5 files changed, 1430 insertions, 1 deletions

diff --git a/fiz/vaje/1/dokument.lyx b/fiz/vaje/1/dokument.lyx
index 55e1637..745646e 100644
--- a/fiz/vaje/1/dokument.lyx
+++ b/fiz/vaje/1/dokument.lyx
@@ -86,11 +86,13 @@ Ravnovesje togega telesa
 \end_layout
 
 \begin_layout Author
+
+\noun on
 Anton Luka Šijanec
 \end_layout
 
 \begin_layout Date
-2.
+3.
  oktober 2022
 \end_layout
 
diff --git a/fiz/vaje/2/.gitignore b/fiz/vaje/2/.gitignore
new file mode 100644
index 0000000..420a327
--- /dev/null
+++ b/fiz/vaje/2/.gitignore
@@ -0,0 +1 @@
+vsi.tsv
diff --git a/fiz/vaje/2/dokument.lyx b/fiz/vaje/2/dokument.lyx
new file mode 100644
index 0000000..fcd20d4
--- /dev/null
+++ b/fiz/vaje/2/dokument.lyx
@@ -0,0 +1,1411 @@
+#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}
+\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 false
+\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 true
+\use_refstyle 1
+\use_minted 0
+\index Index
+\shortcut idx
+\color #008000
+\end_index
+\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
+Kotaljenje kroglice po klancu
+\end_layout
+
+\begin_layout Author
+
+\noun on
+Anton Luka Šijanec
+\end_layout
+
+\begin_layout Date
+3.
+ oktober 2022
+\end_layout
+
+\begin_layout Abstract
+Poročilo druge vaje pri predmetu 
+\noun on
+F41
+\noun default
+ na Gimnaziji Bežigrad v 4.
+ letniku.
+ Vaja je potekala 15.
+ septembra 2022.
+\end_layout
+
+\begin_layout Standard
+\begin_inset CommandInset toc
+LatexCommand tableofcontents
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Section
+Naloga
+\end_layout
+
+\begin_layout Enumerate
+Dokaži, da je kotaljenje kroglice po klancu enakomerno pospešeno gibanje.
+\end_layout
+
+\begin_layout Enumerate
+Za gibanje kroglice po klancu navzdol določi povprečno hitrost in pospešek
+ pri kotaljenju.
+ Določi tudi napako obeh količin.
+\end_layout
+
+\begin_layout Enumerate
+Dobljeni pospešek primerjaj s pospeškom za telo, ki bi brez trenja drselo
+ po klancu z enakom naklonom.
+\end_layout
+
+\begin_layout Section
+Potrebščine
+\end_layout
+
+\begin_layout Itemize
+aluminijast profil dolžine 
+\begin_inset Formula $\SI{1}{\meter}$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Itemize
+kovinska kroglica
+\end_layout
+
+\begin_layout Itemize
+merilna ura
+\end_layout
+
+\begin_layout Itemize
+ravnilo ali merilni trak
+\end_layout
+
+\begin_layout Section
+Potek dela
+\end_layout
+
+\begin_layout Subsection
+Spreminjanje lege po klancu kotaleče se kroglice s časom
+\end_layout
+
+\begin_layout Enumerate
+Kroglico spusti po klancu in izmeri, koliko časa kroglica potuje prvih 
+\begin_inset Formula $\SI{4,0}{\centi\meter}$
+\end_inset
+
+, 
+\begin_inset Formula $\SI{16}{\centi\meter}$
+\end_inset
+
+, 
+\begin_inset Formula $\SI{36}{\centi\meter}$
+\end_inset
+
+ in 
+\begin_inset Formula $\SI{100}{\centi\meter}$
+\end_inset
+
+.
+ Vse meritve zapiši v ustrezno tabelo.
+ Nariši graf 
+\begin_inset Formula $x\left(t\right)$
+\end_inset
+
+.
+ Za kakšno gibanje gre? Kako lahko to dokažeš?
