows when the opportunity presents itself; however, recently I have developed an unhealthy obsession with the Disney cartoon Phineas and Ferb. There are several reasons for this, but mostly it is because it is a smart, well-written show that doesn’t take itself too seriously and feels free to be really geeky.

Another thing I enjoy about the show is that they try to get science right (when it is brought up) sure they violate the laws of physics all the time but it is a cartoon about tweens building rockets and rollercoasters. However, when they show physics formulas they use the correct ones, not just complicated science babble (except when using a formula for a visual gag).

However, in one episode they demonstrate a common misconception between weight and mass, which I think is very common among people raised in the US (I single out my country because the Imperial System is stupid). In the scene the kids are floating through town in a helium-filled bouncy house when they pass over their destination. So the largest kid, Buford, jumps out of their floating vehicle and grabs onto a rope to allow the kids to sink to the ground. At this point another child points out that he doesn’t weigh any more at the lower height than when he was higher, and the two boy geniuses do not correct him. Well I thought I would, as there is a fundamental difference between mass and weight, in that mass is the amount of “stuff” in an object (usually measured in grams) and weight is the force due to gravity on an object thus it is a measurement of the interaction between the mass of an object and gravity (measured in pounds or Newtons). So what’s the deal his weight shouldn’t have changed just due to a difference in altitude right? Actually yes, yes it would have, you see the effect of gravity lessens the farther from the center of mass (center of the Earth) one is from it. So Buford’s weight would have changed when he lowered his elevation, as he would have experienced a greater force due to gravity.

How much you ask? Well currently I don’t know, but I do know that there is a physics formula for that:

  • Where G is the gravitational constant (6.674*10^-11 m3/(kg*s2))
    •  Newton figured it out and he was one smart cookie, so we will go with it.
  • The little m is the mass of Buford, which according to my fiancĂ© (an Elementary Education major) would be about 50kg
  • The big M is the mass of the Earth (5.974*10^24 kg)
    •  They used a really big scale to measure it
  •  And the r is the radius or distance from the center of the Earth (6.371*10^6 meters plus the elevation of the objects (or children) in question
    • They used a really big tape measure
  • Also the F stands for force, as in the force exerted on the objects by gravity, but we can also consider this weight
So first let’s talk about assumptions first off we are assuming that the Earth is a perfect sphere (not true) so that we won’t have to change the value for the radius as the jump house floats through the air, secondly we will assume that there is no change in mass for either object during this time period. So what happens?

Well first we need to figure out how high the jump house is above the ground and then how far below the jump house Buford is when he is hanging by the rope. So since this is a cartoon I’m going to make educated guesses rather than attempt to use some type of computer software to analyze the scene and get some hard numbers. I’m doing this for two reasons first I don’t have experience with that kind of software, and second it’s a cartoon and I’m just trying to make a point.

So let’s look at this video, the scene in question starts about at the 6:20 point and it looks as if the floating jump house is about 30 meters above the ground, and the rope Buford hangs off of is about 8 meters long, so we now have all the info we need.

F1 is the original height in the jump house, and F2 will be Buford’s second lower height.

F1=[(6.674*10^-11 m3/(kg*s2)) (50kg) (5.974*10^24 kg)]/(6.371*10^6m + 30m) ^2
F1=(1.99*10^16kg m3/ s2)/ (6.371*10^6 + 30m) ^2
F1=491.1364025 kg*m/s2 aka Newtons
Converts to 110.41 lbs

F2= [(6.674*10^-11 m3/(kg*s2)) (50kg) (5.974*10^24 kg)]/(6.371*10^6m + (30-8)m) ^2
F2=(1.99*10^16kg m3/ s2)/ (6.371*10^6 + 22m) ^2
F2=491.1364025 kg*m/s2 aka Newtons
Also converts to 110.41 lbs

So for all practical purposes there is no change in weight, however if my calculator could show more decimal points you would be able to see a difference eventually. If you don’t believe me we can check Buford’s weight at vastly different elevations, to see if this changes at all.

Radius in Earth radii

Weight in Newtons


Remember, all we changed was the distance from the center we moved Buford; we didn’t change the mass of any of the objects. The cool thing is that the first row shows that Buford is about 5 thousandths of a newton lighter 30 feet in the air than he is on the ground (or a 0.001 pound difference).

