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--- electrical_engineering_1:task_239xqp7zjr32bv4a_with_calculation [2023/04/03 12:38] – angelegt mexleadmin
+++ electrical_engineering_1:task_239xqp7zjr32bv4a_with_calculation [Unbekanntes Datum] (aktuell) – gelöscht - Externe Bearbeitung (Unbekanntes Datum) 127.0.0.1
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-{{tag>conversions speed energy power chapter1_1}}
-{{include_n>100}}
-#@TaskTitle_HTML@##@Lvl_HTML@#~~#@ee1_taskctr#~~  Conversions: Speed, Energy, and Power                   #@TaskText_HTML@#
-Convert the following values step by step:
-.  A vehicle speed of $80.00~{\rm {km}\over{h}}$ in ${\rm {m}\over{s}}$
-#@HiddenBegin_HTML~f1, Fast Solution~@#
-\begin{align*}
-v = 80.00~{\rm {km}\over{h}} \qquad \rightarrow \qquad {{\rm {numerical~value}}\over{3.6}} \qquad \rightarrow \qquad
-v = 22.22~{\rm { m}\over{s}}
-\end{align*}
-#@HiddenEnd_HTML@#
-#@PathBegin_HTML~1~@#
-\begin{align*}
-v &= 80.00~{\rm {km}\over{h}} = 80~{\rm {1'000~m}\over{3'600~s}} = 80~{\rm {m}\over{3.6~s}} \\
-  &= 22.22~{\rm {m}\over{s}}
-\end{align*}
-#@PathEnd_HTML@#
-#@ResultBegin_HTML~1~@#
-\begin{align*}
-v = 22.22~{\rm {m}\over{s}}
-\end{align*}
-#@ResultEnd_HTML@#
-. An energy of $60.0~{\rm J}$ in ${\rm kWh}$ ($1~{\rm J} = 1~{\rm Joule} = 1~{\rm Watt}\cdot {\rm second}$).
-#@PathBegin_HTML~2~@#
-\begin{align*}
-P = 60.0~{\rm J} = 60.0~{\rm Ws} = 0.06~{\rm kWs} = 0.0000167~{\rm kWh}= 1.67 \cdot 10^{-5}~{\rm kWh}
-\end{align*}
-#@PathEnd_HTML@#
-#@ResultBegin_HTML~2~@#
-\begin{align*}
-P = 1.67 \cdot 10^{-5}~{\rm kWh}
-\end{align*}
-#@ResultEnd_HTML@#
-. The number of electrolytically deposited single positively charged copper ions of $1.2 ~\rm Coulombs$ (a copper ion has the charge of about $1.6 \cdot 10^{-19}{\rm C}$)
-#@PathBegin_HTML~3~@#
-\begin{align*}
-n_{\rm ions}= {{{\rm charge}}\over{{\rm charge\,per\,ion}}}={{1.2~{\rm C}}\over{1.6\cdot10^{-19}~{\rm C/ion}}}=7.5 \cdot 10^{18}~{\rm ions}
-\end{align*}
-#@PathEnd_HTML@#
-#@ResultBegin_HTML~3~@#
-\begin{align*}
-n_{\rm ions}= 7.5 \cdot 10^{18}~{\rm ions}
-\end{align*}
-#@ResultEnd_HTML@#
-. Absorbed energy of a small IoT consumer, which consumes $1~{\rm µW}$ uniformly in $10 ~\rm days$
-#@PathBegin_HTML~4~@#
-\begin{align*}
-~{\rm days} &= 10 \cdot {{24 ~\rm h}\over{1 ~\rm day}} \cdot {{60 ~\rm min}\over{1 ~\rm h}} \cdot {{60 ~\rm s}\over{1 ~\rm min}} \\
-               &= 10 \cdot   24                           \cdot   60                           \cdot   60~{\rm s} \\
-               &= 864'000 ~{\rm s} \\ \\
-W_{\rm absorbed} &= 1~{\rm µW} \cdot 864'000~{\rm s} \\
-                &= 864'000~{\rm µWs} \\
-                &= 864~{\rm mWs}     \\
-                &= 0.864~{\rm Ws}    \\
-                &= 0.864~{\rm J}
-\end{align*}
-#@PathEnd_HTML@#
-#@ResultBegin_HTML~4~@#
-\begin{align*}
-W_{\rm absorbed} = 0.864~{\rm Ws} = 0.864~{\rm J}
-\end{align*}
-#@ResultEnd_HTML@#
-#@TaskEnd_HTML@#

conversions speed energy power chapter1 1