+\begin_inset Newline newline
+\end_inset
+
+
+\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="7" columns="7">
+<features tabularvalignment="middle">
+<column alignment="center" valignment="top">
+<column alignment="center" valignment="top">
+<column alignment="center" valignment="top">
+<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 $d\text{\left[\si{\meter}\right]}$
+\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 $t_{1}\left[\si{\second}\right]$
+\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 $t_{2}\left[\si{\second}\right]$
+\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 $t_{3}\left[\si{\second}\right]$
+\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 $t_{4}\left[\si{\second}\right]$
+\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 $\overline{{t}}$
+\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 $t^{2}\left[\si{\second\squared}\right]$
+\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
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+0
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
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+\begin_layout Plain Layout
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+\end_layout
+
+\end_inset
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+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
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+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
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+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+0
+\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
+0
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
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+\begin_layout Plain Layout
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+\end_layout
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+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
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+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+0,5
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+0,5
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+0,5
+\end_layout
+
+\end_inset
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+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
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+\end_layout
+
+\end_inset
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+</row>
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+\begin_inset Text
+
+\begin_layout Plain Layout
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+\end_layout
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+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+1,0
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
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+\end_layout
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+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
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+\begin_layout Plain Layout
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+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+1,3
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
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+\end_layout
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+\end_inset
+</cell>
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+\begin_inset Text
+
+\begin_layout Plain Layout
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+\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
+0,36
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+2
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+2,1
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+2,4
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+2,1
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+2,15
+\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
+4,6225
+\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
+0,64
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+2,8
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+2,9
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+3,2
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+2,8
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+2,925
+\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
+8,555625
+\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
+1
+\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
+3,6
+\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
+3,5
+\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
+4,0
+\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
+3,6
+\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
+3,675
+\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
+13,505625
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset Caption Standard
+
+\begin_layout Plain Layout
+Čas, potreben za dosego določenih točk
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\begin_inset Newline newline
+\end_inset
+
+Gre za enakomerno pospešeno gibanje, kar je razvidno iz dejstva, da 
+\begin_inset Formula $d$
+\end_inset
+
+ raste s kvadratom 
+\begin_inset Formula $t$
+\end_inset
+
+.
+ Če torej lineariziramo, 
+\begin_inset Formula $d$
+\end_inset
+
+ raste linearno s 
+\begin_inset Formula $t^{2}.$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Enumerate
+Nariši graf, iz kategega lahko razbereš pospešek gibanja, ter določi pospešek.
+ Kako lahko iz grafa oceniš napako pospeška?
+\begin_inset Newline newline
+\end_inset
+
+S programom 
+\family typewriter
+gnuplot
+\family default
+ izračunamo enačbi krivulj, ki se točkam najbolj prilegajo:
+\begin_inset Newline newline
+\end_inset
+
+
+\begin_inset ERT
+status open
+
+\begin_layout Plain Layout
+
+
+\backslash
+begin{lstlisting}
+\end_layout
+
+\begin_layout Plain Layout
+
+fit sqrt(x*a) "podatki.tsv" using 1:6 via a
+\end_layout
+
+\begin_layout Plain Layout
+
+fit (x*b) 
+\begin_inset Quotes gld
+\end_inset
+
+podatki.tsv
+\begin_inset Quotes grd
+\end_inset
+
+ using 1:7 via b
+\end_layout
+
+\begin_layout Plain Layout
+
+
+\backslash
+end{lstlisting}
+\end_layout
+
+\end_inset
+
+in dobimo vrednosti parametrov 
+\begin_inset Formula $a=12,9273$
+\end_inset
+
+ s standardno napako 
+\begin_inset Formula $\pm0,6204$
+\end_inset
+
+ oziroma 
+\begin_inset Formula $4,799\%$
+\end_inset
+
+ in 
+\begin_inset Formula $b=\SI{13,3468}{\meter\per\second\squared}$
+\end_inset
+
+ s standardno napako 
+\begin_inset Formula $\pm0,2407$
+\end_inset
+
+ oziroma 
+\begin_inset Formula $1,803\%$
+\end_inset
+
+.
+ 
+\begin_inset Formula $b$
+\end_inset
+
+ je koeficient premice na grafu 
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "fig:graf"
+plural "false"
+caps "false"
+noprefix "false"
+
+\end_inset
+
+, torej iskani pospešek.
