[4-color ma] The physics of cats and (wonder) dogs

Anyone who reads genre comics - superhero in particular, but including adventure and war and western - gets used to improbable physics, those apparently impossible leaps and lifts and feats and flights. But sometimes the impossible is only unlikely.


Some time ago, Mike Sterling ran a post on Progressive Ruin entitled Adventures in Improbable Physics with Rex the Wonder Dog, in which he looked dubiously at this sequence:

Well, being a community college teacher and all, I figured it might be useful to let some students have a go at seeing if this scenario could indeed happen, at least without violating any laws of physics. So I sent the link to Dr. Burn, who is not a supervillian (although the way I render her name makes her look like one) but our resident math/physics guru. The time was right for her to introduce the problem in her class last week, and she sent me this rumination on the scenario, written while she was in her lair lab, proctoring a test:

I'm thinking about Rex the Wonder Dog. This problem is a bit complicated because of the torsional aspect of the tree branch. On one level, it is acting like a spring, which is a simple analysis. However, the spring force happens because of torque on the branch. As you know from changing a tire and using a lug wrench, torque depends on the amount of force as well as how far from the rotation point that you apply that force. The big cat has more force on the branch because it is heavier than the Wonder Dog. However, Rex is further out from the branch. So, one way to look at this is depending on the different masses, they have the same torque. But then, that wouldn't be good, because Rex would still be holding the branch and stuck in the quicksand.

But wait! The big cat "leaped" on the branch. Therefore the cat has more torque on the branch than just its own weight and a certain distance. What we can use is a conservation of energy analysis and sidestep questions about the springiness of the branch. We can say that the energy state of a closed system is always the same amount. When the big cat is at the highest point of its leap, it has maximum potential energy due being up in the air. The dog has zero potential energy because it is at ground level. The branch has zero potential energy because it hasn't been sprung yet.

At the end of the comic, the potential energy of the big cat is zero, because it is at ground level. The potential energy of the stick is zero because it isn't bent anymore by the weight of either animal (we'll ignore that it is probably still oscillating). The potential energy of the dog is at its maximum because of its height above the ground.

When we do an energy analysis, we also have to think about kinetic energy, but at the moments I am talking about, nobody is moving (at the top of a leap, you are momentarily at rest). So, kinetic energy is zero at these two points.

OK, now the numbers. Potential energy due to a spring has an equation associated with it, but we don't care because of the points we are choosing. Potential energy due to height from the ground is equal to mass*height*g where g is associated with what planet one is on (sometimes hard to determine). So, [mass of cat] *[max height it reached in its leap] is equal to [mass of dog] * [max height it reached on the ledge]. Or, height of ledge = cat to dog ratio times how high the cat leaped.

This is the scenario Dr. B was going to walk her students through. I set up an Excel spreadsheet to run some numbers and found that if we estimate the cat at 200 lbs (top end for a black panther) and Rex at 77 lbs (mid-range for a German Shepherd), and guess the cat's jump was 10 feet, the Wonder Dog could have been thrown 26 feet up to the ledge, bob's your uncle, and it's all not so improbable after all!

But wait! What about the quicksand? I emailed Dr. B to remind her of this niggling detail. She replied:

I used the comic in my class yesterday. It was a great teaching device.

I was trying to ignore the quicksand, but my students wouldn't let me. It is hard to predict the average dragging force due to the quicksand (at least for me). By the way, we can't talk about the sucking force of the quicksand, since there is no such thing as a sucking force. There is only a pressure differential. So, there could be a low pressure situation at Rex's bottom paws. Or, the frictional force could just be the scraping force as Rex gets pulled out by the branch. That is quite a range in terms of possible amount the quicksand will hinder Rex the Wonder Dog.

Frictional force is often just measured and then you know. So, we need to get a panther, the dog, the branch, and the quicksand. We can estimate how far up Rex should go. The amount under that he actually goes tells us the amount of friction. [Weight of Cat] * [height cat jumps] minus [Weight Dog]*[height dog goes]" is equal to [Friction] * [distance in the quicksand] (where distance is equal to the length of Rex's body).

