Illinois Junior Academy of Science - Yearbook (Urbana, IL)

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221 5.02 3.59 251 3.99 280 3.45 These corrected points form one possible curve for K I 36.8 ntfcm, and make clearer the curve for K I 25.8 ntlcm. The equations obtained defining c for varying K values may then be summarized: 1 For K I 4.87 ntfcm, c 'J 9.21 M-2-16 For K 2 6.38 ntfcm, c 2 5.32 M-1-11 For K I 25.8 ntfcm, c I 8.97 M--82 For 'K I 36.8 ntfcm, c I 19.83 M-2-52 Iuncorrectedl c 2 9.78 M-1-01 C corrected J Unfortunately, these four equations fail to suggest some function relating a and n in the Ngeneral equation c 2 a 11 to K. Additional trials for other values of K and the inclu- sion of more individual measurements in average values of c used to determine the c vs. M equations may improve this data to make it posible to determine f and g in the ideal general equation c 2 ffKl M2410 d fcentimetersl M fhectogramsl d vs. M, Rubber Tires, Double Square Cross Section Bump, No Shock Absorbers Um Q0 wg- mn Qu. FD CD g 5.6 56 E. 33 aff 0. 3 'O 'P ' 25 31- 94 U5 5,5 U1 EW SJ el.. Ss ag HH Oll EQ Q-il Um G 5 UQ E- gn-I Hg wg Og 5 mm 260 S00 8' '85 cg. 5 5 mx lm B0 U1 PP' V' Um Q- m 7' 'X n- fDn-4Z'U- X n- On U10 Oomll Una: gg gs ganmmguz 'RUE' C ::' gg??3f1gbo og QI mf 295'-gif 5- 2 , 33 333133370 -I+? +71 LU o 3' 0 m WZ I lim? sl'55'f'i3551lD 53' I 11 :I U55 as ggxoagf-Qiggx Q,-5 g+xo+xo s A ' xr1 or+ VG. Q' ,5fg,.9,-,Q Q aim gf' gaaawam 525555 Q ,gnu mn uuuu Masai? Q Sfggw- Q 'Eg gm-sv - 'Q..m Hn. In 0--Woo m Q: . oo -1 gunna ard na 55000-J In mo 000021100 io 'zo HUD: U2 55:15 'US' 'UE' Q. 'I' Q QQ 2 QQQQ aff 9.-+ g 553 sf gegg 3 3 g a S 5 '1 -'I 36.8 ntfcm nt! cm Analysis of Error All values analyzed thus far have been averages of many measurements. The accuracy of this method might easily be questioned. Through the use of standard deviation and Stu- dent's t on typical points, an accurate estimate of the validity of the averages analyzed may be made. Standard deviation for M 2 221 g, K I 3.78 ntfcm with two obstructions using rubber tires and the square cross- section bump fwithout shock absorbersl, a value which exhibited comparatively good consistency among the indi- vidual measurements composing the average, has been com- . Sd' s I - n-1 .2884 17 2 .13 This indicates that a zone .13 on either side of the average value for this point, 1.46 cm, will include 68.2716 of the indi- vidual readings likely to occur. For one of the most incon- sistent values such as M 2 251 g., K I 110 ntfcm with two obstructions, rubber tires, squarepcross-sectioned bumps, and without shock absorbers puted to be 50.13 S.. 15 : 1.83 This is nearly a third of the average value, 5.62 cm. 1 How close, then, can we be sure that the averages given are to the true values which would be obtained by averag- ing an infinite number of infinite number of individual meas- urements, if this were possible? The equation S l A21- gives a range, A , within which a probability can be as- signed of having the true value. A is the span on either side of the average, s, is the standard deviation for a given point, n is the number of values averaged, and t is Student's t. If a A for which a 904, probability exists that the ran e extending from the mean plus A to the mean minus lg contains the true value is desired, and eighteen values are known, as for M -'I 221, K I 3.78 ntlcm for which s was Ezalculated earlier, t is found from tables to be 1.746. There- ore, - A 2 1.746 i 'JE' 2 .054 cm For the less consistent d of M I 251 g., K I 110 ntfcm, 1.83 A :- 1.753 i Al15 2 .83 cm A for M : 221 g., K 2 3.78 ntlcm is 3.7'Z. of the average: A for M 2 251 g., K I 110 ntfcm is 14.841 of the average. Since the consistency of most sets of d values lies between these two extreme cases, it would be safe to generalize regarding the accuracy of the various values for d that there is a 90'-Z1 chance for most values of d and c being within roughly 993 of what would be the average of an infinite number of individual measurements. A 9'Z: variation in certain d and c values could well account for a number of irregularities in various graphs. Of course, the possibility must not be ignored that such a variation pro- duced by new data and introduced into present averages could well yield new discrepancies. Sullllnary of project lwestinghousel My project consisted of finding equations defining the amplitude of the vibrations of a model automobile chassis as a function of the chassis mass and the spring constant in the suspension. Low Voltage DC to High Voltage DC Power Supply PAUL FROM In order to obtain 60 volts DC from a 1.2 volt battery, DC must be changed to AC, then transformed to a higher voltage and finally changed back to DC using a full wave rectifier. To change DC to AC I used a two transistor power oscillator. The design proved to be unstable, hard to start and developed high transient voltages because of such a low operating voltage. After much experimentation, the perform- ance was greatly improved, but there is still much to be desired. The following is the modified circuit performance compared to the original and desired performance. Original Modified Desired Maximum output .03 W 2W 30 W Starting only when starts at starts at Capabilities unloaded any load any load

