From 0a39997c12f0d872413f6f08f16dfd65b191ccdd Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Anton=20Luka=20=C5=A0ijanec?= <anton@sijanec.eu>
Date: Thu, 17 Nov 2022 00:21:55 +0100
Subject: fiz/vaje/{3..4}

---
 fiz/vaje/3/dokument.lyx | 1073 +++++++++++++++++++++++++++++++++++++++++++++++
 fiz/vaje/3/meritev.tsv  |    8 +
 2 files changed, 1081 insertions(+)
 create mode 100644 fiz/vaje/3/dokument.lyx
 create mode 100644 fiz/vaje/3/meritev.tsv

(limited to 'fiz/vaje/3')

diff --git a/fiz/vaje/3/dokument.lyx b/fiz/vaje/3/dokument.lyx
new file mode 100644
index 0000000..194d065
--- /dev/null
+++ b/fiz/vaje/3/dokument.lyx
@@ -0,0 +1,1073 @@
+#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"
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+\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
+Energija prožne vzmeti
+\end_layout
+
+\begin_layout Author
+
+\noun on
+Anton Luka Šijanec
+\end_layout
+
+\begin_layout Date
+16.
+ november 2022
+\end_layout
+
+\begin_layout Abstract
+Poročilo tretje vaje pri predmetu 
+\noun on
+F41
+\noun default
+ na Gimnaziji Bežigrad v 4.
+ letniku.
+ Vaja je potekala 13.
+ oktobra 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
+S pomočjo prožne vzmeti poženi leseno klado po vodoravni podlagi in opazuj,
+ na kakšni poti se ustavi.
+ Iz meritev določi koeficient vzmeti.
+\end_layout
+
+\begin_layout Enumerate
+Koeficient vzmeti določi tudi s pomočjo elektronske merilne tehtnice in
+ primerjaj obe vredosti.
+\end_layout
+
+\begin_layout Section
+Potrebščine
+\end_layout
+
+\begin_layout Itemize
+cev iz pleksi stekla z zatičem
+\end_layout
+
+\begin_layout Itemize
+vzmet
+\end_layout
+
+\begin_layout Itemize
+lesena klada
+\end_layout
+
+\begin_layout Itemize
+silomer
+\end_layout
+
+\begin_layout Itemize
+merilni trak
+\end_layout
+
+\begin_layout Itemize
+elektronska tehtnica
+\end_layout
+
+\begin_layout Section
+Potek dela
+\end_layout
+
+\begin_layout Subsection
+Izstreljevanje klade
+\begin_inset CommandInset label
+LatexCommand label
+name "subsec:Izstreljevanje-klade"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Vzmet vstavi v cev iz pleksi stekla in zatič namesti v tako lego, da bo
+ iz cevi gledalo 
+\begin_inset Formula $\SI{3}{\centi\meter}$
+\end_inset
+
+ vzmeti.
+\end_layout
+
+\begin_layout Standard
+Pred vzmet postavi leseno klado in s klado stisni vzmet tako, da bo vsa
+ v cevi.
+\end_layout
+
+\begin_layout Standard
+Klado spusti in izmeri, kako daleč se premakne (
+\begin_inset Formula $s$
+\end_inset
+
+).
+ Meritev ponovi vsaj petkrat.
+\end_layout
+
+\begin_layout Standard
+Prestavi zatič za eno luknjo tako, da bo iz cevi gledal 
+\begin_inset Formula $\SI{1}{\centi\meter}$
+\end_inset
+
+ daljši kos vzmeti in ponovno izstreli klado.
+ Poskus ponavljaj na enak način z različnimi legami zatiča tako, da gleda
+ pri vsaki naslednji ponovitvi iz cevi 
+\begin_inset Formula $\SI{1}{\centi\meter}$
+\end_inset
+
+ daljši del vzmeti.
+ Vsako meritev petkrat ponovi.
+ Meritve zaključiš pri tisti dolžini vzmeti, ko klada doseže rob mize.
+\end_layout
+
+\begin_layout Standard
+Nariši graf premika klade po izstrelitvi (
+\begin_inset Formula $s$
+\end_inset
+
+) v odvisnosti od deformacije vzmeti pred izstrelitvijo (
+\begin_inset Formula $x$
+\end_inset
+
+) ter graf 
+\begin_inset Formula $s(x^{2})$
+\end_inset
+
+.
