Northeast High School - Nor Easter Yearbook (Kansas City, MO)

Page 30 text:

26 OP' QELSTC-il? VC13-d55 lil in the equation v2MVfm for V, we have Vilxlvlzg 1 1-VC19-C125 Hfm. It will be seen, however, that this for- mula is inconvenient, especially when using logarithms, as it is necessary to take the square root of a square root. By the use of 'trigonometry a much shorter formula may be obtained, which eliminates the ex- pression VC13-d95. C15 sin a2df1 Cthe sine of an angle in a right triangle equals the opposite side di- vided by the hypotenuse5, From this equation, since d and 1 are both known, we can find the sine of oi. Then, by a table of sines and cosines, we can find the cosine of CL. C25 cos cL2OBf1 Cthe cosine of an angle in a right triangle equals the adjacent side divided by the hypotenuse5. C35 OB:1 cos a Csolving C21 for OB5- C45 1-OBZ1-1 cos a Cequals subtracted from equals are equalj, C55 1-OB2l C1-cos 005 Cfactoring 1-1 cos in equation C415 C65 1-OB:S Cby figure, since OC equals 15. C75 S11 C1--cos a5 Csubstituting S for 1-OB in ' C85 v2MVfm Csee geometrical proof5. C95 V: V C2 S5 Cs ?e geometrical proof5, C105 v2MVC2 g S5!m Csubstituting C91 in f815. C115 v:11V1sVIi2 g 1 C1-cos cc5jfm Csubsti- tuting for S in C1015 Wve took the necessary measurements for finding the velocity of the bullets. In tak- ing these measurements we neglected the errors caused by the blast of air that comes out of the barrel of the gun and the weight of the bullet, which was added to the weight of the pendulum, because of their infinitesi- mal values. A piece of paper CP5 between the pendulum and the revolver will stop the blast of air from affecting the velocity of the pendulum. The measurements were taken after Mr. Pinkney said: Now open your mouths. They are: Calibre M 1 m d .22 12 lbs. 305 cm. 2.0 g. 2.375 in, .32 12 lbs. 305 cm. 5.5 g. 5.25 in. .38 12 lbs. 305 cm. 9.4 g. 10.5 in. The acceleration due to gravity at Kansas City, MO., is 32.1514 ft.fsec. 2-exponent. In calculating the velocity of these bul- lets, the measurements must be in pounds and feet to have the result in feet per sec- ond, or in grams and centimeters to have the result in centimeters per second. The vC1OCity Of the .22 is worked by trigonometry and logarithms, the .32 by 'geometry and logarithms and the .38 by geometry and the usual arithmetrical process. The computations, substituting in the for- mula, are: C.225 log sin ClilOg .l9625Cl0'.007. 21.29281-1.00030 12.29251 6. By table of the logarithnzs of sines and cosines of angles, log cos a21.9899 then cos 66209998 1-cos di -0002 , Then, VI125! C2 - 32.1514 - 10.007 ' .00025 7 .0044092 log v21.07918 -l- 1f2C0.30103 -lr 1.50720 + 1.00030 -lr 4.301035-3.64436 log v22.98960. v2976.34 feet per second. C.325 Vi12V I:2 - 32.1514 4 101007-V C10.0072. --.437525 H C.325 VZ12V C2 - 32.1514 110.007-V C100072- .4-375251 5!-012125 I9.62255f.012125: 793.62 feet per second. - C385 V':12Vli2 ' 32.151 4 305730.48-VC305f I 30.482-105971235 H ' 453.6794 212V 164.302 4 1000656167- V C100.l3127-.87535 l 17020723104 2188467447 .fQ0723104 2 909.45556 feet per second. It probably seems queer that the velocity of the .22 is greater than the velocity of the .32 or .38. But this is due to the differ- ence between the barrels of the different revolvers. The .22 that was us Ed was a long- barreled army target revolver and the others were the regular .32s and .38s. The detona- tions of these revolvers caused the mem- bers of these classes, especially the girls, to assume strange postures, so as to avoizl any unpleasant effects on the ears. We laughed and laughed at each other's open mouths and ridiculous attitudes. We will always remember this experiment as the most pleasant and interesting one we ever performed under Mr. Pinkney's guidance. MARTIN DICKINSON. 322. ' OLIN W. MUNGER '22, LE ROY SMITH, '23. Who up there inthe balcony said that the Mathematics-Department of iNtwtheastlHigh Schoolxvas notcnithe map? We wish that person would come to the front and we will show him that besides being on the map it is well represented. The names of three of our Northeast students, Fannie Roll, Martin Dickin- son and Dorsey Dsborne earned their recognition in the School Science and Mathematics Magazine by solving an algebraic quadratic equation. The problem was: X+y?23,X2+y:3. The solution by Fannie Roll was given in full in the january, 1922, number. The other two students received credit for the solution. This was not the first Ng' Ni pa M lis ye ali th an tai by nc wl 'EEL lei ke Hi 311 O11 if ha: ani nir act bas Th the try cip tes tis1 r the ica un Eig Lai icai wh titg ten poi aft- for ing it The hea per