Well, that didn't give me as clear an answer as I wanted. I checked some internet sources on quicksand and found this from an entry on HowStuffWorks: "Quicksand is basically just ordinary sand that has been so saturated with water that the friction between sand particles is reduced." The reason things get stuck in quicksand is that it can't support any weight because it is saturated, not because there is any sucking - a pressure differential doesn't play into it. So, the actual friction of quicksand should not be terribly high and certainly less than being stuck in a pile of regular sand.

So, if we just make the cat a little heavier, and his leap just a little higher, and the ledge just a foot or two lower, we should be able to offset any dragging force from the quicksand, and it is all still plausible.

I pity the fool who doubts the Wonder Dog.

[apparatus] In the meme time

Wikipedia says a meme (pronounced /miːm/) consists of any idea or behavior that can pass from one person to another by learning or imitation. Examples include thoughts, ideas, theories, gestures, practices, fashions, habits, songs, and dances. Memes propagate themselves and can move through the cultural sociosphere in a manner similar to the contagious behavior of a virus.

I say a meme is a groovy little blogosphere interaction you engage in, like this one, the alphabet meme, that I got from blogging buddy RAB at Estoreal, who got it from Blog Cabins via Movie Chunks. Here are the rules:

1. Pick one film to represent each letter of the alphabet.

2. The letter "A" and the word "The" do not count as the beginning of a film's title, unless the film is simply titled A or The, and I don't know of any films with those titles.

3. Return of the Jedi belongs under "R," not "S" as in Star Wars Episode IV: Return of the Jedi. This rule applies to all films in the original Star Wars trilogy; all that followed start with "S." Similarly, Raiders of the Lost Ark belongs under "R," not "I" as in Indiana Jones and the Raiders of the Lost Ark. Conversely, all films in the LOTR series belong under "L" and all films in the Chronicles of Narnia series belong under "C," as that's what those filmmakers called their films from the start. In other words, movies are stuck with the titles their owners gave them at the time of their theatrical release. Use your better judgement to apply the above rule to any series/films not mentioned.

4. Films that start with a number are filed under the first letter of their number's word. 12 Monkeys would be filed under "T."

5. Link back to Blog Cabins in your post so that I can eventually type "alphabet meme" into Google and come up #1, then make a post where I declare that I am the King of Google.

6. If you're selected, you have to then select 5 more people.

Like RAB, I'm not specifically tagging anyone, but feel free to jump in with your own list. Here's mine:

Antonia's Line
Bubba Ho-Tep
Crimes and Misdemeanors
The Day the Earth Stood Still
Elling
Fast, Cheap, and Out of Control
The General
House of Games
I Heart Huckabees
Joe versus the Volcano
Kiss Kiss Bang Bang
Little Voice
Millions
Nausicaa of the Valley of the Wind
Once
Pieces of April
Quigley Down Under
Run Lola Run
Spring, Summer, Fall, Winter... and Spring
The Third Man
Until the End of the World
A Very Long Engagement
The Wedding Banquet
X The Man with the X-Ray Eyes
You Can Count on Me
Zatoichi

As a bonus, here's Otis's list:

Amelie
Bourne Identity Series
Chocolat
The Darjeeling Limited
Escape from Alcatraz
Fargo
The Great Escape
Hero
In America
Joe versus the Volcano
King of California
Lars and the Real Girl
The Man who Knew Too Much
North by Northwest
Once
The Piano
The Quiet American
Rear Window
The Secret of Roan Inish
Thoroughly Modern Millie
Unbreakable
Vertigo
The Wild Parrots of Telegraph Hill
The X-Men Series
You Can Count on Me
Zatoichi

Jump in on your bog - just post the rules and the link. Here's the LNTAM index if you need some memory-jogging.

