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\begin_layout Title
Centripetalni pospešek
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\begin_layout Author
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Anton Luka Šijanec
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\begin_layout Date
14.
december 2022
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\begin_layout Abstract
Poročilo pete vaje pri predmetu
\noun on
F41
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na Gimnaziji Bežigrad v 4.
letniku.
Vaja je potekala 10.
novembra 2022.
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LatexCommand tableofcontents
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\begin_layout Section
Potrebna oprema
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\begin_layout Itemize
kos plastične cevi
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\begin_layout Itemize
vrvica
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\begin_layout Itemize
zamašek z luknjico
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\begin_layout Itemize
štoparica
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\begin_layout Itemize
ravnilo
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\begin_layout Itemize
tehtnica
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\begin_layout Itemize
uteži
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Cilj naloge
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\begin_layout Standard
S poskusom preveriti veljavnost drugega Newtonovega zakona za kroženje.
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\begin_layout Section
Potek meritve
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Izmeri maso uteži in maso zamaška.
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\[
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Primi za cev in jo vrti tako, da zamašek kroži v vodoravni ravnini s stalno
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Izmeri čas desetih obhodnih časov.
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\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
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