2008_term_one_key

# 2008_term_one_key - SC/BIOL 2090.02 Current Topics in...

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SC/BIOL 2090.02— Current Topics in Biophysics — T ERM T EST O NE There are three questions. You must complete all of them. Ensure that you show your work (that is, equations and calculations). Q UESTION O NE Many organismal functions (for example, metabolic rates and rates of biomass accumulation) scale as the power 0.75 (rate ~ mass 0.75 ), and the ratios of surface area to volume scale as the power 0.67 (A/V ~ mass 0.67 ) (for mammals). But other functions scale differently. For example, longevity versus organismal mass (left) scales as the power 0.137 (longevity ~ mass 0.137 ) (for vertebrates). In fact, within the mammalian clade, all species die after approximately 3.3 • 10 8 breath cycles and 1.5 • 10 9 heart beats, regardless of size (that is, small animals with brief life spans have a faster heart rate). Propose a reason why all mammals, regardless of size, have the same total breath cycles and heart beats, bearing in mind that both functions are directly linked to repetitive cycles of muscle contraction. Q UESTION T WO The integral forms for the first and second moments of either mass or area — r dm ± r 2 dm ± y dA ± y 2 dA ± — play surprisingly important and fundamental roles in diverse biological processes. Select one and only one of the four integral equations and explain its biophysical application(s). Excessive length is not encouraged, but clarity is. Q UESTION T HREE The ‘universe’ of low Reynolds number involves not only bacteria but other organisms as well. Compare the Reynolds number for a gnat (right) flying at about 30 mm sec –1 in air ( J Exp Biol 208:2963, 2005 ) and a human free- falling in the same medium (say, 60 m sec –1 ). Values for air viscosity are given in the equations/constants appendix.

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2008_term_one_key - SC/BIOL 2090.02 Current Topics in...

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