#LyX 2.3 created this file. For more info see http://www.lyx.org/ \lyxformat 544 \begin_document \begin_header \save_transient_properties true \origin unavailable \textclass article \begin_preamble \usepackage{siunitx} \usepackage{pgfplots} \usepackage{listings} \usepackage{multicol} \sisetup{output-decimal-marker = {,}, quotient-mode=fraction, output-exponent-marker=\ensuremath{\mathrm{3}}} \end_preamble \use_default_options true \maintain_unincluded_children false \language slovene \language_package default \inputencoding auto \fontencoding global \font_roman "default" "default" \font_sans "default" "default" \font_typewriter "default" "default" \font_math "auto" "auto" \font_default_family default \use_non_tex_fonts false \font_sc false \font_osf false \font_sf_scale 100 100 \font_tt_scale 100 100 \use_microtype false \use_dash_ligatures true \graphics default \default_output_format default \output_sync 0 \bibtex_command default \index_command default \paperfontsize default \spacing single \use_hyperref false \papersize default \use_geometry true \use_package amsmath 1 \use_package amssymb 1 \use_package cancel 1 \use_package esint 1 \use_package mathdots 1 \use_package mathtools 1 \use_package mhchem 1 \use_package stackrel 1 \use_package stmaryrd 1 \use_package undertilde 1 \cite_engine basic \cite_engine_type default \biblio_style plain \use_bibtopic false \use_indices false \paperorientation portrait \suppress_date false \justification false \use_refstyle 1 \use_minted 0 \index Index \shortcut idx \color #008000 \end_index \leftmargin 1cm \topmargin 2cm \rightmargin 1cm \bottommargin 2cm \headheight 1cm \headsep 1cm \footskip 1cm \secnumdepth 3 \tocdepth 3 \paragraph_separation indent \paragraph_indentation default \is_math_indent 0 \math_numbering_side default \quotes_style german \dynamic_quotes 0 \papercolumns 1 \papersides 1 \paperpagestyle default \tracking_changes false \output_changes false \html_math_output 0 \html_css_as_file 0 \html_be_strict false \end_header \begin_body \begin_layout Title Centripetalni pospešek \end_layout \begin_layout Author \noun on Anton Luka Šijanec \end_layout \begin_layout Date 14. december 2022 \end_layout \begin_layout Abstract Poročilo pete vaje pri predmetu \noun on F41 \noun default na Gimnaziji Bežigrad v 4. letniku. Vaja je potekala 10. novembra 2022. \end_layout \begin_layout Standard \begin_inset CommandInset toc LatexCommand tableofcontents \end_inset \end_layout \begin_layout Section Potrebna oprema \end_layout \begin_layout Itemize kos plastične cevi \end_layout \begin_layout Itemize vrvica \end_layout \begin_layout Itemize zamašek z luknjico \end_layout \begin_layout Itemize štoparica \end_layout \begin_layout Itemize ravnilo \end_layout \begin_layout Itemize tehtnica \end_layout \begin_layout Itemize uteži \end_layout \begin_layout Section Cilj naloge \end_layout \begin_layout Standard S poskusom preveriti veljavnost drugega Newtonovega zakona za kroženje. \end_layout \begin_layout Section Potek meritve \end_layout \begin_layout Enumerate Izmeri maso uteži in maso zamaška. \begin_inset Newline newline \end_inset \begin_inset Formula \[ m_{\text{{uteži}}}=\SI{30,5}{\gram} \] \end_inset \begin_inset Formula \[ m_{\text{zamaška}}=\SI{3,5}{\gram} \] \end_inset \end_layout \begin_layout Enumerate Primi za cev in jo vrti tako, da zamašek kroži v vodoravni ravnini s stalno hitrostjo. Pri tem pazi, da je razdalja od vrha cevi do zamaška ves čas enaka izbranemnu polmeru. Izmeri čas desetih obhodnih časov. Meritev ponovi za deset različnih polmerov. \end_layout \begin_layout Standard \begin_inset Float table placement H wide false sideways false status open \begin_layout Plain Layout \align center \begin_inset Tabular \begin_inset Text \begin_layout Plain Layout \begin_inset Formula $r\left[\si{\meter}\right]$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \begin_inset Formula $t_{10}\left[\si{\second}\right]$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \begin_inset Formula $t\left[\si{\second}\right]$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \begin_inset Formula $a_{r}\left[\si{\meter\per\second\squared}\right]$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 0,15 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 2,55 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 0,255 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 91,069014 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 0,3 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 3,55 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 0,355 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 93,977586 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 0,47 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 5,32 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 0,532 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 65,559303 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 0,43 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 4,08 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 0,408 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 101,978323 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 0,33 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 3,87 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 0,387 