From 341308c0714028484c4e1ae828c82e8d72ebf2e0 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Anton=20Luka=20=C5=A0ijanec?= Date: Thu, 15 Dec 2022 00:38:24 +0100 Subject: fizvaje56 --- fiz/vaje/5/.gitignore | 1 + fiz/vaje/5/dokument.lyx | 952 ++++++++++++++++++++++++++++++++++++++++++++++++ fiz/vaje/5/meritev.py | 14 + fiz/vaje/5/meritev.tsv | 12 + 4 files changed, 979 insertions(+) create mode 100644 fiz/vaje/5/.gitignore create mode 100644 fiz/vaje/5/dokument.lyx create mode 100755 fiz/vaje/5/meritev.py create mode 100644 fiz/vaje/5/meritev.tsv (limited to 'fiz/vaje/5') diff --git a/fiz/vaje/5/.gitignore b/fiz/vaje/5/.gitignore new file mode 100644 index 0000000..557a91a --- /dev/null +++ b/fiz/vaje/5/.gitignore @@ -0,0 +1 @@ +podatki.tsv diff --git a/fiz/vaje/5/dokument.lyx b/fiz/vaje/5/dokument.lyx new file mode 100644 index 0000000..eeb36ac --- /dev/null +++ b/fiz/vaje/5/dokument.lyx @@ -0,0 +1,952 @@ +#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 diff --git a/fiz/vaje/5/meritev.py b/fiz/vaje/5/meritev.py new file mode 100755 index 0000000..1c6859e --- /dev/null +++ b/fiz/vaje/5/meritev.py @@ -0,0 +1,14 @@ +#!/usr/bin/python3 +import pandas +import math +import sys +m=pandas.read_csv("meritev.tsv", sep='\t') +m.index.name = "idx" +m["t"] = (m["t10"]/10) +m["centripetalni"] = (4*math.pi**2*m["r"]/m["t"]**2) +m["tt"] = (m["t"]**2) +print("sredina:", file=sys.stderr) +print(m.mean(), file=sys.stderr) +print("standardna deviacija", file=sys.stderr) +print(m.std(), file=sys.stderr) +m.to_csv("/dev/stdout", sep="\t") diff --git a/fiz/vaje/5/meritev.tsv b/fiz/vaje/5/meritev.tsv new file mode 100644 index 0000000..a7a199d --- /dev/null +++ b/fiz/vaje/5/meritev.tsv @@ -0,0 +1,12 @@ +r t10 +0.15 2.55 +0.3 3.55 +0.47 5.32 +0.43 4.08 +0.33 3.87 +0.23 2.6 +0.45 4.21 +0.2 3.012 +0.29 2.98 +0.4 3.62 +0.4 4.21 -- cgit v1.2.3