Mathcad Professional 14.0 <description/> <author>Suoregnad</author> <company/> <keywords/> <revisedBy>xxx</revisedBy> </userData> <identityInfo> <revision>2</revision> <documentID>03DD8820-E40E-40F7-8D5F-AEAEA89ED3A6</documentID> <versionID>88617431-5C81-43CD-BAD9-C3AC32D70E3C</versionID> <parentVersionID>00000000-0000-0000-0000-000000000000</parentVersionID> <branchID>00000000-0000-0000-0000-000000000000</branchID> </identityInfo> </metadata> <settings> <presentation> <textRendering> <textStyles> <textStyle name="Normal"> <blockAttr margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit"/> <inlineAttr font-family="Arial" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false" line-through="false" vertical-align="baseline"/> </textStyle> <textStyle name="Überschrift 1"> <blockAttr margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit"/> 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text-align="center" list-style-type="inherit" tabs="inherit"/> <inlineAttr font-family="Times New Roman" font-charset="0" font-size="24" font-weight="bold" font-style="normal" underline="false" line-through="false" vertical-align="baseline"/> </textStyle> <textStyle name="Untertitel" base-style="Titel"> <blockAttr margin-left="0" margin-right="0" text-indent="inherit" text-align="center" list-style-type="inherit" tabs="inherit"/> <inlineAttr font-family="Times New Roman" font-charset="0" font-size="18" font-weight="normal" font-style="normal" underline="false" line-through="false" vertical-align="baseline"/> </textStyle> </textStyles> </textRendering> <mathRendering equation-color="#000"> <operators multiplication="narrow-dot" derivative="derivative" literal-subscript="large" definition="colon-equal" global-definition="triple-equal" local-definition="left-arrow" equality="bold-equal" symbolic-evaluation="right-arrow"/> <mathStyles> <mathStyle name="Variablen" font-family="Times New 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name="Benutzer 6" font-family="Arial" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="Benutzer 7" font-family="Times New Roman" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="Mathematische Textschriftart" font-family="Arial" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false"/> </mathStyles> <dimensionNames mass="Masse" length="Länge" time="Zeit" current="Strom" thermodynamic-temperature="Temperatur" luminous-intensity="Leuchtstärke" amount-of-substance="Stoff" display="false"/> <symbolics derivation-steps-style="vertical-insert" show-comments="false" evaluate-in-place="false"/> <results> <general precision="3" show-trailing-zeros="false" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i" exponential-threshold="3"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="true" simplify-units="true" fractional-unit-exponent="false"/> </results> </mathRendering> <pageModel show-page-frame="false" show-header-frame="false" show-footer-frame="false" header-footer-start-page="1" paper-code="9" orientation="portrait" print-single-page-width="false" page-width="594.75" page-height="842.25"> <margins left="86.4" right="86.4" top="86.4" bottom="86.4"/> <header use-full-page-width="false"/> <footer use-full-page-width="false"/> </pageModel> <colorModel background-color="#fff" default-highlight-color="#ffff80"/> <language math="en" UI="en"/> </presentation> <calculation> <builtInVariables array-origin="0" convergence-tolerance="0.001" constraint-tolerance="0.001" random-seed="1" prn-precision="4" prn-col-width="8"/> <calculationBehavior automatic-recalculation="true" matrix-strict-singularity-check="true" optimize-expressions="false" exact-boolean="false" strings-use-origin="false" zero-over-zero="0"> <compatibility multiple-assignment="MC12" local-assignment="MC12"/> </calculationBehavior> <units> <currentUnitSystem name="si" customized="false"/> </units> </calculation> <ws:editor view-annotations="false" view-regions="false"> <ruler is-visible="false" ruler-unit="cm"/> <plotTemplate> <xy item-idref="1"/> </plotTemplate> <grid granularity-x="6" granularity-y="6"/> </ws:editor> <fileFormat image-type="image/png" image-quality="75" save-numeric-results="true" exclude-large-results="false" save-text-images="false" screen-dpi="96"/> <miscellaneous> <handbook handbook-region-tag-ub="663" can-delete-original-handbook-regions="true" can-delete-user-regions="true" can-print="true" can-copy="true" can-save="true" file-permission-mask="4294967295"/> </miscellaneous> </settings> <regions> <region region-id="662" left="18" top="30.75" width="395.25" height="14.25" align-x="24" align-y="42" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f size="12"> <b>Der Anfang ist für das erläuterte Problem völlig uninteressant.