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C160 2 0, 175.6 2 'l'l'!10, etc.l in order that M might be the independent variable in a Fourier expansion, d 1, -5- alcos M' + alcos 2M' +...+ acos nM' 2- n 2 + b,sin M' + basin 2M' +...+ bsin nM' n 2 Tl' where M' I -Q KM - 1601. 212 The various constants ao, ai, . . . and bl, b., . . . are determined by the equations 2m ta -4-a +a +...J 2 m 3m 5m 'Tl' 2'l'1' 2m-1 ft0J ft J + ft J ft 'ITD m m m and A 2m tb - b + b - ...l : m 3m 5m 'IT 3'l'l' 5'l'l' 4m-1 ft J ft J + ft l . ft 'TT 2m 2m 2m 2m form-2 1,2,3,... Since the series extends to infinity, the number of terms to be taken is determined by the point at which a succeeding term becomes negligibly small. Some preliminary calculations indicated that any rela- tionship that might be derived from this procedure would contain so many terms as to be forced and not particularly enlightening. For example, aw was calculated to be .77 for K 2 4.87 ntfcm. Since we may stop at ten terms only if am is very near zero tsince cos nM' may be as large as 11 it was evident that many more terms would be needed to ade- quately describe the graph, so this procedure was pursued no further. Additional reading on this method of curve fit- ting indicated that it is intended to be applied to the actual graph of the vibration itself rather than a graph derived from the amplitude of these vibrations as was actually done. Therefore, harmonic analysis was applied to actual data traces, but again the relatively high values of the later co- efficients suggested that this procedure had little to offer: this was probably due to the fact that the vibrations under analysis were somewhat heavily damped. Another method of data analysis which was used was the graphing of d as a function of K for a given mass value: although the graphs appeared to be similar, the standard pattern was so irregular that it was not deemed worthwhile to apply the detailed procedures used on the d vs. M graphs to this set. Finally an analytical procedure which to a considerable degree explained that data was found. The natural period of a mass and spring system ch as an automobile chassis M fignoring dampingl is 2'l'l' IE- where M is the mass sup- ported by each wheel and K is the spring constant of each spring in the suspension system. In order to investigate any possible relationship between d and e natural period, d was graphed as a function of 2'TT K . Bunches of points emerged, suggesting that certain natural periods produce consistent values of d. Two rather solid conclusions can be drawn from this somewhat confusing mass of data. First, the similarity among the curves for d vs. M for different constant values of K strongly suggests that there exists some sort of regu- larity in this situation, though more sophisticated methods of analysis than those applied may be needed to give a full explanation of what is happening. Second, the graph of d vs. the natural period contains clusters of low d value points where the ratio of M and K produces natural periods of .15 and .06 seconds. For this particular frequency of bumps, then, these are the best natural periods for a low d value and hence a smooth ride. .15 seconds has a special signific- ance which serves to help explain why it produced low values of d. The period of drum rotation land hence the time between bumpsl was .33 sec. If the pen arm and other friction were to slow the natural vibration period of the chassis to some multiple of the drum period, the chassis would be in a certain phase of harmonic motion at the be- ginning of each impact which would probably have some consistent effect on d. An examination of the data traces, however, showed that in reality friction had slowed the nat- ural motion so that the chassis made only one and a half cyclessbetween impacts when the natural tundampedl period was. sec. f- 1, upward motion at impact reduces d For K 2 4.87 ntfcm, M 2 311 g., for instance, the pen trace shows the chassis beginning to move upward just