Now In Graph Form! (I labeled my axis when I made this, but they disappeared!)
As you can see there is a downward trend as you move Buford farther from the surface of the Earth (note do not try to extrapolate to the left to R*0 as there the formula is undefined and also if you go below the Earth’s surface you have to start subtracting mass from your value of big M so the force of gravity becomes weaker—however if you had an Earth mass black hole you could find the force of gravity approaching zero *hint* that number would be really big! As in 49114.103 Newtons (11041.290 pounds) at R*.1)

So while they were right for all intensive purposes in the episode, two boys able to build an interstellar space ship should have known better.


  1. You know, as a writer on "Phineas," I always get a little irked when anyone in animation, to justify cutting some corner or going with some lazy solution, says "It's just a kid's cartoon," so things like quality, intelligence, research, originality, etc. don't REALLY matter. They matter. I believe they matter A LOT.

    As an example, you're point is well taken. While none of us on "Phineas" are scientists, we really do try to ground the characters' projects and inventions in the realities of the physical world with some sense of integrity. I mean, if you consider the old cliche, "Truth is stranger than fiction," and that quote from the physicist (sorry, I'm forgetting which one and also paraphrasing): "The universe is not only stranger than we know, it's stranger than we're CAPABLE of knowing," and apply these ideas to science-related storytelling, than creating our science-related stories within the context of the realities of the physical laws of nature is actually a much richer and more valuable goldmine of fun, whacked, cool and mind-blowing ideas and concepts than if we just made the stuff up off the top of our heads and ignored reality. I'm sure that's why the best science fiction has always had the healthiest respect for the "science" part of its genre's title.

    I would go so far as to say, like a medical or law show on television have doctors and/or lawyers on staff as consultants for the technical stuff, we should probably have a scientist or professor with whom we can consult at all stages of story creation. It would be so nice to not have to bang our heads' against the wall and/or have to reinvent the wheel every time we start dealing with multiverses, alternative energy sources, cold fusion or even where the interesting work, research and breakthroughs are happening in the field of science at any given time that could suggest an idea for a story or project for the brothers that day (or a cool scheme for Doofenshmirtz).

    Anyway, thank you for keeping us honest with our show's science (and characters). You're absolutely correct that our characters should and would know this information. After all, we went and established that they (well, at least Phineas, Baljeet and Ferb) are scientific geniuses, so, again, while we really do TRY and keep it real in terms of physical, natural law, every now and then something will drop through the cracks and fall, apparently, becoming heavier as it gets closer to the center of mass.

    Thanks for paying attention,
    Jon Colton Barry

  2. Jon I'm going to be honest, I'm a little skeptical as to the validity of your identity (sorry it is the internet).

    However, I'm going to optimistic and say you are who you say you are. That being the case, first let me say thank you for your kind words it was great to hear from you. Secondly, it was a very easy mistake to make and as I showed would have had no consequences in the real world. Please don't be hard on yourself, I was just having a little fun.

    Secondly, I believe you can contact the Science and Entertainment Exchange at to put you in contact with professional scientists or engineers to fact check your scripts. Also feel free to ask my help, if you don't mind getting advice from an undergraduate.

    Finally, thank you for making one of the most enjoyable shows on television. I really do believe it is one of the few shows on television that can still inspire children to begin a career in Science Technology Engineering or Mathematics. And I'm not sure if you realize how popular your show is with college students, but I know several of us greatly enjoy it.

    Thanks again

  3. Okay, my turn. First of all Jon is who he says he is. He is a writer and storyboard artist on Phineas and Ferb. He is responsible for introducing the world to such anomalies as "Klimpaloon" the Magical old-timey bathing suit that lives in the Himalayas and the nameless Zebra that calls Candace, "Kevin". You can trust me when I say that.

    Second, the gag you are referring to was in a show that I directed. Again, you are going to have to trust me.
    But, you're right about the common misconception between weight and mass. Up until I read your post I was one of the common. The joke in question was based on a gut feeling I had about the an objected having a different weight the further it was from the object that suspended it or, in this case, closer to the center of the earth. But, I thought there's no way that could be right, everything in the basket of the balloon was still being suspended by the balloon, nothing new was added. The truth is, I had to get them to the ground and there was no time for a reasonable explanation. Some joke, eh? You just blew my mind with this explanation.
    I'll bet you can't explain why Buford is actually heaver on the moon.

    We live in an age of instant facts and paused DVR examination, so it's important for us to try to get the show as right as a bunch of animators can.

    Thank you for the kind words. There are a lot of us working very hard to make a show that can keep up with the new wave of smarter kids and their parents.
    Robert F. Hughes Director

    PS Hi, Jon!