</b> </f> </p> </text> </region> <region region-id="578" left="18" top="62.25" width="404.25" height="24" align-x="43.5" align-y="72" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Magnetische Kraft in Abhängigkeit vom Abstand zur Spule und Weg-Zeit-Verlauf des mag. Antriebs</p> </text> </region> <region region-id="579" left="18" top="98.25" width="75" height="24" align-x="29.25" align-y="108" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">Dauer der ersten </p> <p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">Halbwelle</p> </text> </region> <region region-id="580" left="126" top="105" width="30" height="16.5" align-x="139.5" align-y="114" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define> <ml:id xml:space="preserve" subscript="0">t</ml:id> <ml:apply> <ml:mult style="auto-select"/> <ml:real>0</ml:real> <ml:id xml:space="preserve">s</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="2"/> </region> <region region-id="581" left="234" top="105" width="40.5" height="16.5" align-x="247.5" align-y="114" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define> <ml:id xml:space="preserve" subscript="1">t</ml:id> <ml:apply> <ml:mult style="auto-select"/> <ml:real>35</ml:real> <ml:id xml:space="preserve">μs</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="3"/> </region> <region region-id="582" left="18" top="134.25" width="81" height="12" align-x="29.25" align-y="144" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Strom in der Spule</p> </text> </region> <region region-id="583" left="126" top="135" width="57" height="16.5" align-x="150" align-y="144" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define> <ml:id xml:space="preserve" subscript="max">I</ml:id> <ml:apply> <ml:mult style="auto-select"/> <ml:real>100</ml:real> <ml:id xml:space="preserve">kA</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="4"/> </region> <region region-id="584" left="234" top="128.25" width="88.5" height="31.5" align-x="253.5" align-y="144" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define> <ml:function> <ml:id xml:space="preserve">I</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="max">I</ml:id> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:id xml:space="preserve">π</ml:id> <ml:id xml:space="preserve" subscript="1">t</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="5"/> </region> <region region-id="585" left="126" top="153.75" width="109.5" height="46.5" align-x="154.5" align-y="180" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define> <ml:id xml:space="preserve" subscript="mitte">I</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:minus/> <ml:id xml:space="preserve" subscript="1">t</ml:id> <ml:id xml:space="preserve" subscript="0">t</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:integral auto-algorithm="true" algorithm="adaptive"/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve">I</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:lambda> <ml:bounds> <ml:id xml:space="preserve" subscript="0">t</ml:id> <ml:id xml:space="preserve" subscript="1">t</ml:id> </ml:bounds> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="6"/> </region> <region region-id="586" left="258" top="171" width="74.25" height="16.5" align-x="285.75" align-y="180" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval> <ml:id xml:space="preserve" subscript="mitte">I</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">kA</ml:id> </ml:unitOverride> <ml:result> <ml:unitedValue> <ml:real>63.661977236758133</ml:real> <u:unitMonomial> <u:unitReference unit="kiloampere"/> </u:unitMonomial> </ml:unitedValue> </ml:result> </ml:eval> </math> <rendering item-idref="7"/> </region> <region region-id="587" left="18" top="176.25" width="95.25" height="12" align-x="38.25" align-y="186" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Mittelwert des Stroms</p> </text> </region> <region region-id="588" left="18" top="206.25" width="70.5" height="12" align-x="30.75" align-y="216" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Mag. Feldstärke</p> </text> </region> <region region-id="589" left="126" top="196.5" width="61.5" height="31.5" align-x="154.5" align-y="216" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define> <ml:function> <ml:id xml:space="preserve" subscript="s">H</ml:id> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="mitte">I</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="8"/> </region> <region region-id="590" left="228" top="200.25" width="111.75" height="27.75" align-x="270" align-y="216" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval> <ml:apply> <ml:id xml:space="preserve" subscript="s">H</ml:id> <ml:apply> <ml:mult style="auto-select"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">mm</ml:id> </ml:apply> </ml:apply> <ml:result> <ml:unitedValue> <ml:real>5066059.1821168885</ml:real> <u:unitMonomial> <u:unitReference unit="ampere"/> <u:unitReference unit="meter" power-numerator="-1"/> </u:unitMonomial> </ml:unitedValue> </ml:result> </ml:eval> </math> <rendering item-idref="9"/> </region> <region region-id="591" left="18" top="236.25" width="75" height="12" align-x="27.75" align-y="246" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Mag. Flussdichte</p> </text> </region> <region region-id="592" left="126" top="237" width="66.75" height="16.5" align-x="149.25" align-y="246" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define> <ml:function> <ml:id xml:space="preserve">B</ml:id> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="0">μ</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="s">H</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="10"/> </region> <region