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\begin_body
\begin_layout Title
Kotaljenje kroglice po klancu
\end_layout
\begin_layout Author
\noun on
Anton Luka Šijanec
\end_layout
\begin_layout Date
3.
oktober 2022
\end_layout
\begin_layout Abstract
Poročilo druge vaje pri predmetu
\noun on
F41
\noun default
na Gimnaziji Bežigrad v 4.
letniku.
Vaja je potekala 15.
septembra 2022.
\end_layout
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LatexCommand tableofcontents
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\end_layout
\begin_layout Section
Naloga
\end_layout
\begin_layout Enumerate
Dokaži, da je kotaljenje kroglice po klancu enakomerno pospešeno gibanje.
\end_layout
\begin_layout Enumerate
Za gibanje kroglice po klancu navzdol določi povprečno hitrost in pospešek
pri kotaljenju.
Določi tudi napako obeh količin.
\end_layout
\begin_layout Enumerate
Dobljeni pospešek primerjaj s pospeškom za telo, ki bi brez trenja drselo
po klancu z enakom naklonom.
\end_layout
\begin_layout Section
Potrebščine
\end_layout
\begin_layout Itemize
aluminijast profil dolžine
\begin_inset Formula $\SI{1}{\meter}$
\end_inset
\end_layout
\begin_layout Itemize
kovinska kroglica
\end_layout
\begin_layout Itemize
merilna ura
\end_layout
\begin_layout Itemize
ravnilo ali merilni trak
\end_layout
\begin_layout Section
Potek dela
\end_layout
\begin_layout Subsection
Spreminjanje lege po klancu kotaleče se kroglice s časom
\end_layout
\begin_layout Enumerate
Kroglico spusti po klancu in izmeri, koliko časa kroglica potuje prvih
\begin_inset Formula $\SI{4,0}{\centi\meter}$
\end_inset
,
\begin_inset Formula $\SI{16}{\centi\meter}$
\end_inset
,
\begin_inset Formula $\SI{36}{\centi\meter}$
\end_inset
in
\begin_inset Formula $\SI{100}{\centi\meter}$
\end_inset
.
Vse meritve zapiši v ustrezno tabelo.
Nariši graf
\begin_inset Formula $x\left(t\right)$
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.
Za kakšno gibanje gre? Kako lahko to dokažeš?
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Čas, potreben za dosego določenih točk
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Gre za enakomerno pospešeno gibanje, kar je razvidno iz dejstva, da
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raste s kvadratom
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.
Če torej lineariziramo,
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raste linearno s
\begin_inset Formula $t^{2}.$
\end_inset
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\begin_layout Enumerate
Nariši graf, iz kategega lahko razbereš pospešek gibanja, ter določi pospešek.
Kako lahko iz grafa oceniš napako pospeška?
\begin_inset Newline newline
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S programom
\family typewriter
gnuplot
\family default
izračunamo enačbi krivulj, ki se točkam najbolj prilegajo:
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begin{lstlisting}
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fit sqrt(x*a) "podatki.tsv" using 1:6 via a
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fit (x*b)
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podatki.tsv
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using 1:7 via b
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end{lstlisting}
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in dobimo vrednosti parametrov
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s standardno napako
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oziroma
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in
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s standardno napako
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oziroma
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.
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je koeficient premice na grafu
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, torej iskani pospešek.
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Standardna napaka pospeška je
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Standardni odklon se izračuna po enačbi
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begin{tikzpicture}
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begin{axis}[width=0.75
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color{red}t
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Grafa
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in
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v odvisnosti od
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.
Čas se tukaj sicer neobičajno pojavi na ordinatni osi, kar je smiselno,
saj je to izmerjena količina.
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Čas, potreben za kotaljenje kroglice po celotni dolžini klanca
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\begin_layout Enumerate
Kroglico spusti po rahlo nagnjenem klancu ter meri čas gibanja.
Pazi, da ta čas ni prekratek.
Meritev ponovi vsaj osemkrat, izračunaj povprečni čas ter zapiši rezultat
meritve z absolutno in relativno napako.
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Ne pozabi izmeriti naklonskega kota klanca!
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\[
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status open
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\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset Formula $t_{7}\left[\si{\second}\right]$
\end_inset
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset Formula $t_{8}\left[\si{\second}\right]$
\end_inset
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset Formula $\overline{{t}}\left[\si{\second}\right]$
\end_inset
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset Formula $\sigma_{\overline{{t}}}\left[\si{\second}\right]$
\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
\begin_inset Formula $\sigma_{\overline{{t}}}:\overline{{t}}\left[\si{\second\per\second}\right]$
\end_inset
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
4,3
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
3,9
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
3,8
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
3,8
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
4,2
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
3,8
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
3,7
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
3,8
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
3,9125
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
0,20
\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
\begin_inset Formula $5,18\%$
\end_inset
\end_layout
\end_inset
</cell>
</row>
</lyxtabular>
\end_inset
\end_layout
\begin_layout Plain Layout
\begin_inset Caption Standard
\begin_layout Plain Layout
Čas, potreben za spust kroglice po klancu nizdol.
\end_layout
\end_inset
\end_layout
\end_inset
\end_layout
\begin_layout Enumerate
Izračunaj povprečno hitrost ter zapiši rezultat z absolutno in relativno
napako.
\begin_inset Formula
\[
\overline{v}=\overline{{t}}^{-1}=\SI{0,255591}{\meter\per\second}\left(1\pm0,0518\right)=\SI{0,255591}{\meter\per\second}\pm\SI{0,013}{\meter\per\second}
\]
\end_inset
\end_layout
\begin_layout Enumerate
Izračunaj pospešek ter zapiši rezultat z absolutno in relativno napako.
\begin_inset Formula
\[
v_{\text{{max}}}=2\overline{{v}}
\]
\end_inset
\begin_inset Formula
\[
\overline{{a}}=\frac{v_{\text{{max}}}}{\overline{{t}}}=\SI{0,065326}{\meter\per\second\squared}1\pm2\cdot0,0518=\SI{0,065326}{\meter\per\second\squared}\pm\SI{0,003384}{\meter\per\second\squared}
\]
\end_inset
\end_layout
\begin_layout Subsection
Izračun pospeška po klancu brez trenja drsečega telesa
\end_layout
\begin_layout Standard
Izračunaj pospešek za telo, ki bi brez trenja drselo po klancu iz naloge
\begin_inset CommandInset ref
LatexCommand ref
reference "subsec:Čas,-potreben-za"
plural "false"
caps "false"
noprefix "false"
\end_inset
, primerjaj rezultata ter zapiši ugotovitve.
\end_layout
\begin_layout Standard
\begin_inset Formula
\[
F_{g}\tan\phi=F_{d}\rightarrow\cancel{{m}}g(\sin\phi=0,02)=\cancel{m}a=\SI{0,1962}{\meter\per\second\squared}
\]
\end_inset
\end_layout
\begin_layout Standard
Kroglica med premikanjem nekaj energije porablja tudi za vrtenje — to je
moja hipoteza, zakaj je pospešek drsečega telesa večji od izmerjenega pospeška
kotalegeča se telesa.
\end_layout
\end_body
\end_document
