#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
<lyxtabular version="3" rows="12" columns="4">
<features tabularvalignment="middle">
<column alignment="center" valignment="top">
<column alignment="center" valignment="top">
<column alignment="center" valignment="top">
<column alignment="center" valignment="top">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset Formula $r\left[\si{\meter}\right]$
\end_inset
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset Formula $t_{10}\left[\si{\second}\right]$
\end_inset
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset Formula $t\left[\si{\second}\right]$
\end_inset
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\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
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
0,15
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
2,55
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
0,255
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
91,069014
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
0,3
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
3,55
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
0,355
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
93,977586
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
0,47
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
5,32
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
0,532
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
65,559303
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
0,43
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
4,08
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
0,408
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
101,978323
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
0,33
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
3,87
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
0,387
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
86,986478
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
0,23
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
2,6
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
0,206
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
134,320060
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
0,45
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
4,21
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
0,421
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
100,232384
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
0,2
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
3,012
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
0,3012
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
87,032167
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
0,29
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
2,98
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
0,298
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
128,921457
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
0,4
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
3,62
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
0,362
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
120,504312
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
0,4
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
4,21
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
0,421
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
89,095452
\end_layout
\end_inset
</cell>
</row>
</lyxtabular>
\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