Page 29 text:

i- 1' 10 F 'H 1' -,H .sytzwrnevmsq fn,.4-asv,-+,,., i P ,,... 1 ake east Qt is 134 odels very t ma- Our OTP, QHSTQI' 25 cabinets cost us about 31500, the in- lay from 31.00 to 3500 and a good motor can be bought for 34000, so a 3350000 Console is made complete here at school for about 35000 to 36500. So-me of the pupils who are skilled with tools, prefer a great deal of in- lay and design the doors, the sides and the two front legs of the Console. It takes much extra time for inlaying, so the pupil must be a swift worker to finish this wonderful model before the end of the year. We are expecting several inlaid Consoles and several plain ones. We will have them on dis- play at the end of the Year, and every- body is welcome to come and see them. GERTRUDE BROUILLETTE. THE VELOCITY OF A BULLET. To every action there is an equal and opposite reaction. -Newton. One peaceful day'the students CH who .are in the north wing of the school heard a series of shots in room 207 during the fourth and fifth hours and possibly thought: 'VVhat is Mr. Pinkney doing to those poor kids now? Those who were in there could answer: We were only measuring the velocities of some bullets. Gee! but it was interesting. And this was one of the most interesting experiments we have performed this year. The two classes Cor, rather, Mr. Pinkneyj measured the velocity of bullets used in 22, .32 and .38 calibre revolvers. The first hour class was luckyg they didn't have to do this experiment. We had to develop the formula Cby geometryj: A ballistic pendulum Csee fig- urej was used. to determine these veloci- ties. This is a pendulum which is sus- pended from a beam on the ceiling by four strings or wires to which are attached the four upper corners of a block of wood. This block swings like any other pendulum, ex- cept that it is suspended by four strings in- stead of one. In fll'l'll11'f,' the velocity of the bullet we first had to find the distance the block M Csee fifjurej would fall. ln order to find this distance we have to know how much the center of gravity moves, ver- tically, from rest at C. When M moves through the arc AC. its center of gravity mpves a distance horizontally equal to d CABJ and vertically equal to S CBCD. The distance cl CAB is perpendicular to OCD is measured by a yardstick placed underneath M fthe pendulumj and by a s'nall block which is placed along the side of the yard- stick and which is attached to M at E. When the pendulum moves. it pulls this small block along the yardstick and thus meas- ures the distance. It will take M the same 'flme to move from rest at C to A as it will take M. to fall freely from rest at B to C. Now, since- we have found the distance M moves horizontally, we want the distance CSD that M falls in terms of 1 and d. 1 is the distance from the center of gravity of M to the point of suspension from the ceil- lllg- SO, by the corollary to the Pythagorean 7 I ,f f :f if fx f I ff f X . I f f ff 1 x X X f ' ff ll I ff 1 X 1 I f f If I If fbsx ' rl, ff ' Aff' NX! ff ,I l X CN I ff 7 XX XX, ' N f 21 I X I I I x I f,r , E ski' : X I s I N hx: E NN' xxg,,f X I l 'X 0 . l . -E! A ' 3 X C -s BALLISTIC DENDULUIVI Theorem fthe square of either leg of a right triangle is equal to the square of the hypot- enuse minus the square of the other legb, OBIVCIQ-d2j, also SZOC-OB. Substi- tuting in the equation SIOC-OB for OC and OB, we have S11-AV C12-d2J. By Galileo's law of freely falling bodies fthe velocity of an object equals the square root of two times the acceleration due to grav- ity ligj times the distance ISI through which it fallsj, VIVCZ g SD. Substituting fl-V C12-d2jfI for S, we have VZVIZ g Q l-VCI?-d2D H, which is the velocity of a pendulum passing through the point C after it has been displaced a distance d. According to Newton's third law of mo- tion Cto every action there is an equal and opposite reactionj, it is evident that the momentum of the bullet equals the momen- tum of the pendulum, and, since momentum is measured by the product of M-V, we have MV:mv, when M is the weight of the block, V the velocity of the block, m the weight of the bullet and v the velocity of the bullet. Then the velocity of the bullet Qquglg MV!m. Substituting VIZ g -ll- - 1 F ? '14 .f - ' :EEET 2if'fiiF,3.:-?