+\begin_inset Newline newline
+\end_inset
+
+Standardna napaka pospeška je
+\begin_inset Formula 
+\[
+\sigma_{\overline{{t^{2}}}}=\SI{0,2407}{\meter\per\second\squared}\text{{.}}
+\]
+
+\end_inset
+
+
+\begin_inset Foot
+status open
+
+\begin_layout Plain Layout
+Standardni odklon se izračuna po enačbi
+\begin_inset Formula 
+\[
+\sigma_{\overline{{x}}}=\sqrt{{\frac{{\mathop{\sum_{i=0}^{n}\left(x_{i}-\overline{{x}}\right)^{2}}}}{{n}}}}\text{{.}}
+\]
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ 
+\begin_inset Float figure
+placement h
+wide false
+sideways false
+status open
+
+\begin_layout Plain Layout
+\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=$
+\backslash
+color{red}t
+\backslash
+color{black}$, domain=0:1, ytick pos=left, samples=256]
+\end_layout
+
+\begin_layout Plain Layout
+
+
+\backslash
+addplot[red, only marks] table [x=d, y=t] {podatki.tsv};
+\end_layout
+
+\begin_layout Plain Layout
+
+
+\backslash
+addplot[red] (x, {sqrt(x*12.9273)});
+\end_layout
+
+\begin_layout Plain Layout
+
+
+\backslash
+addplot[green] (x, {sqrt(x*(12.9273+0.6204))});
+\end_layout
+
+\begin_layout Plain Layout
+
+
+\backslash
+addplot[green] (x, {sqrt(x*(12.9273-0.6204))});
+\end_layout
+
+\begin_layout Plain Layout
+
+\end_layout
+
+\begin_layout Plain Layout
+
+
+\backslash
+end{axis}
+\end_layout
+
+\begin_layout Plain Layout
+
+
+\backslash
+begin{axis}[width=0.75
+\backslash
+textwidth, scale only axis, xlabel=$d$, ylabel=$t^2$, ylabel near ticks,
+ domain=0:1, xtick pos=bottom, ytick pos=right, axis y line*=right]
+\end_layout
+
+\begin_layout Plain Layout
+
+
+\backslash
+addplot[only marks] table [x=d, y=t2] {podatki.tsv};
+\end_layout
+
+\begin_layout Plain Layout
+
+
+\backslash
+addplot[black] (x, {x*13.3468});
+\end_layout
+
+\begin_layout Plain Layout
+
+
+\backslash
+addplot[green] (x, {x*(13.3468+0.2407)});
+\end_layout
+
+\begin_layout Plain Layout
+
+
+\backslash
+addplot[green] (x, {x*(13.3468-0.2407)});
+\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
+
+Grafa 
+\begin_inset Formula $t$
+\end_inset
+
+ in 
+\begin_inset Formula $t^{2}$
+\end_inset
+
+ v odvisnosti od 
+\begin_inset Formula $d$
+\end_inset
+
+.
+ Čas se tukaj sicer neobičajno pojavi na ordinatni osi, kar je smiselno,
+ saj je to izmerjena količina.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Čas, potreben za kotaljenje kroglice po celotni dolžini klanca
+\begin_inset CommandInset label
+LatexCommand label
+name "subsec:Čas,-potreben-za"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Enumerate
+Kroglico spusti po rahlo nagnjenem klancu ter meri čas gibanja.
+ Pazi, da ta čas ni prekratek.
+ Meritev ponovi vsaj osemkrat, izračunaj povprečni čas ter zapiši rezultat
+ meritve z absolutno in relativno napako.
+\begin_inset Newline newline
+\end_inset
+
+Ne pozabi izmeriti naklonskega kota klanca!