+ Iz naklona drugega grafa in izmerjene sile trenja izračunaj koeficient
+ uporabljene vzmeti.
+ Tako izračunani koeficient primerjaj z vrednostjo, ki si jo dobil pri meritvi
+ 
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "subsec:Določanje-koeficienta-s-tehtnico"
+plural "false"
+caps "false"
+noprefix "false"
+
+\end_inset
+
+.
+\begin_inset Formula 
+\[
+m_{\text{{klade}}}=\SI{193}{\gram}
+\]
+
+\end_inset
+
+
+\begin_inset Formula 
+\[
+m_{\text{{pleksi}}}=\SI{63,6}{\gram}
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula 
+\[
+m_{\text{{vzmeti}}}=\SI{13,7}{\gram}
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula 
+\[
+l_{\text{{vzmeti}}}=\SI{16,7}{\centi\meter}
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula 
+\[
+l_{\text{{pleksi}}}=\SI{25}{\centi\meter}
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula 
+\[
+l_{\text{{pleksi}}_{\text{{luknja0}}}}=\SI{8}{\centi\meter}
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula 
+\[
+l_{\text{{pleksi}}_{\text{{\Delta med\ luknjami}}}}=\SI{1}{\centi\meter}
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Vleka klade
+\end_layout
+
+\begin_layout Standard
+Z elastiko pripni na klado silomer in izmeri silo trenja pri premikanju
+ klade po mizi.
+ Oceni napako meritve.
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula 
+\[
+F_{\text{{lepenja}}}=\SI{0,9}{\newton}
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula 
+\[
+F_{\text{{trenja}}}=\SI{0,7}{\newton}
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula 
+\[
+\overline{{F}}x=E=\frac{{1}}{2}kx^{2}=F_{\text{{trenja}}}s\rightarrow k=2\frac{{F_{\text{{trenja}}}s}}{x^{2}}
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status open
+
+\begin_layout Plain Layout
+
+
+\backslash
+begin{lstlisting}
+\end_layout
+
+\begin_layout Plain Layout
+
+fit (x*q)**2 "meritev.tsv" using 2:4 via q
+\end_layout
+
+\begin_layout Plain Layout
+
+fit (x*p) 
+\begin_inset Quotes gld
+\end_inset
+
+meritev.tsv
+\begin_inset Quotes grd
+\end_inset
+
+ using 3:4 via p
+\end_layout
+
+\begin_layout Plain Layout
+
+
+\backslash
+end{lstlisting}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Naklonski kot premice je 
+\begin_inset Formula $p=\SI{35,1}{\per\meter}\pm\SI{0,4462}{\per\meter}$
+\end_inset
+
+, koeficient vzmeti je torej po zgornji enačbi 
+\begin_inset Formula $k=2F_{\text{{trenja}}}p=\SI{51,2568}{\kilo\gram\per\second\squared}$
+\end_inset
+
+.
+ Za kvadratno krivuljo pa je 
+\begin_inset Formula $q=6,05079\pm0,03686$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Določanje koeficienta s tehtnico
+\begin_inset CommandInset label
+LatexCommand label
+name "subsec:Določanje-koeficienta-s-tehtnico"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Koeficient vzmeti določi še na drug način: vzmet vstavi v cev iz pleksija,
+ tako da je še nekaj gleda iz cevi in postavi vse skupaj navpično na elektronsko
+ tehtnico.
+ Preberi, kaj kaže tehtnica, ko vzmet v cevi samo stoji na tehtnici in koliko,
+ ko cev pritisneš navzdol, da se vzmet skrči.
+ Iz obeh odčitanih vrednosti in deformacije vzmeti izračunaj koeficient
+ vzmeti.
+ Meritev ponovi za vsaj štiri različne deformacije vzmeti.
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula 
+\[
+k=\frac{F}{x}=\frac{{m_{\text{{kot\ jo\ kaže\ tehtnica}}}g}}{x}
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula 
+\[
+\overline{{k}}=\SI{65,381}{\kilo\gram\per\second\squared}
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Čeprav je red velikosti na oba načina izmerjenega koeficienta vzmeti enak,
+ se pojavi razlika; predvidevam, da zato, ker se klada ustavi nekoliko prej,
+ kot bi se, če lepenja ne bi bilo.