as each impact occurs. The reason that upward residual motion dur- ing impact diminishes values of d is apparent: as the chassis moves upward, it in effect pulls the springs away from the force imparted to them as the wheel passes over the ob- struction. The compression which takes place is not as great as that which would occur if the mass exerted its normal weight on the spring from above. Further, since the initial upward movement is not as great as it usually is, the chassis does not fall as far as it usually does, and thus the distance below the equilibrium position, which is an important com- ponent of d, is diminished in this case as well as that por- tion of the motion which is above the equilibrium position. It is important to realize that the .15 sec. figure is not quite so significant as it might appear to be at first glance. In the first place, this figure would have to be scaled up for it to have any practical application, taking into account the greater mass and higher spring constants of real vehicles. Furthermore, .15 was the value found only because that natural period combined with the friction present and the speed of the drum to produce a fortunate chassis vibration pattern. If the speed of the drum were change or if the im- pacts were to come in an irregular manner, as on actual roads, the .15 sec. figure would lose its significance. The data Kas yet incompletel for c as a function of M were far easier to analyze than was that for d. The smooth curve for the graphs of c vs. M tsee graphs at the end of this se-ctionl suggested an equaslon of the form c 2 a I1 where a and n are some constants. If the logarithms of both sides are taken, the equation becomes logc 2 nlogM+loga which is a linear form. When these data were placed on log -- log co-ordinates, the points did indeed suggest a line. From the graph of c vs. M for K 2 4.87 ntfcm, for example, the slope was found to be -2.16. The intercept was calculated from point-slope form to be .964, giving log c 2 -2.16 log M + .964 or, taking the antilogarithm of each side, c 2 9.21 M-2-16 where c is in centimeters and M is in hectograms. This ex- ponential relationship is not unlike the simplified model which suggested that amplitude might be inversely propor- tional to mass, though here c is inversely proportional to the 2.16 power of M rather than the first power. Before all values of K were tested to determine c as function of M, it was hoped that the general form .. c 2 aMf1 would fit the graphs of c vs. M for all values of K. Then the values of a and n could be examined in the light of the K values which produced them. If a and n could be found to be functions of K, then a general equation of the form c 2 f KKJ MENU where f and g are some functions. Such a relationship would predict average values of c for any combination of M and K. The analysis of the rest of the data relating c and M in order to define c as one function of M and K was carried out in a manner identical to that used for K 2 4.87 nt! cm. One serious difficulty arose, however, when it was observed that a number of points did not fit the expected graphs at all well. The original data traces were examined. and in many cases it became apparent that the shock absorbers did not work as well as it had been hoped. As a result, residual harmonic motion affected the value of c obtained and rend- ered certain values for c inconsistent with data taken when the chassis was allowed to approach equilibrium. To remedy this situation, new averages were taken in which only those impacts which began as the chassis was approximately at equilibrium were counted. The averages computed in this manner were used to graph the corrected points which appear on the various graphs. These corrected values are: M K 25.8 ntscm 36.8 ntfcm 160 g. 6.23 cm 191 4.99 cm l 4 4

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Wave forms Minimum overshoot 30W 15W 0111 Maximum overshoot 27592 2052 0f1, Output voltage unloaded 60V unloaded 59.4V unloaded 60V vs. load .03W . . 42V .03W . . 59.4V 30W . . . 60V 2W .... 