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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
\noun default
 na Gimnaziji Bežigrad v 4.
 letniku.
 Vaja je potekala 10.
 novembra 2022.
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\begin_layout Section
Potrebna oprema
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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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S poskusom preveriti veljavnost drugega Newtonovega zakona za kroženje.
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Potek meritve
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Izmeri maso uteži in maso zamaška.
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<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
89,095452
\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\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