region-id="593" left="18" top="272.25" width="77.25" height="12" align-x="30" align-y="282" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Länge des Leiters</p> </text> </region> <region region-id="594" left="126" top="273" width="38.25" height="16.5" align-x="138.75" align-y="282" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define> <ml:id xml:space="preserve" subscript="s">l</ml:id> <ml:apply> <ml:mult style="auto-select"/> <ml:real>0.5</ml:real> <ml:id xml:space="preserve">m</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="11"/> </region> <region region-id="595" left="18" top="302.25" width="76.5" height="12" align-x="29.25" align-y="312" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Breite des Leiters</p> </text> </region> <region region-id="596" left="126" top="303" width="41.25" height="16.5" align-x="141.75" align-y="312" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define> <ml:id xml:space="preserve" subscript="s">b</ml:id> <ml:apply> <ml:mult style="auto-select"/> <ml:real>6</ml:real> <ml:id xml:space="preserve">mm</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="12"/> </region> <region region-id="597" left="126" top="327" width="45" height="16.5" align-x="144" align-y="336" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define> <ml:id xml:space="preserve" subscript="s">A</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="s">l</ml:id> <ml:id xml:space="preserve" subscript="s">b</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="13"/> </region> <region region-id="598" left="204" top="321" width="79.5" height="22.5" align-x="221.25" align-y="336" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval> <ml:id xml:space="preserve" subscript="s">A</ml:id> <ml:result> <ml:unitedValue> <ml:real>0.003</ml:real> <u:unitMonomial> <u:unitReference unit="meter" power-numerator="2"/> </u:unitMonomial> </ml:unitedValue> </ml:result> </ml:eval> </math> <rendering item-idref="14"/> </region> <region region-id="599" left="18" top="332.25" width="80.25" height="12" align-x="30.75" align-y="342" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Fläche des Leiters</p> </text> </region> <region region-id="576" left="18" top="372.75" width="186.75" height="14.25" align-x="24" align-y="384" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f size="12"> <b>Ab hier gehts eigenlich erst los...</b> </f> </p> </text> </region> <region region-id="561" left="18" top="410.25" width="57.75" height="24" align-x="27.75" align-y="420" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Kraft in Abh.</p> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">d. Abstandes</p> </text> </region> <region region-id="562" left="126" top="394.5" width="105" height="43.5" align-x="165" align-y="420" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define> <ml:function> <ml:id xml:space="preserve" subscript="mag">F</ml:id> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="s">A</ml:id> <ml:id xml:space="preserve" subscript="0">μ</ml:id> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="mitte">I</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>8</ml:real> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">π</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:parens> <ml:id xml:space="preserve">x</ml:id> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="15"/> </region> <region region-id="563" left="252" top="410.25" width="248.25" height="12" align-x="258.75" align-y="420" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <b>Zur Vereinfachung: Kraft wirkt konstant über die Zeit</b> </p> </text> </region> <region region-id="564" left="96" top="452.25" width="28.5" height="12" align-x="107.25" align-y="462" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Probe:</p> </text> </region> <region region-id="565" left="132" top="453" width="98.25" height="16.5" align-x="189" align-y="462" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval> <ml:apply> <ml:id xml:space="preserve" subscript="mag">F</ml:id> <ml:apply> <ml:mult style="auto-select"/> <ml:real>10</ml:real> <ml:id xml:space="preserve">mm</ml:id> </ml:apply> </ml:apply> <ml:unitOverride> <ml:id xml:space="preserve">kN</ml:id> </ml:unitOverride> <ml:result> <ml:unitedValue> <ml:real>1.935092065991969</ml:real> <u:unitMonomial> <u:unitReference unit="kilonewton"/> </u:unitMonomial> </ml:unitedValue> </ml:result> </ml:eval> </math> <rendering item-idref="16"/> </region> <region region-id="566" left="24" top="480" width="358.5" height="240.75" align-x="24" align-y="480" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="17"/> <rendering item-idref="18"/> </region> <region region-id="567" left="30" top="758.25" width="85.5" height="12" align-x="42.75" align-y="768" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Masse des Stößels</p> </text> </region> <region region-id="568" left="132" top="759" width="48.75" height="16.5" align-x="152.25" align-y="768" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define> <ml:id xml:space="preserve" subscript="st">m</ml:id> <ml:apply> <ml:mult style="auto-select"/> <ml:real>1.6</ml:real> <ml:id xml:space="preserve">kg</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="19"/> </region> <region