a) (12 points) Only small animals hibernate (not completely true...black bears a

Question

a) (12 points) Only small animals hibernate (not completely true...black bears are now believed to hibernate, however it's a different mechanism than small animals-more on this later in the semester). Perhaps we can understand why by considering stored energy and the rate of energy metabolism (utilization). If we compare a 1200 pound polar bear and a 1.5 pound Abert's squirrel (like those living here in Flagstaff) we can compare how long each could survive during a winter fast if they used body fat as their only energy source. The weight-specific Basal metabolic rate (BMR) of mammals is 4.46 W-0.30 when expressed in units of mLO2 consumed per gram of body tissue per hour and (importantly) weight is calculated in grams. For this simple estimate, you may use BMR, but keep in mind that small animals have a larger increase in metabolism with temperature than large animals. Calculate how long each animal could survive on stored fat equal to 20% of its total body weight (this is a fairly reasonable fat amount found in both squirrels and bears in nature). Make sure you keep all units very clear during this calculation, there are many steps. Potentially useful information: The value of energy content of fat is 9.3 kCal per gram of fat and 0.84 L of O2 are consumed per gram of fat metabolized. There are 5280 feet in a mile, and 1.0 foot = 0.3048 meters. One calorie = 4.184 joules. One pound (lb) = 454 grams and one ounce is 28.375 grams.

Explanation / Answer

1- fat content in the polar bear=1200*.20=240 pounds=108.96 kg

fat content in squirrrel=1.5*.20=.3 pounds=136.2 g

the energy content of fat in bear=9.3*108.96*1000 kcal

=1013.328 *103 Kcal

the energy content of fat in squirrel=9.3*136.2kcal

=1266.66 Kcal

amount of O2 mobilised in bear =.84*108.96*1000

=91526.4 L

amount of O2 mobilised in squirrel =.84*136.2

=114.408 L

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