From d4422f27c424cce84d8d0a1f40ab65ef07d8376e Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Anton=20Luka=20=C5=A0ijanec?= Date: Sat, 20 Nov 2021 20:25:59 +0100 Subject: f31 naloga --- .gitignore | 1 + Makefile | 5 +- fiz/matura/.gitignore | 1 - fiz/matura/klanec.tex | 126 +++++++++++++++++++++++++++++++++++++++++++++----- zgo/zvezek.md | 2 +- 5 files changed, 120 insertions(+), 15 deletions(-) delete mode 100644 fiz/matura/.gitignore diff --git a/.gitignore b/.gitignore index 34e8fae..b583dd9 100644 --- a/.gitignore +++ b/.gitignore @@ -11,3 +11,4 @@ *.toc *.bbl *.blg +*.docx diff --git a/Makefile b/Makefile index 8bf8275..c356e47 100644 --- a/Makefile +++ b/Makefile @@ -1,6 +1,7 @@ +SHELL := /bin/bash dirs := $(subst . , ,$(subst /Makefile,,$(shell find -name Makefile))) pdfs := $(subst .md,.pdf,$(shell find -name *.md)) -texs := $(subst .tex,.pdf,$(shell find -name dokument.tex)) +texs := $(subst .tex,.pdf,$(shell find -name *.tex)) .PHONY: clean default default: $(dirs) $(pdfs) $(texs) $(dirs): @@ -9,7 +10,7 @@ $(dirs): pandoc -V geometry:margin=1cm $< -o $@ %.pdf: %.tex @echo za tole rabiš moje magične skripte - cd $(subst dokument.pdf,,$@) && ~/projects/doc/f5ff.sh dokument && biber dokument && ~/projects/doc/f5ff.sh dokument + n=`rev <<< $@ | cut -d/ -f1 | cut -d. -f2- | rev` && cd `rev <<< $@ | cut -d/ -f2- | rev` && ~/projects/doc/f5ff.sh $$n && (test -e `rev <<< $@ | cut -d. -f2- | rev`.bib && biber $$n ||:) && ~/projects/doc/f5ff.sh $$n clean: @echo cleaning $(dirs) for dir in $(dirs); do \ diff --git a/fiz/matura/.gitignore b/fiz/matura/.gitignore deleted file mode 100644 index e050548..0000000 --- a/fiz/matura/.gitignore +++ /dev/null @@ -1 +0,0 @@ -*.docx diff --git a/fiz/matura/klanec.tex b/fiz/matura/klanec.tex index fef48b0..cb02959 100644 --- a/fiz/matura/klanec.tex +++ b/fiz/matura/klanec.tex @@ -9,9 +9,13 @@ \usepackage[hidelinks,unicode]{hyperref} \usepackage{datetime} \usepackage{tkz-euclide} -\sisetup{output-decimal-marker = {,}, quotient-mode=fraction, per-mode=fraction} % per-mode=symbol +\usepackage{amssymb} +% \sisetup{output-decimal-marker = {,}, quotient-mode=fraction, per-mode=fraction} % frac način +% \sisetup{output-decimal-marker = {,}, quotient-mode=fraction, per-mode=symbol} % poševnica način +\sisetup{output-decimal-marker = {,}, quotient-mode=fraction} % na -1 način \settimeformat{hhmmsstime} \newcommand{\razhroscevanje}{1} +\newcommand{\razhroscevanjeg}{0} % grafično razhroščevanje \makeatletter \newcommand{\xslalph}[1]{\expandafter\@xslalph\csname c@#1\endcsname} \newcommand{\@xslalph}[1]{% @@ -31,41 +35,141 @@ Rešitev ponedeljkove naloge pri maturitetni fiziki. \end{abstract} \tableofcontents \section{Naloga} +\newcommand{\njuton}{2} +\newcommand{\alfa}{25} +\newcommand{\koef}{0,8} +\subsection{Navodilo} +Na klancu z naklonom $\measuredangle{\alpha}=\ang{\alfa}$ je telo z maso $m=\SI{\njuton}{\kilo\gram}$. Gravitacijski pospešek je $g=\SI{10}{\meter\per\second\squared}$. Koeficient lepenja telesa s klancem je $k_l=\koef$. Kolikšna je največja sila $F_r$, s katero lahko telo vzporedno s klancem vlečemo navkreber, da le-to ne bo zdrsnilo? Kolikšen je največji kot $\measuredangle{\alpha}$, pri katerem brez $F_r$ telo ne bo zdrsnilo? +\subsection{Skice} +\subsubsection{Privzeti pogoji} \begin{center} \begin{tikzpicture} - \tkzDefPoint(0,0){A} \tkzDefPoint(1,0){B} \tkzDefPoint(25:3){C} + \tkzDefPoint(0,0){A} \tkzDefPoint(1,0){B} \tkzDefPoint(\alfa:3){C} \tkzInterLC(C,A)(C,A) \tkzGetPoints{D}{D2} \tkzInterLC(A,C)(D,C) \tkzGetPoints{E2}{E} \tkzInterCC(E,C)(C,E) \tkzGetPoints{F2}{F} \tkzInterCC(A,D)(D,A) \tkzGetPoints{G}{G2} \tkzDefMidPoint(C,G) \tkzGetPoint{H} \tkzDefMidPoint(D,F) \tkzGetPoint{I} - \tkzDefMidPoint(C,I) \tkzGetPoint{J} \tkzDefShiftPointCoord[J](-90:4){K} + \tkzDefMidPoint(C,I) \tkzGetPoint{J} \tkzDefShiftPointCoord[J](-90:\njuton*2){K} \tkzDefLine[parallel=through K](A,C) \tkzGetPoint{L} \tkzDefMidPoint(C,D) \tkzGetPoint{M} \tkzInterLL(J,M)(K,L) \tkzGetPoint{N} \tkzDefMidPoint(C,H) \tkzGetPoint{O} \tkzDefLine[parallel=through K](C,O) \tkzGetPoint{P} \tkzInterLL(P,K)(O,J) \tkzGetPoint{R} - \tkzDefMidPoint(J,K) \tkzGetPoint{S} + \tkzDefMidPoint(J,K) \tkzGetPoint{S} \tkzDefMidPoint(I,D) \tkzGetPoint{T} + \tkzDefShiftPointCoord[T](\alfa:\njuton*1){U} + \tkzDefMidPoint(J,M) \tkzGetPoint{V} \tkzInterLC(V,N)(V,N) \tkzGetPoints{Z}{Z2} + \tkzInterLC(M,D)(V,R) \tkzGetPoints{W}{W2} \tkzDefLine[parallel=through W](M,Z) + \tkzGetPoint{X} \tkzDefLine[parallel=through Z](C,D) \tkzGetPoint{Y} + \tkzInterLL(Z,Y)(W,X) \tkzGetPoint{Q} \tkzDefMidPoint(M,Q) \tkzGetPoint{1} \tkzDrawLine[add = 5 and 6](A,B) \tkzDrawLine[add = 0 and 0](A,E) \tkzDrawLine[dotted](K,N) \tkzDrawLine[dotted](R,K) + \tkzDrawLine[dotted](Q,W) \tkzDrawLine[dotted](Z,Q) \tkzMarkRightAngles(R,J,N C,M,N) \tkzDrawPolygon[fill=red!30, opacity=.3](C,D,I,H) \tkzFillAngle[fill=green!30, opacity=.3, size=3](B,A,C) \tkzLabelAngle[pos=2](B,A,C){$\alpha$} \tkzDrawSegments[->](J,K) \tkzLabelLine[left, pos=.69](J,K){$\vec{F_g}$} - \tkzDrawSegments[->](J,N) \tkzLabelLine[above right](J,N){$\vec{F_s}$} - \tkzDrawSegments[->](J,R) \tkzLabelLine[above](J,R){$\vec{F_d}$} + \tkzDrawSegments[->, dashed](J,N) \tkzLabelLine[above