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ASSINGMENT 1 2009 - SC/BIOL 2090.02 Current Topics in...

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Unformatted text preview: SC/BIOL 2090.02 - Current Topics in Biophysics ASSIGNMENT ONE There are two questions. You must complete both. QUESTION ONE As presented in lecture, the ratio of surface area to volume is a key element of biological shape and form, since some physiological functions scale with surface area while others scale with volume. The surface area to volume ratios of cubes and spheres are simple to evaluate, but rectangular shapes pose problems, as do the ratios for a cylinder (if the surface area of the circular top and bottom are included). Many organisms are cylindrical in shape; for example, the filamentous forms of fungal hyphae and algae. Amongst the algae, the size of the . = cylindrical form varies a lot: from exceedingly long narrow cylindrical filaments about 20 pm in diameter (Spirogyra spp., left) to the relatively wide cylinders - (about 5000 pm in diameter) for the intemodal cells of Chara spp. (right). Evaluate the surface area to volume ratio of a cylindrical form that includes the areas at the top and bottom of the cylinder for various ratios of the radius to height. Hints: The surface area of a cylinder is equal to 2-31.»? + Z'mr-h (where r is the radius and h is the height), and the volume is equal to mfih. A graphic plot is likely to be crucial (AfV versus hlr is one possibility) with diagrams of the cylindrical shapes. QUESTION Two For the case of a Dyson tree (see course notes), propose a mechanism for moving water from the comet surface to the photosynthetic apparatus at the ‘top’ of the tree (and back again, since this is a closed system). Your mechanism must rely on already existent anatomical features. It must be physically realistic (you are required to show that it is). Hint: I wonder if a heat gradient (evaporative) might work, resulting in a pressure gradient sufficient to move water through xylem for a tree as tall as a Dyson tree. Guidelines: I expect that students may wish to work together on the assignment, that is fine, but, be sure that your assignment is in your own words. Remember that you have to explain your answers with sufficient clarity, so that a non-physicist like Dr. LeW will understand them. He often finds diagrams helpful and is obsessed with ensuring that the units work, so showing the units is obligatory. Excessive length is not encouraged. height 0.01 0.05 100 .2 a & o E :I T: > “in... § t :I tn 0 radius r 100 80 60 40 35 30 20 15 10 9.5 \lmko 6.5 5.5 4.5 4.25 HNW 0.5 0.25 0.1 0.05 0.01 h/r 1.0E-04 6.3E-04 1.7E-03 6.3E-O3 1.4E-02 3.3E-02 1.0E-01 2.0E—01 4.0E-01 4.5E-01 5.0E-01 6.3E-01 7.9E-01 9.2E-01 1.1E+00 1.3E+00 1.6E+00 2.0E+00 2.2E+00 2.5E+00 5.0E+00 1.0E+01 3.0E+01 7.0E+01 1.6E+02 6.0E+02 1.6E+03 1.0E+04 SA 6.3E+04 4.0E+04 2.3E+04 1.0E+04 7.8E+03 5.8E+03 2.8E+03 1.7E+03 8.8E+02 8.2E+02 7.6E+02 6.5E+02 5.5E+02 S.1E+02 4.7E+02 4.3E+02 4.1E+02 3.8E+02 3.7E+02 3.5E+02 3.4E+02 2.8E+02 1.9E+02 1.1E+02 6.3E+01 3.8E+01 2.5E+01 6.3E+00 volume SA/vol 3.1E+02 2.0E+02 1.0E+03 4.0E+01 1.1E+03 2.0E+01 1.3E+03 8.1E+00 1.9E+03 4.1E+00 2.8E+03 2.1E+00 2.5E+03 1.1E+00 2.1E+03 8.0E—01 1.3E+03 7.0E-Dl 1.2E+03 6.8E-01 1.1E+D3 6.7E—01 1.0E+03 6.5E-01 8.5E+02 6.5E-01 8.0E+02 6.4E—01 7.3E+02 6.4E-01 6.6E+02 6.5E—01 6.3E+02 6.5E~01 5.7E+02 6.7E—01 5.4E+02 6.8E—01 5.0E+02 7.0E-01 4.2E+02 8.0E-01 2.5E+02 1.1E+00 9.4E+01 2.1E+00 2.7E+01 4.1E+00 7.9E+00 8.1E+00 1.9E+00 2.0E+01 6.3E-01 4.0E+01 3.1E-02 2.0E+02 Surface/Volume Ratio 2.5E+02 2. 0E+02 1.5E+02 1.0E+02 1. E-02 1.E+00 OSurface Area 1' Volume 0 1.E+02 Height] Radius Ratio ((2*3.14*r"2)+(2*3.14*r*h))/(3.14*r"2*h) Guam 0m (Nanak-u u... Than ix) Exsamxuon . 2T 70 'fik‘rixm. .M‘. i [ [can — JR] + PIP $m+-k _ _ I m Q la?- 924,-“th AMM— Pom 4.90 . .5) A-La. Bun. .mucbk ‘1wa Mk—w / x932: a» ma... RA: an - loop. 3) wax-tea Puma WA JLALEA AA MAB ALA. ERMA) TREE Lam-b lop hm) irgr-ohw Wang About} ZOD_}4.¢A My». Quay-3 I131; ._._I..o.£ .d-Wk‘ \ao. MLLS—F‘a (Low ‘ _ iii—fl E_ axial—PX?“ __| .5- ). - M (mm )wa in low A?“ «I, Mai-_mt J'QMA'. Aim” “AL BA»; ”bib“ L. 50 .m5_[ 1M!" FOIL" C"' 500 K?a.) -mu3‘5. h _‘amiw..t r5) n _m..A-_z_e'?..__ :Imb._ 5mm. 1+ ‘5 [email protected] “A... WILL; thing-k r2 "5:? 2-50 $1170.. Hun 1w. .k— Am. Ind- ; b312,- .muki :2an. ‘bad; “u. Magyk .e— “an. lat-e __. _M‘r \9 KM. m‘s-M hum. “AL rash-k cum-Sag. A3 LPMARR ‘Kl’aE 3 Law) p- -k_ LUT‘) CS9“; ' _ ' ' C§fw \kbm‘ Tabb-i. L'+ MD M- {M3 5”." ...
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