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|
#LyX 2.3 created this file. For more info see http://www.lyx.org/
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\end_header
\begin_body
\begin_layout Title
Ravnovesje togega telesa
\end_layout
\begin_layout Author
Anton Luka Šijanec
\end_layout
\begin_layout Date
2.
oktober 2022
\end_layout
\begin_layout Abstract
Poročilo prve 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
Uvod
\end_layout
\begin_layout Standard
Za ravnovesje togega telesa morata biti izpolnjena dva pogoja:
\end_layout
\begin_layout Enumerate
vsota vseh zunanjih sil mora biti nič in
\end_layout
\begin_layout Enumerate
vsota navorov zunanjih sil mora biti nič.
\end_layout
\begin_layout Section
Naloga
\end_layout
\begin_layout Standard
Opazuj ravnovesje lesene palice v različnih legah!
\end_layout
\begin_layout Section
Potrebščine
\end_layout
\begin_layout Itemize
palica
\end_layout
\begin_layout Itemize
silomer (2)
\end_layout
\begin_layout Itemize
meter
\end_layout
\begin_layout Itemize
geotrikotnik
\end_layout
\begin_layout Section
Potek dela
\end_layout
\begin_layout Subsection
Vleka palice do premika
\begin_inset CommandInset label
LatexCommand label
name "subsec:Vleka-palice-do-premika"
\end_inset
\end_layout
\begin_layout Standard
Palico na levi strani pridrži tako, da se lahko vrti okrog krajišča.
Na desnem krajišču jo vleci s silomerom pravokotno na palico tako, da se
ravno še dotika tal (se še ne dviguje).
Izmeri silo ter rezultat meritve preveri še računsko! Manjkajoče količine
za izračun izmeri.
Izračunaj silo v osi!
\end_layout
\begin_layout Standard
\begin_inset Formula
\[
F_{\text{{izmerjena}}}=\SI{3,4}{\newton}
\]
\end_inset
\end_layout
\begin_layout Standard
\begin_inset Formula
\[
l=\SI{0,6}{\meter}
\]
\end_inset
\end_layout
\begin_layout Standard
\begin_inset Formula
\[
m=\SI{0,6992}{\kilo\gram}
\]
\end_inset
\end_layout
\begin_layout Standard
\begin_inset Formula
\[
x_{F_{g}}=\frac{{l}}{2}
\]
\end_inset
\end_layout
\begin_layout Standard
\begin_inset Formula
\[
F_{\text{{teoretična}}}=mg\frac{{x_{F_{g}}}}{l}=\SI{0,6992}{\kilo\gram}\cdot\SI{9,81}{\kilo\gram\meter\per\second\squared}\cdot\frac{{1}}{2}=\SI{3,429576}{\newton}
\]
\end_inset
\end_layout
\begin_layout Standard
\begin_inset Formula
\[
F_{\text{{os}}}=F_{\text{{teoretična}}}
\]
\end_inset
\end_layout
\begin_layout Subsection
Vleka silomera vedno navpično
\begin_inset CommandInset label
LatexCommand label
name "subsec:Vleka-silomera-vedno-navpično"
\end_inset
\end_layout
\begin_layout Standard
Palico dviguj okoli osi tako, da vlečeš silomer še vedno navpično navzgor.
Silo, s katero vlečeš, izmeri ter jo izračunaj pri kotih
\begin_inset Formula $\ang{30}$
\end_inset
in
\begin_inset Formula $\ang{45}$
\end_inset
.
Kolikšna je v teh primerih sila v osi? Primerjaj rezultate za različne
lege palice in jih komentiraj.
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\begin_layout Standard
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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
kot
\begin_inset Formula $\left[^{\circ}\right]$
\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
sila
\begin_inset Formula $\left[\si{\newton}\right]$
\end_inset
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
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\begin_layout Plain Layout
30
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\end_inset
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\begin_layout Plain Layout
3,5
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\end_inset
</cell>
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45
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\begin_inset Text
\begin_layout Plain Layout
3,4
\end_layout
\end_inset
</cell>
</row>
</lyxtabular>
\end_inset
\end_layout
\begin_layout Plain Layout
\begin_inset Caption Standard
\begin_layout Plain Layout
Izmerjene količine pri različnih kotih pri nalogi
\begin_inset CommandInset ref
LatexCommand ref
reference "subsec:Vleka-silomera-vedno-navpično"
plural "false"
caps "false"
noprefix "false"
\end_inset
\end_layout
\end_inset
\end_layout
\end_inset
\end_layout
\begin_layout Paragraph
Rešitev
\end_layout
\begin_layout Standard
Sila je ne glede na kot enaka in sledi predpisu
\begin_inset Formula $F=\frac{{1}}{2}F_{g}$
\end_inset
, torej je teoretična sila enaka kot pri nalogi
\begin_inset CommandInset ref
LatexCommand ref
reference "subsec:Vleka-palice-do-premika"
plural "false"
caps "false"
noprefix "false"
\end_inset
.
\end_layout
\begin_layout Subsection
Vleka pravokotno na palico
\begin_inset CommandInset label
LatexCommand label
name "subsec:Vleka-pravokotno-na-palico"
\end_inset
\end_layout
\begin_layout Standard
Palico dviguj okrog osi tako, da je silomer ves čas pravokoten na palico.