+\begin_inset Newline newline
+\end_inset
+
+
+\begin_inset Formula 
+\[
+\phi=\sin\frac{{\SI{0,02}{\meter}}}{\SI{1,00}{\meter}}=\ang{1,14699199839}
+\]
+
+\end_inset
+
+
+\begin_inset Float table
+wide false
+sideways false
+status open
+
+\begin_layout Plain Layout
+\begin_inset Tabular
+<lyxtabular version="3" rows="2" columns="11">
+<features tabularvalignment="middle">
+<column alignment="center" valignment="top">
+<column alignment="center" valignment="top">
+<column alignment="center" valignment="top">
+<column alignment="center" valignment="top">
+<column alignment="center" valignment="top">
+<column alignment="center" valignment="top">
+<column alignment="center" valignment="top">
+<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 $t_{1}\left[\si{\second}\right]$
+\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
+
+\series bold
+\begin_inset Formula $t_{2}\left[\si{\second}\right]$
+\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 $t_{3}\left[\si{\second}\right]$
+\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 $t_{4}\left[\si{\second}\right]$
+\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 $t_{5}\left[\si{\second}\right]$
+\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 $t_{6}\left[\si{\second}\right]$
+\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 $t_{7}\left[\si{\second}\right]$
+\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 $t_{8}\left[\si{\second}\right]$
+\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 $\overline{{t}}\left[\si{\second}\right]$
+\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 $\sigma_{\overline{{t}}}\left[\si{\second}\right]$
+\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 $\sigma_{\overline{{t}}}:\overline{{t}}\left[\si{\second\per\second}\right]$
+\end_inset
+
+
+\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
+4,3
+\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
+3,9
+\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
+3,8
+\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
+3,8
+\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
+4,2
+\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
+3,8
+\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
+3,7
+\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
+3,8
+\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
+3,9125
+\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
+0,20
+\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 $5,18\%$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset Caption Standard
+
+\begin_layout Plain Layout
+Čas, potreben za spust kroglice po klancu nizdol.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Enumerate
+Izračunaj povprečno hitrost ter zapiši rezultat z absolutno in relativno
+ napako.
+\begin_inset Formula 
+\[
+\overline{v}=\overline{{t}}^{-1}=\SI{0,255591}{\meter\per\second}\left(1\pm0,0518\right)=\SI{0,255591}{\meter\per\second}\pm\SI{0,013}{\meter\per\second}
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Enumerate
+Izračunaj pospešek ter zapiši rezultat z absolutno in relativno napako.
+\begin_inset Formula 
+\[
+v_{\text{{max}}}=2\overline{{v}}
+\]
+
+\end_inset
+
+
+\begin_inset Formula 
+\[
+\overline{{a}}=\frac{v_{\text{{max}}}}{\overline{{t}}}=\SI{0,065326}{\meter\per\second\squared}1\pm2\cdot0,0518=\SI{0,065326}{\meter\per\second\squared}\pm\SI{0,003384}{\meter\per\second\squared}
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Izračun pospeška po klancu brez trenja drsečega telesa
+\end_layout
+
+\begin_layout Standard
+Izračunaj pospešek za telo, ki bi brez trenja drselo po klancu iz naloge
+ 
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "subsec:Čas,-potreben-za"
+plural "false"
+caps "false"
+noprefix "false"
+
+\end_inset
+
+, primerjaj rezultata ter zapiši ugotovitve.
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula 
+\[
+F_{g}\tan\phi=F_{d}\rightarrow\cancel{{m}}g(\sin\phi=0,02)=\cancel{m}a=\SI{0,1962}{\meter\per\second\squared}
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Kroglica med premikanjem nekaj energije porablja tudi za vrtenje — to je
+ moja hipoteza, zakaj je pospešek drsečega telesa večji od izmerjenega pospeška
+ kotalegeča se telesa.
+\end_layout
+
+\end_body
+\end_document
diff --git a/fiz/vaje/2/podatki.sh b/fiz/vaje/2/podatki.sh
new file mode 100755
index 0000000..eff7ce6
--- /dev/null
+++ b/fiz/vaje/2/podatki.sh
@@ -0,0 +1,8 @@
+#!/bin/bash
+while read line
+do
+	t=`cut -f6 <<<$line`
+	t2=`cut -f7 <<<$line`
+	d=`cut -f1 <<<$line`
+	[ x$d = xd ] && echo $line tn t2n || echo $line `dc -e "10k$d 12.9273*v$t-p"` `dc -e "10k$d 13.3468*$t2-p"`
+done < podatki.tsv > vsi.tsv
diff --git a/fiz/vaje/2/podatki.tsv b/fiz/vaje/2/podatki.tsv
new file mode 100644
index 0000000..aa98925
--- /dev/null
+++ b/fiz/vaje/2/podatki.tsv
@@ -0,0 +1,7 @@
+d	t1	t2	t3	t4	t	t2
+0	0	0	0	0	0	0
+0.04	0.6	0.5	0.5	0.5	0.525	0.275626
+0.16	1.0	1.3	1.4	1.3	1.25	1.5625
+0.36	2	2.1	2.4	2.1	2.15	4.6225
+0.64	2.8	2.9	3.2	2.8	2.925	8.555625
+1	3.6	3.5	4.0	3.6	3.675	13.505625