right](J,N){$\vec{F_s}$} + \tkzDrawSegments[->, dashed](J,R) \tkzLabelLine[above](J,R){$\vec{F_d}$} + % \tkzDrawSegments[->](T,U) \tkzLabelLine[above](T,U){$\vec{F_r}$} + \tkzDrawSegments[->, dashed, color=blue](M,Z) \tkzLabelLine[above](M,Z){$\vec{F_0}$} + \tkzDrawSegments[->, dashed, color=cyan](M,W) \tkzLabelLine[above](M,W){$\vec{F_l}$} + \tkzDrawSegments[->](M,Q) \tkzLabelLine[left](M,Q){$\vec{F_p}$} \tkzDrawPoint[shape=cross out, color=red, size=12](S) -\if\razhroscevanje1 - %\tkzDrawPoints(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,R,S) - %\tkzLabelPoints(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,R,S) + \tkzDrawPoint[shape=cross out, color=red, size=12](1) +\if\razhroscevanjeg1 + \tkzDrawPoints(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,R,S,T,U,V,Z,W,X,Y,Q,1) + \tkzLabelPoints(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,R,S,T,U,V,Z,W,X,Y,Q,1) +\fi +\end{tikzpicture} +\end{center} +\subsubsection{Vleka navkreber} +\begin{center} +\begin{tikzpicture} + \tkzDefPoint(0,0){A} \tkzDefPoint(1,0){B} \tkzDefPoint(\alfa:3){C} + \tkzInterLC(C,A)(C,A) \tkzGetPoints{D}{D2} \tkzInterLC(A,C)(D,C) \tkzGetPoints{E2}{E} + \tkzInterCC(E,C)(C,E) \tkzGetPoints{F2}{F} \tkzInterCC(A,D)(D,A) \tkzGetPoints{G}{G2} + \tkzDefMidPoint(C,G) \tkzGetPoint{H} \tkzDefMidPoint(D,F) \tkzGetPoint{I} + \tkzDefMidPoint(C,I) \tkzGetPoint{J} \tkzDefShiftPointCoord[J](-90:\njuton*2){K} + \tkzDefLine[parallel=through K](A,C) \tkzGetPoint{L} + \tkzDefMidPoint(C,D) \tkzGetPoint{M} \tkzInterLL(J,M)(K,L) \tkzGetPoint{N} + \tkzDefMidPoint(C,H) \tkzGetPoint{O} \tkzDefLine[parallel=through K](C,O) + \tkzGetPoint{P} \tkzInterLL(P,K)(O,J) \tkzGetPoint{R} + \tkzDefMidPoint(J,K) \tkzGetPoint{S} \tkzDefMidPoint(I,D) \tkzGetPoint{T} + \tkzDefShiftPointCoord[T](\alfa:\njuton*1.45){U} + \tkzDefMidPoint(J,M) \tkzGetPoint{V} \tkzInterLC(V,N)(V,N) \tkzGetPoints{Z}{Z2} + \tkzDefShiftPointCoord[M](\alfa:\njuton*-1.45){W} + \tkzDefLine[parallel=through W](M,Z) + \tkzGetPoint{X} \tkzDefLine[parallel=through Z](C,D) \tkzGetPoint{Y} + \tkzInterLL(Z,Y)(W,X) \tkzGetPoint{Q} \tkzDefMidPoint(M,Q) \tkzGetPoint{1} + \tkzDrawLine[add = 5 and 6](A,B) \tkzDrawLine[add = 0 and 0](A,E) + \tkzDrawLine[dotted](K,N) \tkzDrawLine[dotted](R,K) + \tkzDrawLine[dotted](Q,W) \tkzDrawLine[dotted](Z,Q) + \tkzMarkRightAngles(R,J,N C,M,N) + \tkzDrawPolygon[fill=red!30, opacity=.3](C,D,I,H) + \tkzFillAngle[fill=green!30, opacity=.3, size=3](B,A,C) \tkzLabelAngle[pos=2](B,A,C){$\alpha$} + \tkzDrawSegments[->](J,K) \tkzLabelLine[left, pos=.69](J,K){$\vec{F_g}$} + \tkzDrawSegments[->, dashed](J,N) \tkzLabelLine[above