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 86,986478 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 0,23 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 2,6 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 0,206 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 134,320060 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 0,45 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 4,21 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 0,421 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 100,232384 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 0,2 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 3,012 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 0,3012 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 87,032167 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 0,29 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 2,98 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 0,298 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 128,921457 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 0,4 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 3,62 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 0,362 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 120,504312 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 0,4 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 4,21 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 0,421 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout 89,095452 \end_layout \end_inset \end_inset \end_layout \begin_layout Plain Layout \begin_inset Caption Standard \begin_layout Plain Layout Meritve \end_layout \end_inset \end_layout \end_inset \end_layout \begin_layout Section Naloge \end_layout \begin_layout Enumerate Za vsako meritev določi obhodni čas in izračunaj centripetalni pospešek. Določi povprečni pospešek in njegovo napako. \begin_inset Formula \[ \overline{a_{r}}=\SI{99,970594}{\meter\per\second\text{\squared}} \] \end_inset \begin_inset Formula \[ \sigma_{a_{r}}=\SI{20,487365}{\meter\per\second\squared} \] \end_inset \end_layout \begin_layout Enumerate Centripetalni pospešek izračunaj tudi iz mas zamaška in uteži. Ali se dobljena rezultata ustrezno ujemata? \begin_inset Formula \[ a_{r}=\frac{{F_{c}=gm_{\text{{uteži}}}}}{m_{\text{{zamaška}}}}=\frac{\SI{9,81}{\meter\per\second\squared}\cdot\SI{0,0305}{\kilo\gram}=\SI{0,299205}{\newton}}{\SI{0,0035}{\kilo\gram}}=\SI{85,487}{\meter\per\second\squared} \] \end_inset \begin_inset Newline newline \end_inset Upoštevajoč napako merjenja se izračunana vrednost ustrezno ujema z izmerjeno. \end_layout \begin_layout Enumerate Izpelji izraz, ki povezuje kvadrat nihajnega časa \begin_inset Formula $t^{2}$ \end_inset z radijem \begin_inset Formula $r$ \end_inset ! \begin_inset Formula \[ t^{2}=\frac{{4\pi^{2}r}}{a_{r}} \] \end_inset \end_layout \begin_layout Enumerate Nariši graf \begin_inset Formula $t^{2}(r)$ \end_inset . Skozi narisane točke lahko narišemo premico skozi izhodišče. Določi naklon te premice, pri tem pazi na enote rezultata! \begin_inset Float figure placement H wide false sideways false status open \begin_layout Plain Layout \align center \begin_inset ERT status open \begin_layout Plain Layout \backslash begin{tikzpicture} \end_layout \begin_layout Plain Layout \backslash begin{axis}[width=0.75 \backslash textwidth, scale only axis, ylabel=$t^2$, domain=0:0.5, ytick pos=left, samples=2 56, xlabel=$r$, xtick pos=bottom] \end_layout \begin_layout Plain Layout \backslash addplot[only marks] table [x=r, y=tt] {podatki.tsv}; \end_layout \begin_layout Plain Layout \backslash addplot[green] (x, {x*(0.425193+0.02904)}); \end_layout \begin_layout Plain Layout \backslash addplot[green] (x, {x*(0.425193-0.02904)}); \end_layout \begin_layout Plain Layout \backslash addplot[red] (x, {x*(0.425193)}); \end_layout \begin_layout Plain Layout \backslash end{axis} \end_layout \begin_layout Plain Layout \backslash end{tikzpicture} \end_layout \end_inset \end_layout \begin_layout Plain Layout \begin_inset Caption Standard \begin_layout Plain Layout \begin_inset CommandInset label LatexCommand label name "fig:graf" \end_inset Graf kvadrata nihajnega časa v odvisnosti od polmera. \end_layout \end_inset \end_layout \end_inset \begin_inset ERT status open \begin_layout Plain Layout \backslash begin{lstlisting} \end_layout \begin_layout Plain Layout fit (x*p) \begin_inset Quotes gld \end_inset podatki.tsv" using 2:6 via p \end_layout \begin_layout Plain Layout \backslash end{lstlisting} \end_layout \end_inset \begin_inset Formula \[ p=\SI{0,425193}{\second\squared\per\meter}\pm\SI{0,02904}{\second\squared\per\meter} \] \end_inset \end_layout \begin_layout Enumerate Naklon premice izrazi z maso zamaška in uteži in ga tako tudi izračunaj. \begin_inset Formula \[ k=\frac{{t^{2}}}{r}=\frac{{4\pi^{2}}}{a_{r}}=\frac{{4\pi^{2}m_{\text{{uteži}}}}}{gm_{\text{{uteži}}}}=\SI{0,461805}{\second\squared\per\meter} \] \end_inset Izračunana vrednost je izven standardne napake, vendar ne pretirano. \end_layout \begin_layout Section Uporabljen program \end_layout \begin_layout Standard \begin_inset ERT status open \begin_layout Plain Layout \backslash lstinputlisting[language=Python]{meritev.py} \end_layout \end_inset \end_layout \end_body \end_document