Thursday, September 22, 2011
The following was taken from Peter's Physics homework. I added two sets of parentheses to make the example more accurate...
Humans rarely survive long falls, but cats apparently have much better luck. A study published in 1987 considered 132 cats who had "accidentally" fallen from heights of two to 32 floors (6 to 98 meters), most of them landing on concrete. About 90% survived, and about 60% even escaped injury. Strangely, the extent of injury (such as the number of fractured bones or the certainty of death) decreased with height if the fall was more than seven or eight floors. (The cat that fell 32 floors had only slight damage to its thorax and one tooth and was released after 48 hours of observation.) Why might a cat have a better chance of survival in a longer fall? (The survival is by no means guaranteed, so if you live in a high-rise apartment, be sure to keep your cat away from any open window.)
Answer If a drowsy cat "accidentally" topples from a window sill, it quickly and instinctively reorients its body until its legs are underneath. The cat then uses the flexibility of its legs to absorb the shock of the landing: The flexibility lengthens the time of the landing and thereby reduces the force on the cat.
As a cat falls, the force of air drag that pushes upward on the cat increases. If the fall is from the sill onto the floor, the air drag is never very much. But if the fall is longer, then the air drag may become large enough to reduce the cat’s downward acceleration. In fact, if the fall is more than about six floors, the air drag can become large enough to match the gravitational force pulling downward on the cat. The cat then falls without acceleration and with a constant speed called terminal speed.
Unless terminal speed is reached, the cat is frightened by its acceleration and keeps its legs beneath its body, ready for the landing. (Your body is also sensitive to accelerations rather than speeds.) But if terminal speed is reached, the acceleration disappears, and the cat relaxes somewhat, instinctively spreading its legs outward (in order to increase the air drag on it) until it must finally get ready for the landing.
Once the cat spreads out, the air drag automatically increases, which reduces the speed of the cat. The longer the fall, the more the speed is reduced, until a new and reduced terminal speed of about 100 kilometers per hour is reached. Thus, a cat falling from, say, 10 floors will land with a speed that is less than that of a cat falling from five floors and will have a better chance of escaping serious injury.
Copyright © 2007 John Wiley & Sons, Inc. All rights reserved.
