EXPERIMENT AND THEORISATION: AN APPLICATION OF THE HYDROSTATIC EQUATION AND ARCHIMEDES THEOREM Santos Lucía, Taaa Máro, Departamento de Físca, Unversdade de Avero, Avero, Portuga 1. Introducton Today s teachng s st under the nfuence of the od habt of packng knowedge n dfferent and non-nteractng feds, and, therefore, t becomes too spt n dfferent dscpnes. Ths basc mafuncton seems to be one of the reasons to expan the separaton between forma teachng and practca everyday ssues, or between the admnstered teachng and the student s nterests and expectatons. As suggested by Hodson (1996) the reconceptuazaton of expermenta work must be based on three essenta ponts, namey, to hep students to earn scence, to earn about scence, and to earn to do scence. Ths new perspectve of facng expermenta work settes a contrbuton to research actvty and to a better teachng/earnng achevement. Barberá e Vadés (1996) have shown that most of practca work (aboratory and/or fed work) performed n schoos can be consdered ony as ustratve because t eads to experments of the recpe knd, and because t causes some sort of apathy or, at east, very ow motvaton on the students. In ths expermenta actvty the students estabsh, by themseves, from regstered observatons, concepts and scentfc theores that were mnstered before, n forma teachng, n dfferent dscpnes. In ths study students understand basc concepts of physcs of fuds (mass, weght, pressure and mpuson, see, for exampe, Massey, B.S. (1983) that affect ther everyday fe, and aso may dea wth the nteracton of theory and experence. 2. Theory In ths work t s our nterest that the expermenta actvty may rase some unexpected questons on the student. Namey, t s our am to anayse the nfuence of the readng process n a U manometer, when dfferent densty quds are used (on the manometer and on the tank). Ths research actvty makes use of the Fundamenta Law of Hydrostatcs and of the Archmedes Theorem. The Fundamenta Law of Hydrostatcs, or Stevn s Law, states that the pressure dfference between any two consdered ponts nsde a qud n statc equbrum, under the nfuence of gravty, s numercay equa to the weght of a coumn of the qud, that has a unt area n the base and s as hgh as the vertca dstance between the two consdered ponts. Generay speakng, the pressure p on a certan pont n the qud s gven by p = p 0 + ρ gh (1) where p 0 s the pressure exerted by the atmospherc ar on the free surface of the qud, ρ the qud densty, g the gravty acceeraton and h the depth of the pont nsde the qud. Expresson (1) ndcates that the pressure nsde a qud ncreases wth ncreasng depth and s the same n every pont ocated at the same eve nsde the qud. Archmedes Prncpe, states that every body that s dved nto a qud n equbrum receves, from the qud, a vertca upwards mpuson that s numercay equa to the weght of a voume of qud equa to the voume of the mmersed body. The mathematca reaton that transates Archmedes Prncpe, for foatng bodes, s gven by the expresson
P = ρ gsh (2) Here P represents the weght of the body and Sh the voume of the mmersed part, S beng the straght secton of the contaner, and h the eve dfference between the two surfaces, read on the tank that contans the qud. On the other hand P = Mg (3) where, n our case, M s cacuated from M = M 0 + M (4) In expresson (4), M 0 M represents the summng up of the oads paced on the upper top of the recpent wth mass (see fgure 1). Through mathematca treatment t s possbe to wrte h = 1 M ρ S (5) From expresson (2) the pressure of the ar n the recpent can be evauated. The same vaue shoud be measured by the dfferenta U manometer. Agan through mathematca manpuatons eq.(5) can be rewrtten as h ρ = h (6) ρ ρ where s the manometrc qud densty and h the eve dfference regstered by the dfferenta U manometer. 3. Expermenta set-up In Fgure 1 the expermenta set-up s schematcay represented. It s composed of three man components: a water manometer (a tube of 10mm nterna dameter), a recpent (10cm sze and 50cm heght) and a tank (22cm sze and 70cm heght). On the top of the recpent there s a tube system that aows the student to use an automatc data acquston system (ADAS) and/or a water manometer. On budng ths expermenta set-up care was taken on usng ow cost, market accessbe materas, so that t coud be an affordabe devce. As can be seen on Fgure 1, connecton C aows smutaneous data regstraton by means of an ADAS chart and a water manometer, when vaves A and B are open. The researcher can choose one of the two aternatves. Exempfyng, he can use ony the ADAS chart, when vave A s open and B s cosed or ony the water manometer, when vave A s cosed and B s open. Fnanca avaabty may be the crtera to decde the aternatve to be used.