Page 31 text:

' 'ri-: 'Hives-921124:-l:--2-.xii-1 2-waexzwfa-:e:frm'i:-155-o.'.r,a.,,,,, .. 2 63,53 ,,. ,Im L 1165 7 . 3720 00-72 . 72- per 305f I4 14 feet Bcity v of ffer- :rent ong- :hers ona- ienv s, to Lvoid VVe open Xvill the ever e. 22 said it of 1 the fould show ap it aeast ckin- their : and I2 Pm The The en in . The it for first OID' 83.511813 27 Northeast representation in that paper. The school Science and Mathematics Monthly, as the name implies, is pub- lished every month during the school year. Several interesting topics are always printed as well as problems and their solutions in both fields of Science and Mathematics. Every issue con- tains a problem capable' of being solved by the average high school student, not only in America, but over the whole world. The last issue even con- tained a solution for the above proh- lem by Richard Cumming from Dal- keith, Scotland. . So you see that the name Northeast High School, Kansas City, Missouri, and its representatives, does travel outside of its own vicinity. ARTS AND SCIENCE EDITOR. CGNCERNING CHEMISTRY .We would not be far from wrong if we said that the study of chemistry has advanced more in the last century and a half, than it has since its begin- ning. The ancients studied chemical actions, and the art of changing some baser metal into a more precious metal. This study was called alchemy. We therefore have no old laws in chemis- try, as for instance, Archimedes Prin- ciple in Physics which has stood the test of the Twentieth Century scien- tists. ' ' ' ' The entire reason for this lies in the fact that the most important chem- ical action, namely: burning, was not understood until the middle of the Eighteenth Century, when Antoine Laurent Lavoiser discovered the chem- ical change which a metal undergoes when heated in air. He took a quan- tity of mercury, and heating it to the temperature just below the boiling point of mercury C357OCj, noticed that after a few days, a red powder was formed Qmercuric oxidej. On weigh- ing this mercuric oxide he found that it weighed more than the mercury. Then he took this mercuric oxide, an-il, heating it for several days to a tem- perature above the boiling point of mercury, found that a quantity of gas was evolved, and that small particQes of mercury were clinging to the sices of the vessel. The evolved gas he called oxygen. Un again weighing tfie mercury he found that it had the same weight as the mercury with which he had started. Then on weighing the gas he found that the loss of weigfit of the mercuric oxide was equal to the weight of the oxygen. On investigat- ing further, he found that in burning, the weight of the entire products ex- ceeds the weight of the fuel. And with these experiments, and experiments of similar nature by other great scien- tists, such as Joseph Priestly, who was a contemporary of Lavoiser, the study of chemistry was revolutionized. Lavoiser, in 1786, was the first to explain ordinary burning as the com- bining of a substance with oxygen. Such a combining is an oxidation and the compounds formed are known as oxides. There are four different kinds of oxidations, namely: ordinary burn- ing, slow oxidation, spontaneous com- bustion, and explosion. Qrdinary burn- ing is an oxidation accompanied by noticeable light and heat. Take the case of a burning candle fone of the most interesting lectures was given by Michael Faraday at the Royal Institu- tion in London on The Chemical His- tory of a Candle j, we notice the light and heat but do not realize that a chemical change is occurring. Neither would we believe that the gaseous products which are formed, will weigh more than the candle itself unless we were actually shown that such is the case, as was demonstrated in the chem- istry classes. Even then it is hard to believe. This increase in weight is due to the oxygen taken out of the air. In ordinary burning nearly all substances undergo similar changes. In slow oxidation, no noticeable light or heat are evolved.. Neverthe- less the same kind of action is taking place in slow oxidation, the only dif- ference, as the name implies, is that if goes on at a much slower rate. Let us take, for instance, the rusting of a tin can, which really should be 1 1 -. . . . . . . . . . - - - - . ' ' - ' ' :' ' ' - ' .4Z.. : , ..'f'i?1i:'S'EiEiT?ifi7'r -:f:L1?z1f1 'T L55 ' 151' ' -:V f - -- '