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\begin_body

\begin_layout Title
Energija prožne vzmeti
\end_layout

\begin_layout Author

\noun on
Anton Luka Šijanec
\end_layout

\begin_layout Date
16.
 november 2022
\end_layout

\begin_layout Abstract
Poročilo tretje vaje pri predmetu 
\noun on
F41
\noun default
 na Gimnaziji Bežigrad v 4.
 letniku.
 Vaja je potekala 13.
 oktobra 2022.
\end_layout

\begin_layout Standard
\begin_inset CommandInset toc
LatexCommand tableofcontents

\end_inset


\end_layout

\begin_layout Section
Naloga
\end_layout

\begin_layout Enumerate
S pomočjo prožne vzmeti poženi leseno klado po vodoravni podlagi in opazuj,
 na kakšni poti se ustavi.
 Iz meritev določi koeficient vzmeti.
\end_layout

\begin_layout Enumerate
Koeficient vzmeti določi tudi s pomočjo elektronske merilne tehtnice in
 primerjaj obe vredosti.
\end_layout

\begin_layout Section
Potrebščine
\end_layout

\begin_layout Itemize
cev iz pleksi stekla z zatičem
\end_layout

\begin_layout Itemize
vzmet
\end_layout

\begin_layout Itemize
lesena klada
\end_layout

\begin_layout Itemize
silomer
\end_layout

\begin_layout Itemize
merilni trak
\end_layout

\begin_layout Itemize
elektronska tehtnica
\end_layout

\begin_layout Section
Potek dela
\end_layout

\begin_layout Subsection
Izstreljevanje klade
\begin_inset CommandInset label
LatexCommand label
name "subsec:Izstreljevanje-klade"

\end_inset


\end_layout

\begin_layout Standard
Vzmet vstavi v cev iz pleksi stekla in zatič namesti v tako lego, da bo
 iz cevi gledalo 
\begin_inset Formula $\SI{3}{\centi\meter}$
\end_inset

 vzmeti.
\end_layout

\begin_layout Standard
Pred vzmet postavi leseno klado in s klado stisni vzmet tako, da bo vsa
 v cevi.
\end_layout

\begin_layout Standard
Klado spusti in izmeri, kako daleč se premakne (
\begin_inset Formula $s$
\end_inset

).
 Meritev ponovi vsaj petkrat.
\end_layout

\begin_layout Standard
Prestavi zatič za eno luknjo tako, da bo iz cevi gledal 
\begin_inset Formula $\SI{1}{\centi\meter}$
\end_inset

 daljši kos vzmeti in ponovno izstreli klado.
 Poskus ponavljaj na enak način z različnimi legami zatiča tako, da gleda
 pri vsaki naslednji ponovitvi iz cevi 
\begin_inset Formula $\SI{1}{\centi\meter}$
\end_inset

 daljši del vzmeti.
 Vsako meritev petkrat ponovi.
 Meritve zaključiš pri tisti dolžini vzmeti, ko klada doseže rob mize.
\end_layout

\begin_layout Standard
Nariši graf premika klade po izstrelitvi (
\begin_inset Formula $s$
\end_inset

) v odvisnosti od deformacije vzmeti pred izstrelitvijo (
\begin_inset Formula $x$
\end_inset

) ter graf 
\begin_inset Formula $s(x^{2})$
\end_inset

.
 Iz naklona drugega grafa in izmerjene sile trenja izračunaj koeficient
 uporabljene vzmeti.
 Tako izračunani koeficient primerjaj z vrednostjo, ki si jo dobil pri meritvi
 
\begin_inset CommandInset ref
LatexCommand ref
reference "subsec:Določanje-koeficienta-s-tehtnico"
plural "false"
caps "false"
noprefix "false"

\end_inset

.
\begin_inset Formula 
\[
m_{\text{{klade}}}=\SI{193}{\gram}
\]

\end_inset


\begin_inset Formula 
\[
m_{\text{{pleksi}}}=\SI{63,6}{\gram}
\]

\end_inset


\end_layout

\begin_layout Standard
\begin_inset Formula 
\[
m_{\text{{vzmeti}}}=\SI{13,7}{\gram}
\]