56V Efficiency about 15W about 3565 85011 or at .03W at .03W better about 7O'11 at 1.5W sidered in light with the increase in catalase activity, there is a possibility of the enzyme glucose oxidase being active in the tissue. This enzyme oxidizes glucose according to the diagram shown below. In normal tissue, gluconate forma- tion is only the first few steps in glucose metabolism. It is then further oxidized through the Kreb's Cycle to carbon dioxide and water. In aerobic dehydrogenation, the oxida- tion of glucose stops at the gluconate level. Flavin-adenine- dinucleotide QFADJ is the co-enzyme and functions as a hydrogen acceptor. It transfers two hydrogen atoms to a molecule of oxygen which forms hydrogen peroxide. The catalase then decomposes the peroxide as above. This, of course, is just a thedry concerning a possible Although the original objectives were not fully .achieved as of yet, much improved performance has been obtained. This .power supply is to be used for a 15W portable audio amplifier. A Possible Metabolic Alteration in Neoplast Plant Tissue JOHN LAWLER Spalding Institute Peoria Sponsor - Rev. Daniel Reardon, C. S. V. Crown gall is a malignant tumor which affects plants. There are several different causitive agents, such as insects, viruses, nematodes, bacteria, and perhaps others. The tumors I work with are induced in the common sunflower CHelian- thus annuusl by the bacterium Agrobacterium tumefaciens, strain B6. The purpose of the work is to determine if there is any alteration in the metabolic process of the tumor. The part of the Work described in my paper is the initial research on this problem. The first part of the research was to assay catalase activity in the tumors. Catalase is present in most living organisms. Its function is to break down hydrogen peroxide to oxygen and water, because of its toxicity, accoring the equation: 2H,O2 I 2H2O + O, A manometer based on the Warburg Manometer was built to measure changes in gas pressure and volume. For the catalase activity, a substrate of .O6'11 hydrogen peroxide in phosphate buffer, pH 7.0, was used. Young Helianthus seedlings were inoculated with the bacteria and the tumors were allowed to develop to the desired size. A control of the same size and age, only just wounded and not inoculated, was used. When the tissue was to be tested, .1 gram of the tissue was cut and sliced into thin sections and placed in 2 ml. of the substrate. Measurements of the increase of oxygen were made every minute for five minutes and then graphed. The results tan example shown in graph Al showed nearly a twofold increase in catalase activity by the crown gall than by the control plant. The next step is described below. This step is to determine any correlation between cata- lase activity and glucose oxidation. To do this, the mano- meter is again used. The substrate this time is four parts of a 1111 glucose solution added to eleven parts of a Ringer- phosphate buffer in a ratio of 1O:1. The manometer system is filled with oxygen and the tissue to be tested. .1 gram, is added to 2 ml. of the Ringer-phosphate-glucose. The decrease in oxygen level is recorded and graphed every minute for five minutes. The results fa sample given in graph Bl show a marked decrease in oxygen consumption by as much as 50611 in crown gall tumors. In considering this information, we must recall that the tumor tissue is much more active in cell division than normal tissue, but it is seen here that the tumor does not use as much oxygen as the normal tissue. In considering this, Tamaoki et al. 119601 thought this could be a result of Al more efficient use of energy by the tumor cell or BJ a variance of the tissue in its metabolic pathways. When con- change in the enzyme and metabolic activities of crown gall. I I have now started work involving colorimetric study of glucose oxidation and other metabolic intermediates. AEROBIC DEHYDROGENATION H-1 - C - O H . A O H1 F-OH H fi- X OH EXT O xcfon cl '2H HN! HX' OHIXI NH CQH I-ICSO ' c-of f X C - Cf 1 I OH I l H HO H OH glucose gluconolactone H C OH H2 C-OH 2 o C'H l - Hx! l ,OH H H xx C OH H C I O X fC OH H C I O !0H f OHN I lf C -- C E3-'E OH I I H OH H OH gluconolctone gluconic acid il 2H + FAD I FADH2 FADH2 -I- O2 I H,O, + FAD 2H,O. I 2H.O -l- O1 The Specificity of Insulin-Induced Rumplessness in Chicken Embryos THOMAS ZAZECKIS St. Mel High School Chicago Sponsor - Mr. Thomas Gorell The investigation's purpose was to determine the speci- ficity of insulin in causing the phenocopy of rumplessness in White Leghorn embryos and to relate this information to naturally occurring mutations to determine their method of operation. Altogether 234 White Leghorn eggs were used, 138 were injected with .05 ml. Illetin Q2 units insulinl and 96 were injected with .05 ml. sterile distilled water as a control. The embryos were split into 2 groups, the first incubated for 48 hours and the second for 72 hours. Both sets were then prepared for microscopic study ffixed, microtomed, stained! using both Periodic Acid-Schiff's Reagent CPASJ and Pyronin-Methyl Green IPMGJ for the staining process. The slides were then studied and the following conclusions ar- rived at: ll There is no noticeable change in the nucleic acids