Izmeri silo pri kotih
\begin_inset Formula $\ang{30}$
\end_inset
in
\begin_inset Formula $\ang{60}.$
\end_inset
Silo tudi izračunaj!
\end_layout
\begin_layout Standard
\begin_inset Float table
placement h
wide false
sideways false
status open
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\begin_inset Text
\begin_layout Plain Layout
kot
\begin_inset Formula $\left[^{\circ}\right]$
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<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
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sila
\begin_inset Formula $\left[\si{\newton}\right]$
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30
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3,1
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60
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1,8
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\begin_layout Plain Layout
\begin_inset Caption Standard
\begin_layout Plain Layout
Izmerjene količine pri različnih kotih pri nalogi
\begin_inset CommandInset ref
LatexCommand ref
reference "subsec:Vleka-pravokotno-na-palico"
plural "false"
caps "false"
noprefix "false"
\end_inset
\end_layout
\end_inset
\end_layout
\end_inset
\end_layout
\begin_layout Standard
\begin_inset Formula
\[
F_{\ang{30}}=\cos\ang{30}\cdot F_{g}\cdot\frac{{1}}{2}=\cos\ang{30}\cdot\SI{6,859152}{\newton}\cdot\frac{{1}}{2}=\SI{2,97009994021}{\newton}
\]
\end_inset
\end_layout
\begin_layout Standard
\begin_inset Formula
\[
F_{\ang{60}}=cos\ang{60}\cdot F_{g}\cdot\frac{{1}}{2}=\SI{1,714788}{\newton}
\]
\end_inset
\end_layout
\begin_layout Subsection
Vleka do premika z vpenjanjem na drugih mestih
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LatexCommand label
name "subsec:Vleka-do-premika-z-vpenjanjem-na-drugih-mestih"
\end_inset
\end_layout
\begin_layout Standard
Vpni silomer za kaveljček ter izmeri in izračnuaj silo, s katero vlečeš
silomer pravokotno na palico, ta pa se ravno še ne dvigne.
Meritve ponovi tudi pri drugem kaveljčku.
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placement h
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\begin_inset Text
\begin_layout Plain Layout
razdalja med osjo in kaveljčkom
\begin_inset Formula $\left[\si{\meter}\right]$
\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
sila
\begin_inset Formula $\left[\si{\newton}\right]$
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<row>
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\begin_inset Text
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0,405
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5,1
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0,455
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4,5
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\end_inset
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\begin_layout Plain Layout
\begin_inset Caption Standard
\begin_layout Plain Layout
Izmerjene količine na različnih kaveljčkih pri nalogi
\begin_inset CommandInset ref
LatexCommand ref
reference "subsec:Vleka-do-premika-z-vpenjanjem-na-drugih-mestih"
plural "false"
caps "false"
noprefix "false"
\end_inset
\end_layout
\end_inset
\end_layout
\end_inset
\end_layout
\begin_layout Standard
\begin_inset Formula
\[
F_{g}x_{F_{g}}=F_{1}x_{1}\rightarrow F_{1}=\frac{F_{g}x_{F_{g}}}{x_{1}}=\SI{5,080853}{\newton}
\]
\end_inset
\end_layout
\begin_layout Standard
\begin_inset Formula
\[
F_{2}=\frac{{F_{g}x_{F_{g}}}}{x_{2}}=\SI{4,5225178022}{\newton}
\]
\end_inset
\end_layout
\begin_layout Subsection
Vleka do premika pod kotom
\begin_inset CommandInset label
LatexCommand label
name "subsec:Vleka-do-premika-pod-kotom"
\end_inset
\end_layout
\begin_layout Standard
Silomer iz primera
\begin_inset CommandInset ref
LatexCommand ref
reference "subsec:Vleka-do-premika-z-vpenjanjem-na-drugih-mestih"
plural "false"
caps "false"
noprefix "false"
\end_inset
vleci pod kotom
\begin_inset Formula $\ang{30}$
\end_inset
glede na palico tako, da se ta ravno še ne dvigne.
Izmeri silo ter jo tudi izračunaj!
\end_layout
\begin_layout Standard
\begin_inset Formula
\[
F_{\text{{izmerjena}}}=\SI{1}{\newton}
\]
\end_inset
\end_layout
\begin_layout Standard
\begin_inset Formula
\[
F=\frac{F_{y}}{\sin\ang{30}}\wedge F_{y}l=F_{g}x_{F_{g}}\rightarrow F=\frac{{F_{g}x_{F_{g}}}}{\sin\ang{30}l}=F_{g}=\SI{6,859152}{\newton}
\]
\end_inset
\end_layout
\begin_layout Standard
Meritev je bila očitno narobe izvedena, saj se
\begin_inset Formula $F_{\text{{izmerjena}}}$
\end_inset
občutno razlikuje od
\begin_inset Formula $F_{\text{{teoretična}}}$
\end_inset
.
\end_layout
\begin_layout Section
Zaključek
\end_layout
\begin_layout Standard
Razen meritve
\begin_inset CommandInset ref
LatexCommand ref
reference "subsec:Vleka-do-premika-pod-kotom"
plural "false"
caps "false"
noprefix "false"
\end_inset
vse izmerjene sile glede na primerjavo s teoretično napovedjo odstopajo
malo — natančne so vsaj na dve decimalni mesti.
\end_layout
\end_body
\end_document
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