prikaz prve stranice dokumenta Razlika između matematike i fizike na primjeru padajućih ljestvi
  Download
PDF 1.09 MB
undergraduate thesis
Razlika između matematike i fizike na primjeru padajućih ljestvi
2017. urn:nbn:hr:160:873298
Alešković, Marina
Josip Juraj Strossmayer University of Osijek
Department of Physics
Division of Experimental Physics
Division Chair of Fundamental Physics

Cite this document

Alešković, M. (2017). Razlika između matematike i fizike na primjeru padajućih ljestvi (Undergraduate thesis). Osijek: Josip Juraj Strossmayer University of Osijek, Department of Physics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:160:873298

Alešković, Marina. "Razlika između matematike i fizike na primjeru padajućih ljestvi." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Physics, 2017. https://urn.nsk.hr/urn:nbn:hr:160:873298

Alešković, Marina. "Razlika između matematike i fizike na primjeru padajućih ljestvi." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Physics, 2017. https://urn.nsk.hr/urn:nbn:hr:160:873298

Alešković, M. (2017). 'Razlika između matematike i fizike na primjeru padajućih ljestvi', Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Physics, accessed 05 April 2025, https://urn.nsk.hr/urn:nbn:hr:160:873298

Alešković M. Razlika između matematike i fizike na primjeru padajućih ljestvi [Undergraduate thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Physics; 2017 [cited 2025 April 05] Available at: https://urn.nsk.hr/urn:nbn:hr:160:873298

M. Alešković, "Razlika između matematike i fizike na primjeru padajućih ljestvi", Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Physics, Osijek, 2017. Available at: https://urn.nsk.hr/urn:nbn:hr:160:873298

Please login to the repository to save this object to your list.
Metadata
TitleRazlika između matematike i fizike na primjeru padajućih ljestvi
Title (english)The Difference Between Mathematical and Physical View on the Falling Ladder Problem
AuthorMarina Alešković
MentorDario Hrupec (mentor)
GranterJosip Juraj Strossmayer University of Osijek
Department of Physics
(Division of Experimental Physics)
(Division Chair of Fundamental Physics)
Osijek
Defense date and country2017-09-28, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Physics
General and Classical Physics
Abstract
Padajuće ljestve su dobar primjer kojim se može pokazati ključna razlika između matematike i fizike.Jednostavan i naizgled prihvatljiv matematički model daje predviđanje koje se očito ne slaže s iskustvom: brzina vrha padajućih ljestvi teži u beskonačno kad kut koji ljestve zatvaraju s podom teži u nulu. U matematičkom je svijetu takvo ponašanje sasvim legitimno. No takav model očito ne opisuje dobro fizički svjet - svijet u kojem živimo. Za opis fizičkog svijeta model treba nadograditi. Drugim riječima, treba u obzir uzeti neka ograničenja koja nameće fizika. Zbog tih ograničenja jednadžbe obično postaju zamršenije pa ih je teže riješiti, no predviđanja modela bolje se slažu s opažanjima. U ovom radu jednostavan matematički model padajućih ljestvi nadograđen je u dvije etape. U jednostavnijem slučaju uzeta je u obzir činjenica da ljestve imaju masu (zbog koje u gravitacijskom polju padaju), ali je ta masa stavljena u središte ljestvi. Korštena je, dakle, dinamika točkatog tijela. U realističnijem slučaju masa je jednoliko raspoređena po ljestvama. Tu je korištena dinamika krutog tijela. U oba je slučaja, radi jednostavnosti, trenje bilo zanemareno. Oba fizička modela, očekivano, daju konačnu brzinu vrha padajućih ljestvi kad ljestve dođu u vodoravni položaj.
Abstract (english)
Falling ladders is a good example which can show the key difference between mathematics and physics. A simple and seemingly acceptable mathematical model gives prediction which obviously does not agree with experience: the speed at the top of the ladder tends to infinity when the angle between the ladder and the floor tends to zero. In the mathematical world such behavior is quite legitimately. But such model obviously does not describe good physical world – the world we live in. To describe the physical world, the model needs to be upgraded. In other words, it is necessary to take some restrictions imposed by physics. Because of that restrictions, equations usually become more complicated and it's more difficult to solve them. But that model predictions better get along with observations. In this work, a simple mathematical model of falling ladders has been upgraded into two stages. In the easier case we took a fact that ladders have a mass (because they fall in the gravity field), but that mass is placed in the center of the ladder. So, the dynamics of the dot body has been used. In a more realistic case, the mass is uniformly deployed by ladders. Solid body dynamics has been used here. In both cases, for simplicity, friction was neglected. As expected, both physical models give the ultimate speed of the top of the ladder when the ladder comes to the horizontal position.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:160:873298
Study programmeTitle: Physics
Study programme type: university
Study level: undergraduate
Academic / professional title: sveučilišni/a prvostupnik/prvostupnica (baccalaureus/baccalaurea) fizike (sveučilišni/a prvostupnik/prvostupnica (baccalaureus/baccalaurea) fizike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2017-10-06 10:45:09