Queen Kong

You may remember a post from early in my blog, when I mentioned our (relatively) new Boston Terrier, Darcy.  I referred to her as a volatile dog, but didn't give any details, so I thought I might take a moment to quantify her explosive nature.  She enjoys chew toys very much, but we've found that most toys can be destroyed within seconds.  Squeaking weasels have been eviscerated, and bones have been chewed into shreds.  The one type that has stood up to her has been the Kong, a chew toy inspired by a part of the suspension of a VW van.  It's shaped as a conical tube, which she spends hours a day crushing flat, only to have it spring back.  I've tried this myself (with my hands, that is) and it's impressively difficult to do, so I started wondering how many calories she was burning with this jaw exercise.

The only scale we had around was a small kitchen one that only went up to 5 kg, but if we assume the Kong follows Hooke's Law (the usual approximation for a spring) we can figure out the energy involved.

 

Measuring the larger opening closest to the camera, the difference between the uncompressed Kong (left), and the Kong compressed by 4.2 kg (right) is 0.26 cm.  Hooke's Law gives the force exerted by a spring compressed a distance x as

where k is a constant that characterizes the strength of the spring.  Using the information we have, k = 16,000 kg/s^2.  The energy required to compress a Hooke's Law spring is

so squeezing the Kong flat (3.61 cm) requires 10.4 J, or 0.0025 Calories.  It may not seem like much, but that's about equal to the energy involved in one arm-curl of an 8 pound weight.  Also keep in mind that Darcy is only 18 pounds herself, so imagine lifting half your own weight.  I should also note that, if anything, this is an underestimate, since it feels to me as if it gets more difficult to compress as it flattens.  Further evidence that Darcy is not a dog to cross...