right](J,N){$\vec{F_s}$} + \tkzDrawSegments[->, dashed](J,R) \tkzLabelLine[above](J,R){$\vec{F_d}$} + \tkzDrawSegments[->](T,U) \tkzLabelLine[above](T,U){$\vec{F_r}$} + \tkzDrawSegments[->, dashed, color=blue](M,Z) \tkzLabelLine[above](M,Z){$\vec{F_0}$} + \tkzDrawSegments[->, dashed, color=cyan](M,W) \tkzLabelLine[above](M,W){$\vec{F_l}$} + \tkzDrawSegments[->](M,Q) \tkzLabelLine[left](M,Q){$\vec{F_p}$} + \tkzDrawPoint[shape=cross out, color=red, size=12](S) + \tkzDrawPoint[shape=cross out, color=red, size=12](1) +\if\razhroscevanjeg1 + \tkzDrawPoints(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,R,S,T,U,V,Z,W,X,Y,Q,1) + \tkzLabelPoints(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,R,S,T,U,V,Z,W,X,Y,Q,1) +\fi +\end{tikzpicture} +\end{center} +\subsubsection{Največji kot} +\begin{center} +\begin{tikzpicture} + \tkzDefPoint(0,0){A} \tkzDefPoint(1,0){B} \tkzDefPoint(38.6598:3){C} + \tkzInterLC(C,A)(C,A) \tkzGetPoints{D}{D2} \tkzInterLC(A,C)(D,C) \tkzGetPoints{E2}{E} + \tkzInterCC(E,C)(C,E) \tkzGetPoints{F2}{F} \tkzInterCC(A,D)(D,A) \tkzGetPoints{G}{G2} + \tkzDefMidPoint(C,G) \tkzGetPoint{H} \tkzDefMidPoint(D,F) \tkzGetPoint{I} + \tkzDefMidPoint(C,I) \tkzGetPoint{J} \tkzDefShiftPointCoord[J](-90:\njuton*2){K} + \tkzDefLine[parallel=through K](A,C) \tkzGetPoint{L} + \tkzDefMidPoint(C,D) \tkzGetPoint{M} \tkzInterLL(J,M)(K,L) \tkzGetPoint{N} + \tkzDefMidPoint(C,H) \tkzGetPoint{O} \tkzDefLine[parallel=through K](C,O) + \tkzGetPoint{P} \tkzInterLL(P,K)(O,J) \tkzGetPoint{R} + \tkzDefMidPoint(J,K) \tkzGetPoint{S} \tkzDefMidPoint(I,D) \tkzGetPoint{T} + \tkzDefShiftPointCoord[T](38.6598:\njuton*1){U} + \tkzDefMidPoint(J,M) \tkzGetPoint{V} \tkzInterLC(V,N)(V,N) \tkzGetPoints{Z}{Z2} + \tkzInterLC(M,D)(V,R) \tkzGetPoints{W}{W2} \tkzDefLine[parallel=through W](M,Z) + \tkzGetPoint{X} \tkzDefLine[parallel=through Z](C,D) \tkzGetPoint{Y} + \tkzInterLL(Z,Y)(W,X) \tkzGetPoint{Q} \tkzDefMidPoint(M,Q) \tkzGetPoint{1} + \tkzDrawLine[add = 5 and 6](A,B) \tkzDrawLine[add = 0 and 0](A,E) + \tkzDrawLine[dotted](K,N) \tkzDrawLine[dotted](R,K) + \tkzDrawLine[dotted](Q,W) \tkzDrawLine[dotted](Z,Q) + \tkzMarkRightAngles(R,J,N C,M,N) + \tkzDrawPolygon[fill=red!30, opacity=.3](C,D,I,H) + \tkzFillAngle[fill=green!30, opacity=.3, size=3](B,A,C) \tkzLabelAngle[pos=2](B,A,C){$\alpha$} + \tkzDrawSegments[->](J,K) \tkzLabelLine[left, pos=.69](J,K){$\vec{F_g}$} + \tkzDrawSegments[->, dashed](J,N) \tkzLabelLine[above