4. Resuts and dscusson Fgure 1: Outne of the expermenta devce In the experence dfferent densty quds were used on the tank. Fgure 2 shows the nfuence that can be observed on the dfference of eve of the qud, h, when the tank contans o ( ρ = 923 kgm -3 ), ordnary water ( ρ = 1000 kgm -3 ) or saty water ( ρ = 1146 kgm -3 ). The graph on Fgure 2 shows that, for every qud, there s a good agreement between the expermenta recorded data, and the adjust straght ne. It s aso observed that, for a gven vaue of h, mpuson ncreases on qud wth the hgher densty, as expected. The adjustment straght nes for the expermenta data are aso ndcated n the Fgure 2 and they are gven for O: h = 0. 1093M (7) Water: h = 0. 1002M (8) Sated water: h = 0. 0865M (9) Beng M expressed n (kg) and h n (m). On the graphs of Fgures 3 to 5 we present the expermenta data of the eve dfference, read on the water manometer for every qud on the tank, equaton (5), expermenta data read for the eve dfference of the qud on the tank, and the expected vaues for the eve dfference f the manometrc qud was the same as the qud on the tank. Expermenta data: o Expermenta data: water Expermenta data: sated water Equaton (7): o Equaton (8): water Equaton (9): sated water Fgure 2: Expermenta data. Theoretca equatons for every qud on the tank
Expermenta data: dfference n water manometer Equaton (5): o Expermenta data: dfference qud (o) n the tank Predcted data: dfference n o manometer Fgure 3: Expermenta data. Lqud on the tank: o Expermenta data: dfference n water manometer Equaton (5): water Expermenta data: dfference qud (water) n the tank 0 1 2 3 4 5 Fgure 4: Expermenta data. Lqud on tank: ordnary water 6 One must emphasse the reatve postonng of the expermenta data read on the water manometer to the theoretca straght ne. Ths observaton ndcates the nfuence of the densty of the qud on the tank on the vaues read on the water manometer. Aso on the fgures, as expected, the expermenta data read on the tank present an exceent agreement both wth equaton (5), and when the use of a manometer wth the same qud as the tank s proposed. Expermenta data: dfference n water manometer Equaton (5): sated water Expermenta data: dfference qud (sated water) n the tank Predcted data: dfference n sated water Fgure 5: Expermenta data. Lqud on tank: saty water
5. Concuson The expermenta set-up aows a comprehenson of basc notons such as mass, weght, pressure and mpuson. The study shows that there s a dfference between the readngs on the eve dfference of the qud on the tank and the eve dfference for the water n the manometer when the qud n the tank s dfferent from the one on the water manometer. Ths fact contrbutes to a better nterpretaton of the data, due to the densty dfference of the quds. The anayss of the resuts shows the good agreement between the observed data and the expected ones. We thnk that, trough the use of ths expermenta devce, n a practca scence cass, an opportunty s gven to the teacher to ncude, n s practce, actvtes that gve hs students hypothess of expcty speak about ther own concepts. In ths way, condtons w be created so that student s dea wth aternatve conceptons they may have and change them. In ths sense teachng w have to be adaptabe, and ths mpes that ndvdua dfferences on the evouton of earnng are taken nto consderaton and that a standard way of teachng s avoded. References Barberá O. and Vadés P., E Trabajo Prátco en a Ensenanza de as Cencas: una revson, Ensenanza de as Cencas, 14, (3), (1996), 365-375. Hodson D., Practca work n schoo scence: exporng some drectons for change, Internatona Journa of Scence Educaton, Vo 18, (7), (1996), 755-759. Massey B.S., Mechancs of Fuds (5 th. Edton), Van Nostrand Renhod (U K) Co. Ltd., Moy Mars Lane, Wokngham, Berkshre, Engand, (1983).