region-id="569" left="30" top="782.25" width="380.25" height="24" align-x="53.25" align-y="792" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">Bewegungs-DGL für eine Masse m, die durch den magnetischen Druck beschleunigt wird:</p> </text> </region> <region region-id="570" left="90" top="805.5" width="72.75" height="32.25" align-x="119.25" align-y="822" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply> <ml:equal/> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:lambda> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:id xml:space="preserve">t</ml:id> <ml:id xml:space="preserve" subscript="st">m</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">F</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="20"/> </region> <region region-id="571" left="30" top="848.25" width="37.5" height="12" align-x="45" align-y="858" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Lösung: </p> </text> </region> <region region-id="572" left="84" top="849" width="39.75" height="18" align-x="98.25" align-y="858" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:apply> <ml:mult style="auto-select"/> <ml:real>4</ml:real> <ml:id xml:space="preserve">mm</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="21"/> </region> <region region-id="573" left="84" top="872.25" width="92.25" height="31.5" align-x="115.5" align-y="888" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define> <ml:function> <ml:id xml:space="preserve">D</ml:id> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:id xml:space="preserve">t</ml:id> <ml:id xml:space="preserve" subscript="st">m</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="mag">F</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="22"/> </region> <region region-id="661" left="222" top="902.25" width="146.25" height="132" align-x="225.75" align-y="912" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <b>Problem:</b> </p> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <b>Er erwartet hier für x Unitless, genau so wie er meint D(x,t)<sp count="2"/>sollte einheitenlos sein, dabei soll aber x ein Weg und t eine Zeit sein.</b> </p> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"/> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <b>Komplett ohne Einheiten gehts, wie im Folgenden an einer Beispielrechnung zu sehen ist: </b> </p> </text> </region> <region region-id="574" left="84" top="915" width="99" height="12.75" align-x="95.25" align-y="924" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math error="This value has units: Length, but must have units: Unitless." optimize="false" disable-calc="false"> <ml:define> <ml:id xml:space="preserve">u</ml:id> <ml:apply> <ml:id xml:space="preserve">rkfixed</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:real>0</ml:real> <ml:real>2</ml:real> <ml:real>10</ml:real> <ml:id xml:space="preserve">D</ml:id> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="23"/> </region> <region region-id="650" left="36" top="1040.25" width="245.25" height="12" align-x="44.25" align-y="1050" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Beispielrechnung ohne Einheiten, DGL vom gleichen Typ</p> </text> </region> <region region-id="651" left="36" top="1057.5" width="75" height="29.25" align-x="57" align-y="1074" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:provenance expr-id="1"> <p:originRef doc-id="6EB5619D-D3C9-4F99-9AB6-5B5007F9330C" 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<ml:define> <ml:function> <ml:id xml:space="preserve">f</ml:id> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:div/> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve" subscript="st">m</ml:id> </ml:apply> </ml:define> </ml:provenance> </math> <rendering item-idref="26"> <element-image-map> <box left="1.5" top="0.75" width="44.25" height="30" expr-idref="1"/> </element-image-map> </rendering> </region> <region region-id="654" left="108" top="1100.25" width="44.25" height="33.75" align-x="132" align-y="1116" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:provenance expr-id="1"> <p:originRef doc-id="6EB5619D-D3C9-4F99-9AB6-5B5007F9330C" version-id="CE2C60E0-F88F-4378-BC5B-6B087F1206E3" branch-id="00000000-0000-0000-0000-000000000000" revision-num="2" is-modified="true" region-id="0" href="C:\Dokumente und 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DGL-BSP.xmcd"> <p:hash>85079e422984fa4391adf0d00ef89aac</p:hash> </p:parentRef> <p:comment/> <p:originComment/> <p:contentHash>7b8aea25d085fb5e24cdd2cfa1b4f560</p:contentHash> <ml:define> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:real>4</ml:real> </ml:define> </ml:provenance> </math> <rendering item-idref="28"> <element-image-map> <box left="1.5" top="0.75" width="26.25" height="16.5" expr-idref="1"/> </element-image-map> </rendering> </region> <region region-id="656" left="36" top="1155" width="77.25" height="12.75" align-x="69.75" align-y="1164" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:provenance expr-id="1"> <p:originRef doc-id="6EB5619D-D3C9-4F99-9AB6-5B5007F9330C" version-id="CE2C60E0-F88F-4378-BC5B-6B087F1206E3" branch-id="00000000-0000-0000-0000-000000000000" revision-num="2" is-modified="true" 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