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- Ethics?? Here's what I think of your precious "ethics":
Microgravity cat:
http://www.youtube.com/watch?v=QoLekrOBMEw
Look how "calm" he is before hitting the wall of the airplane. That's how "calm" a weightless cat would feel, I'm sure.
- Dan from Illi:
That's a good point. Also check out "space adaptation syndrome" for an effect related to what you're talking about.
- Patrick from California:
He considered real noon, i.e. what them cowboys called "high noon," where the sun appears to be at its highest point in the sky. That's when you're facing closest to the sun for that particular day.
The "noon" that we use to refer to a certain time in our standardized time zones is, generally speaking, not the same time as high noon, as it's a rather arbitrarily set time. Standard time zones were invented originally so that places linked by railroads would have synchronized times. Otherwise, they don't really have much significance in terms of positions of the sun, celestial bodies, etc. I know from my own casual observations that at least for part of the year here on the American east coast, high noon is actually around 1 or 2 PM.
- Part 2 of 2 (part 1 below)
I also found the exact expression[2] for quadratic air resistance and plotted it, and it shows generally the same trend.
Here is image of the plots for jerk vs. story and feline velocity vs. story:
http://img139.imageshack.us/img139/9241/catcatfallin.jpg
Now I just hope I don't dream about falling cats. Although they look comical during descent, there's nothing funny about the crash landing. I'm going to give my cat a big hug when I get home, no matter how much he may try to squirm out of my arms.
[1]Vnuk, D. and others, Journal of Feline Medicine and Surgery, vol. 6, pgs. 305-312 (2001).
[2]K. Szalewicz, http://www.physics.udel.edu/~szalewic/teach/419/cm08ln_quad-drag.pdf, accessed 12/14/10.
- Part 2 of 2 (part 1 below)
I also found the exact expression[2] for quadratic air resistance and plotted it, and it shows generally the same trend.
Here is image of the plots for jerk vs. story and feline velocity vs. story:
http://img139.imageshack.us/img139/9241/catcatfallin.jpg
Now I just hope I don't dream about falling cats. Although they look comical during descent, there's nothing funny about the crash landing. I'm going to give my cat a big hug when I get home, no matter how much he may try to squirm out of my arms.
[1]Vnuk, D. and others, Journal of Feline Medicine and Surgery, vol. 6, pgs. 305-312 (2001).
[2]K. Szalewicz, http://www.physics.udel.edu/~szalewic/teach/419/cm08ln_quad-drag.pdf, accessed 12/14/10.
- Again, with apologies and begging your humor one more time, I make a third consecutive post, as I just noticed Dr. Tyson's comments far below. I promise this'll be my last.
Actually, this is a 2 part post: this is part 1 of 2.
First, I made a mistake--I meant to say that all parts of your body feel the same acceleration when acted upon by gravity, not that all parts of your body feel the same force.
"2) In a gravity field, if you are in free fall -- you are identically weightless no matter your speed. The slight difference here, noted by one among you, is that as air-resistance brings you to terminal velocity, you gain from zero pounds back to your full body weight. But most of this increase takes place during the last increments of speed gained -- just before you reach terminal velocity. [This, because air resistance increases with the square of your velocity, and not with your velocity itself, rendering the effect much more significant at higher speeds than at lower speeds.] So, as stated in the broadcast, for nearly all of a cat's initial fall, from jump point to terminal velocity, the cat is simply weightless. And when you are weightless you do not know your speed."
I must disagree with Dr. Tyson on this point, that our ill-fated feline basically only feels two regimes during the fall: 0 weight and constant weight. I don't think a v^2 term is fast enough for this to be true. If it were exponential or a higher-order power, perhaps, but v^2 is a relatively slowly changing term.
Perhaps some numbers would shed some light on this? As Dr. Tyson claims, we are indeed (probably?) in the regime of air resistance proportional to the square of velocity. The force is modeled as v^2*A, where A is a coefficient.
acat(t) = g - A/mcat*vcat^2
From the literature, I find that the feline terminal velocity vt is 60 mi/h, or 27 m/s[1].
In the equation above, we need to know the value A/mcat.
A/mcat = g/vt^2
A/mcat = 9.8 m/s^2/(27 m/s)^2 = 0.013/m.
One interesting property of this equation is that all terms can be expressed as factors of coefficients consisting only of g and vt. The terminal velocity contains all the information about
I numerically integrated this equation the old fashioned way--with Newton's method--using time steps of 0.5 s. I assumed a story height of 5 m, which is around 16 ft. I found that the literature is wrong in one regard, IF the air resistance is purely quadratic (which it should be, I believe...). The cat gets to within 90% of the terminal velocity only by the 13th floor, so it takes far longer than the suggested value in the literature, and this is a rather big surprise...
If someone can show if I erred, I would appreciate it. It would probably be in the numbers that I have used if anything.
However, something else happens around the 5th story: the rate in change of acceleration, the jerk, begins to decline after it reaches a maxima at around the 4th story. This may be the relevant change that the cat senses.
- Pardon the consecutive posting, but here are literary references for Dr. Tyson and others to peruse if they which to critically review this study and related studies:
First, a brief article from the "News and Views" section of the journal Nature from 1988 giving an overview of the work when it was first released. Please realize that this was an interest piece rather than a true research article, so pardon the fanciful name:
Diamond, J. M., "Why cats have nine lives," Nature, vol. 332, pgs. 586-587 (1988).
Secondly, here is the citation for the originally published article, which was not provided as far as I'm aware:
Whitney,W.O., Mehlhaff, C.J., High-rise syndrome in cats. Journal of the American Veterinary Medical Association, vol. 191, pgs.1399-1403 (1987).
Finally, here is a more recent publication from 2001 with a decent review of the literature which presents another study showing the suggestion of a more complex trend that the one found in the Whitney and Mehlhaff study. Here, the trend seems to point more to the TYPE of injury than the INCIDENCE of injury varying with whether the cat has reached terminal velocity or not:
Vnuk, D. and others, Journal of Feline Medicine and Surgery, vol. 6, pgs. 305-312 (2001).
- With respect to Dr. Tyson, he clearly did not read any published material about the work he is criticizing.
First, the quantity considered was injuries per cat, not total number of cats that survived. So at least among cats that did not instantly die, there were fewer injuries per cat among those that fell from above a certain height, roughly 7 floors. Furthermore, incident of specific sorts of injuries were considered and follow the same trend, such as fractures, most of which are usually not life-threatening. Incidentally, it was noted that 11 cats in the study did eventually die from thorasic injuries and shock.
Secondly, if an object starts falling at an acceleration of 9.8 m/s^2 and then eventually falls at a constant velocity, the object is clearly NOT in free fall. The cats are falling in an "ocean" of air, not in a vacuum.
True, bodies cannot feel velocity because things look the same from all inertial reference frames. It's also true that bodies cannot feel acceleration due to gravity since everything in the body is pulled by the same amount of force. HOWEVER, the body would be QUITE sensitive to CHANGES in the acceleration during the fall.
So cats CAN feel the CHANGE in acceleration from 9.8 m/s^2 to 0 m/s^2, and it is possible they are reacting to that.