[sheepman] A question of balance

The election is over and all the whoop-dee-do is settling down. I must admit that I am more pleased than displeased by the results, but I also have to say that I am not as euphoric as some public demonstrations have indicated many people are. I am trying to figure out just what I feel.



Pal Wheylona posted this image as part of her own post-election analysis from a European perspective. I have to admit that it speaks to me, capturing as it does the historic nature of this election, the end of a regime which I sincerely feel has not had the best interests of most Americans at heart, and the sense of a populist progressivism that I hope will be evident in the new administration. In my estimation, the single most important advantage to an Obama administration is that is should be easier to pull to the left; I will gauge its success by just how far we are able to do that, because I think that more people will be helped more genuinely by that course than by another.

At the same time, we have to remember that the popular vote in the presidential race was split roughly 52% to 48%, a clear victory but not an overwhelming majority. And no matter how much we joke about it or frequently we kid about it, neither half of the population of this country is going to move away, or secede from the union and become Jesusland or The United States of Canada, or change their minds overnight. We have some serious problems ahead, and it's going to take all of us to fix them. How are we going to do that, especially when some of the differences that divide us appear to be so elemental?

That renaissance man of the intarweb, Ze Frank, seems to have taken one small step forward with his From 52 to 48 with Love project. In his own quirky, bloggy way, Ze wants to start off this new era with reconciliation and community, and has asked people to contribute their own expressions of those feelings. Some of the photos contained in the album are just touching and heartbreaking in their sincerity; the responses to it have, of course, been mixed. But I think it's a great place to start.

I have friends in the 48, people whose intelligence I respect and whose integrity is unquestionable. I think they were wrong in where they threw their support and I think they are wrong in some their fundamental assumptions about who we are and how we work as a country. But I want them to be part of my community and part of my country, and I need to pull them closer instead of pushing them away. This might help with that, a little bit.

As Lincoln said to a nation far more divided than ours, We are not enemies, but friends...though passion may have strained it must not break our bonds of affection. And to those Americans whose support I have yet to earn - I may not have won your vote, but I hear your voices, I need your help, and I will be your President too."

--Barack Obama

[apparatus] Whew!

Well, it has been a heck of a week - I really haven't had much time since Halloween for a developed thought unrelated to my classes. But this is a long weekend for me - not holidaywise, just non-instructional-daywise - so maybe I'll get a chance to focus some neurons on issues other than essay organization and poetry analysis. In the meantime, there's this mess.

That blue lady up there is Pa'u Zotoh Zhaan, a character from Farscape, Otis's latest watch-the-series-on-DVD venture. It seems to be a bit like a mix of Bablyon Five and Star Trek: Voyager with more of an edge, or maybe Andromeda on crank. We've watched a few episodes, and it's holding up so far, although the fairly generic spaceship milieu and the Henson puppetworks wear thin easily. Watching this mostly-obscure little series makes me wonder if anyone else remembers White Dwarf, an ill-considered series from 1995 with a semi-steampunk vibe, described by one critic as "a sort of Northern Exposure meets The Princess Bride on the planet Dune."

Speaking of steampunk, here's a bike to reckon with - The Brass Lion:

This wonderful ride is a product of Steuben's Wheelmen, and I'd love to be tooling down the Burke on it.

More steampunkish transportation news: the rigid airship is back! You wouldn't know it by the headline, which sacrificed accuracy for a little pun, but the zeppelin has returned to American skies. I'm not sure I want to pay five yards for a one-hour ride, but I'm happy to know its in the skies. That's cool.

Here's something else that manages to be totally cool and completely boring at the same time, something that I would not have thought possible before:

Um, yeah. Here's a website that I am sure explains how fantastic this really is, but it's even too boring to read. Not cool at all.

Something that everyone else thought was cool was the cloned dinosaurs in Jurassic Park. Sometimes I wonder if I was the only kid who was more excited by Pleistocene mammals than by dinosaurs: sabre-toothed cats and giant sloths, that's where it was at for me! In any case, according to this article, it looks like the mammoths might beat the thunder lizards in the reincarnation race.