right](J,N){$\vec{F_s}$} + \tkzDrawSegments[->, dashed](J,R) \tkzLabelLine[above](J,R){$\vec{F_d}$} + % \tkzDrawSegments[->](T,U) \tkzLabelLine[above](T,U){$\vec{F_r}$} + \tkzDrawSegments[->, dashed, color=blue](M,Z) \tkzLabelLine[above](M,Z){$\vec{F_0}$} + \tkzDrawSegments[->, dashed, color=cyan](M,W) \tkzLabelLine[above](M,W){$\vec{F_l}$} + \tkzDrawSegments[->](M,Q) \tkzLabelLine[left](M,Q){$\vec{F_p}$} + \tkzDrawPoint[shape=cross out, color=red, size=12](S) + \tkzDrawPoint[shape=cross out, color=red, size=12](1) +\if\razhroscevanjeg1 + \tkzDrawPoints(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,R,S,T,U,V,Z,W,X,Y,Q,1) + \tkzLabelPoints(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,R,S,T,U,V,Z,W,X,Y,Q,1) \fi \end{tikzpicture} \end{center} \section{Rešitev} +\subsection{Vleka navkreber} +$$F_r={F_l}_{maks}=k_l\cdot F_0=k_l\cdot F_g\cos\alpha=\koef\cdot\SI{\njuton}{\newton}\cos\ang{\alfa}=\SI{1,45}{\newton}$$ +\subsection{Največji kot} +Telo ne bo zdrsnilo, če je $$F_d \text{ (dinamična komponenta sile teže)}\leq F_l\text{.}$$ +$$k_l=\frac{{F_l}_{maks}}{F_0} \rightarrow F_g\sin\alpha=F_g\cos\alpha\cdot\koef\rightarrow\alpha=\ang{38,6598}$$ \section{Zaključek} \hologo{LaTeX} izvorna koda dokumenta je objavljena na \url{https://git.sijanec.eu/sijanec/sola-gimb-3}. Za izdelavo dokumenta je potreben \texttt{TeXLive 2020}. \if\razhroscevanje1 \vfill \section*{Razhroščevalne informacije} -Te informacije so generirane, ker je omogočeno razhroščevanje. Pred objavo dokumenta izklopite razhroščevanje. To naredite tako, da nastavite ukaz \texttt{razhroščevanje} na 0 v začetku dokumenta. - Konec generiranje dokumenta \today\ ob \currenttime. Dokument se je generiral R0qK1KR2 \SI{}{\second}. % aaasecgeninsaaa diff --git a/zgo/zvezek.md b/zgo/zvezek.md index 190a88e..0b220f9 100644 --- a/zgo/zvezek.md +++ b/zgo/zvezek.md @@ -68,7 +68,7 @@ Francoska Revolucija (1789-1794) * z ustavo, sprejeto 3. 9. 1791 kralju dajo pravico odložilnega veta in izvršilno oblast in ukinejo osnove revolucije * volilna pravica je odvisna od premoženja, visoko meščanstvo poskrbi zase, ustavna monarhija * oktobra pohod žensk v Versaillu, ko ženske prepričajo kralja, da pride živet v Pariz -* kralj ludvik XVI kljub temu, da je poskušal pobegniti, dobi veliko pravic, lastnina se ščiti +* kralj ludvik XVI kljub temu, da je poskušal pobegniti (ujamejo ga v Vasenessu), dobi veliko pravic, lastnina se ščiti * 14. 9. 1791: ustava je sprejeta - žirondinci-visoki meščani so na oblasti * svoboda, bratstvo in enakost so osnove revolucije * evropska plemiška koalicija izda pilniško izjavo: evropski monarhi podprejo FR kralja Ludvika XVI, dobi izvršilno pravico, podlaga za začetek vojne, saj fevdalna evropa skuša zrušiti revolucijo -- cgit v1.2.3