+ Lepenje, izmerjeno 
+\begin_inset Formula $\SI{0,9}{\newton},$
+\end_inset
+
+ povzroči, da se telo ustavi prej, čeprav tega ne upoštevam pri računanju
+ energij, zato izgleda, kakor da je bilo vanjo vložene več energije.
+\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="8" columns="5">
+<features tabularvalignment="middle">
+<column alignment="center" valignment="top">
+<column alignment="center" valignment="top">
+<column alignment="center" valignment="top">
+<column alignment="center" valignment="top">
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+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $n_{\text{{luknje}}}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
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+\begin_layout Plain Layout
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+\end_inset
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+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
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+\begin_layout Plain Layout
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+\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 $m_{\text{{kot\ jo\ kaže\ tehtnica}}}\left[\si{\gram}\right]$
+\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 $k_{\text{{iz\ naloge\ \ref{subsec:Dolo=00003D00003D00010Danje-koeficienta-s-tehtnico}}}}\left[\si{\kilo\gram\per\second\squared}\right]$
+\end_inset
+
+
+\end_layout
+
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+\begin_layout Plain Layout
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+\begin_layout Plain Layout
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+\begin_layout Plain Layout
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+\begin_layout Plain Layout
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+\begin_inset Caption Standard
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+\begin_layout Plain Layout
+Meritve
+\end_layout
+
+\end_inset
+
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+\end_layout
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+\end_layout
+
+\begin_layout Standard
+\begin_inset Float figure
+placement H
+wide false
+sideways false
+status open
+
+\begin_layout Plain Layout
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+\begin_inset ERT
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+\backslash
+begin{tikzpicture}
+\end_layout
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+begin{axis}[width=0.75
+\backslash
+textwidth, scale only axis, ylabel=$s$, domain=0:0.1, ytick pos=left, samples=256
+, xlabel=$
+\backslash
+color{red}x
+\backslash
+color{black}$, xtick pos=bottom, ylabel=$s$]
+\end_layout
+
+\begin_layout Plain Layout
+
+
+\backslash
+addplot[red, only marks] table [x=x, y=s] {meritev.tsv};
+\end_layout
+
+\begin_layout Plain Layout
+
+
+\backslash
+addplot[green] (x, {((x*(6.05079+0.03686))^2});
+\end_layout
+
+\begin_layout Plain Layout
+
+
+\backslash
+addplot[green] (x, {((x*(6.05079-0.03686))^2});
+\end_layout
+
+\begin_layout Plain Layout
+
+
+\backslash
+addplot[red] (x, {((x*(6.05079))^2});
+\end_layout
+
+\begin_layout Plain Layout
+
+
+\backslash
+end{axis}
+\end_layout
+
+\begin_layout Plain Layout
+
+
+\backslash
+begin{axis}[width=0.75
+\backslash
+textwidth, scale only axis, xlabel near ticks, domain=0:0.01, samples=16,
+ xtick pos=bottom, xtick pos=top, axis x line*=top, xlabel=$x^2$]
+\end_layout
+
+\begin_layout Plain Layout
+
+
+\backslash
+addplot[only marks] table [x=x2, y=s] {meritev.tsv};
+\end_layout
+
+\begin_layout Plain Layout
+
+
+\backslash
+addplot[green] (x, {x*(36.612+0.4462)});
+\end_layout
+
+\begin_layout Plain Layout
+
+
+\backslash
+addplot[green] (x, {x*(36.612-0.4462)});
+\end_layout
+
+\begin_layout Plain Layout
+
+
+\backslash
+addplot[black] (x, {x*36.612});
+\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 $s(x)$
+\end_inset
+
+ in 
+\begin_inset Formula $s(x^{2})$
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_body
+\end_document
diff --git a/fiz/vaje/3/meritev.tsv b/fiz/vaje/3/meritev.tsv
new file mode 100644
index 0000000..0165866
--- /dev/null
+++ b/fiz/vaje/3/meritev.tsv
@@ -0,0 +1,8 @@
+n	x	x2	s	m
+0	0.03	0.0009	0.028	190
+1	0.04	0.0016	0.05	260
+2	0.05	0.0025	0.096	340
+3	0.06	0.0036	0.13	400
+4	0.07	0.0049	0.174	470
+5	0.08	0.0064	0.24	540
+6	0.09	0.0081	0.297	620
-- 
cgit v1.2.3