And finally, here's a note from the real world, not the sci-fi past or future. Newsweek ran an article with inside information from the political campaigns that is now leaking out; it included this quotation from Barack Obama talking about the debates:

“I don’t consider this to be a good format for me, which makes me more cautious. I often find myself trapped by the questions and thinking to myself, ‘You know, this is a stupid question, but let me … answer it.’ So when Brian Williams is asking me about what’s a personal thing that you’ve done [that's green], and I say, you know, ‘Well, I planted a bunch of trees.’ And he says, ‘I’m talking about personal.’ What I’m thinking in my head is, ‘Well, the truth is, Brian, we can’t solve global warming because I f—ing changed light bulbs in my house. It’s because of something collective’.”

Bravo! I love this quotation not only because the voice in it is so authentic and direct about the campaign process, but because Obama is echoing a sentiment about environmentalism that I have held and argued for some time now. Yeah, he's got this.

[jet city] Liveblogging election night (sort of)

Well, the munchies are all out and the bevvies are in the fridge, the news Spectration is on the big wall and Sousa is on the CD player - I guess we're ready for the Election Night Open House that we have planned. I think there may be a lot more folks here than we anticipated, but that's cool. I will check in from time-to-time with updates about how the evening is going, both in the political world and our little social world here.

5:43: We're projecting NBC on the wall (we only get broadcast television) and playing the soundtrack from Brassed Off on the CD player. Otis is upstairs taking care of some business and I am watching our freaky cats and the talking heads (better than talking cats and freaky heads, I guess). Polls in the east have only been closed a short time, and already the projection for Obama is something like 103 electoral votes, with McCain getting 58. They may call this election before anyone even gets here at 6:00.

6:24 Johnbai, Dingo, and Sachet are here eating sandwiches and salads as ABC announced that Obama had Ohio in their projection. That gives him 195 according to them, and Stephanapolous has called it over. Hunh. They've switched to local coverage - we don't expect to really know any results for a few days.

6:49 Hi Lai and Welcome Matt just showed up with cupcakes!

Obama is at 200.

7:24 Outside the studios of ABC, people are holding banners that say "Cassoulet Forever." What is up with that? Is he running for something or do they just like French bean dishes?

7:43 Full swing:


Andres(2), Plus-one, and Yojimbo have joined the party. We have lots of champagne but have agreed that none gets opened until Obama hits 270. He has 207 now, so still some time to go. Our polls aren't even closed yet.

8:02 Wow. As soon as the polls closed on the West Coast, ABC gave the election to Obama. So did NPR. It looks like it's over. It's a little confusing, since they haven't called all the states, and no one is showing numbers yet, just cheering crowds. We'll wait for McCain to concede, I think.

8:45 McCain conceded. The champagne was pretty good. During the speech, we were wondering where the hell that guy had been all campaign - his concession was gracious and inspiring. Now we're waiting for Obama's speech. Even Soapy, our resident libertarian.

9:22 The gang just watched Obama's speech. Good stuff. Makes me want to get rid of reds and blues and just be all purple.




10:53 Everybody is gone; the gang grew to include Toke, Reni, JagGirl, Merry, and Mark I as well as the previously aforementioned folks. We watched the gubernatorial campaign come to a much swifter resolution than anyone expected - Gregoire had a substantial lead and claimed victory, attempting to short-circuit any replay of the long-drawn process from four years ago. Most of the local propositions broke the way I wanted to see them go, and my buddy Jim Jacks down in The 'Couv sailed to a stunning victory. All in all a pretty good night, leaving us with a lot of hope for the future, and the anticipation of some fence-mending and community-building, if any of that is at all possible in the polarized nation we have become.

Personally, it was a night of connection and re-connection, as close friends and acquaintances once-removed alike came together to share this historic event. There's nothing like good company and a momentous occasion to turn an evening into an event - and the coincident visit from an out-of-country pal was the cherry on the sundae. Here's looking forward to more opportunities for celebration and communion.

And snacks!

(EOM. G'night!)