\end_inset


\end_layout

\begin_layout Standard
\begin_inset Formula 
\[
l_{\text{{vzmeti}}}=\SI{16,7}{\centi\meter}
\]

\end_inset


\end_layout

\begin_layout Standard
\begin_inset Formula 
\[
l_{\text{{pleksi}}}=\SI{25}{\centi\meter}
\]

\end_inset


\end_layout

\begin_layout Standard
\begin_inset Formula 
\[
l_{\text{{pleksi}}_{\text{{luknja0}}}}=\SI{8}{\centi\meter}
\]

\end_inset


\end_layout

\begin_layout Standard
\begin_inset Formula 
\[
l_{\text{{pleksi}}_{\text{{\Delta med\ luknjami}}}}=\SI{1}{\centi\meter}
\]

\end_inset


\end_layout

\begin_layout Subsection
Vleka klade
\end_layout

\begin_layout Standard
Z elastiko pripni na klado silomer in izmeri silo trenja pri premikanju
 klade po mizi.
 Oceni napako meritve.
\end_layout

\begin_layout Standard
\begin_inset Formula 
\[
F_{\text{{lepenja}}}=\SI{0,9}{\newton}
\]

\end_inset


\end_layout

\begin_layout Standard
\begin_inset Formula 
\[
F_{\text{{trenja}}}=\SI{0,7}{\newton}
\]

\end_inset


\end_layout

\begin_layout Standard
\begin_inset Formula 
\[
\overline{{F}}x=E=\frac{{1}}{2}kx^{2}=F_{\text{{trenja}}}s\rightarrow k=2\frac{{F_{\text{{trenja}}}s}}{x^{2}}
\]

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\backslash
begin{lstlisting}
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fit (x*q)**2 "meritev.tsv" using 2:4 via q
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fit (x*p) 
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meritev.tsv
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\backslash
end{lstlisting}
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\end_inset


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\begin_layout Standard
Naklonski kot premice je 
\begin_inset Formula $p=\SI{35,1}{\per\meter}\pm\SI{0,4462}{\per\meter}$
\end_inset

, koeficient vzmeti je torej po zgornji enačbi 
\begin_inset Formula $k=2F_{\text{{trenja}}}p=\SI{51,2568}{\kilo\gram\per\second\squared}$
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.
 Za kvadratno krivuljo pa je 
\begin_inset Formula $q=6,05079\pm0,03686$
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\begin_layout Subsection
Določanje koeficienta s tehtnico
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\begin_layout Standard
Koeficient vzmeti določi še na drug način: vzmet vstavi v cev iz pleksija,
 tako da je še nekaj gleda iz cevi in postavi vse skupaj navpično na elektronsko
 tehtnico.
 Preberi, kaj kaže tehtnica, ko vzmet v cevi samo stoji na tehtnici in koliko,
 ko cev pritisneš navzdol, da se vzmet skrči.
 Iz obeh odčitanih vrednosti in deformacije vzmeti izračunaj koeficient
 vzmeti.
 Meritev ponovi za vsaj štiri različne deformacije vzmeti.
\end_layout

\begin_layout Standard
\begin_inset Formula 
\[
k=\frac{F}{x}=\frac{{m_{\text{{kot\ jo\ kaže\ tehtnica}}}g}}{x}
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\end_inset


\end_layout

\begin_layout Standard
\begin_inset Formula 
\[
\overline{{k}}=\SI{65,381}{\kilo\gram\per\second\squared}
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\end_inset


\end_layout

\begin_layout Standard
Čeprav je red velikosti na oba načina izmerjenega koeficienta vzmeti enak,
 se pojavi razlika; predvidevam, da zato, ker se klada ustavi nekoliko prej,
 kot bi se, če lepenja ne bi bilo.
 Lepenje, izmerjeno 
\begin_inset Formula $\SI{0,9}{\newton},$
\end_inset

 povzroči, da se telo ustavi prej, čeprav tega ne upoštevam pri računanju
 energij, zato izgleda, kakor da je bilo vanjo vložene več energije.
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Meritve
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begin{axis}[width=0.75
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textwidth, scale only axis, ylabel=$s$, domain=0:0.1, ytick pos=left, samples=256
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color{black}$, xtick pos=bottom, ylabel=$s$]
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