These data were collected by researchers at the Georgia Institute of Technology in 2010. They videotaped wet animals as they shook to rid their coats of water. “They found a mathematical relationship between the radius of the animal and the frequency with which it had to shake in order to dry off. The smaller the animal, the more rotations per second it would have to make in order to dry off.”* Here’s some of their data. Animal Radius of animal Frequency of skin oscillations per second Mouse Rat Guinea Pig Cat Small Husky Dog Labrador Retriever 2 cm 2.5 cm 3 cm 6 cm 8.5 cm 13 cm 27 hz 18 hz 14 hz 8.7 hz 5.8 hz 4.3 hz a. Create a scatterplot of these data. b. How do you know that a linear model is not the best choice for modeling this relationship? c. Create the best linear regression equation you can using the tools you learned in this chapter and write it here. d. Transform the equation into exponential or power form, depending upon which one is appropriate. Be sure to show your steps. (Do not use ExpReg or PowerReg). e. Predict the frequency of skin oscillations per second for an animal that has a radius of 4 cm. As always, show your work. *The Wet Dog Shake: Scientists Uncover Secret, by Ki Mae Heussner. October 22, 2010; ABC News. The Wet Dog Shake: Scientists Uncover Secret Scientists Discover How Fast Dog Must Shake to Dry Off By KI MAE HEUSSNER Oct. 22, 2010; ABC News Call it Fido physics. Intrigued by the infamous wet-dog shake, scientists at the Georgia Institute of Technology have figured how fast a sopping wet pooch must shimmy to dry himself off. How did they do it? Instead of running for the hills when the waterlogged animals got ready to shake, the researchers risked getting wet themselves. They got up close and personal with a slow-motion video camera, and then analyzed the shaking. They discovered that the smaller the animals, the faster they must generally shake to dry themselves off. David Hu, assistant professor of mechanical engineering at the Georgia Institute of Technology, said the research is interesting because drying wet fur is critical to how mammals regulate heat. "A lot of animals have developed fur mostly for thermal insulation purposes and they need special mechanisms to basically get the water off," he said. If the standard 60-pound dog had to rely on evaporation alone to dry off, he would have to spend a quarter of his daily calories to get rid of the water, Hu said. Smaller animals would have to use even more of their daily energy to do the job. Researchers Studied Shaking Mice, Dogs, Grizzly Bears, Panda and More "To evaporate the water is very costly to them," he said. "Physiologists call this the wet-dog shake. That's why this thing evolved, and it's basically a slight variation of shivering." Hu said scientists have studied the phenomenon biologically, but haven't taken a look before at how it works and how efficient it is. Hu said he and the researchers, including graduate student Andrew Dickerson, videotaped 16 different species shaking off water. They studied various breeds of dogs, including the Chihuahua, Labrador, poodle and husky, as well as mice, rats, guinea pigs, grizzly bears and the panda. Some of the researchers got a little wet, they said, but it was worth it: They found a mathematical relationship between the radius of the animal and the frequency with which it had to shake in order to dry off. The smaller the animal, the more rotations per second it would have to make in order to dry off. For example, while a mouse with a radius of 2 cm (less than an inch) would have to shake with a frequency of 27 hz (shakes per second), a dog with a radius of 20 cm would only have to shake with a frequency of 4.7 hz to get comparably dry. The reason the larger animals don't have to shake as quickly has to do with surface tension, the researchers said. Hu said the droplets stick to the animals because of surface tension between the water and the fur. To repel the liquid, the animal must create enough centripetal force to overcome the surface tension. "If a dog shakes at a sufficiently high frequency, that centripetal force can overcome the surface tension and pull it off," he said. "All the animals have to reach the same speed [which is equal to frequency times radius], but because the larger animals have a larger radius, they can move at a slower frequency."