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Lösning 1.5:6 - Versionshistorik
2026-04-08T02:54:03Z
Versionshistorik för denna sida på wikin
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http://wiki.math.se/wikis/forberedandefysik/index.php?title=L%C3%B6sning_1.5:6&diff=2703&oldid=prev
Louwah den 15 december 2017 kl. 10.22
2017-12-15T10:22:59Z
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<td colspan='2' style="background-color: white; color:black;">← Äldre version</td>
<td colspan='2' style="background-color: white; color:black;">Versionen från 15 december 2017 kl. 10.22</td>
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<tr><td colspan="2" class="diff-lineno">Rad 1:</td>
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<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>Båten <del style="color: red; font-weight: bold; text-decoration: none;">undantränger </del><math><del style="color: red; font-weight: bold; text-decoration: none;">0,100 l</del></math> <del style="color: red; font-weight: bold; text-decoration: none;"> vatten, lyftkraften blir då</del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>Båten <ins style="color: red; font-weight: bold; text-decoration: none;">påverkas av en tyngdkraft </ins><math><ins style="color: red; font-weight: bold; text-decoration: none;">F_{\mathrm{mg}} </ins></math> <ins style="color: red; font-weight: bold; text-decoration: none;">och en lyftkraft <math>F_{\mathrm{lyft}} </math> om dessa friläggs och jämvikt råder så syns det att <math>F_{\mathrm{mg}} = F_{\mathrm{lyft}}</math>. Eftersom <math>F = m \cdot g</math> så kan vi skriva: </ins><math>m_<ins style="color: red; font-weight: bold; text-decoration: none;">{\mathrm</ins>{vatten<ins style="color: red; font-weight: bold; text-decoration: none;">}</ins>} \cdot g <ins style="color: red; font-weight: bold; text-decoration: none;">= m_{\mathrm{lera}} </ins>\cdot <ins style="color: red; font-weight: bold; text-decoration: none;">g</math> vilket ger att <math>m_{</ins>\<ins style="color: red; font-weight: bold; text-decoration: none;">mathrm{vatten}} </ins>= <ins style="color: red; font-weight: bold; text-decoration: none;">m_{</ins>\<ins style="color: red; font-weight: bold; text-decoration: none;">mathrm{lera}}<</ins>/<ins style="color: red; font-weight: bold; text-decoration: none;">math> <br/> <br/> Eftersom <math>m = V </ins>\cdot <ins style="color: red; font-weight: bold; text-decoration: none;">\rho <</ins>/<ins style="color: red; font-weight: bold; text-decoration: none;">math> så kan vi skriva: <br/> <math>V_{\mathrm{vatten}} \cdot \rho_{\mathrm{vatten}} </ins>= <ins style="color: red; font-weight: bold; text-decoration: none;">V_{\mathrm{lera}} \cdot \rho_{\mathrm{lera}}</ins></math> <ins style="color: red; font-weight: bold; text-decoration: none;">vilket ger </ins>att<ins style="color: red; font-weight: bold; text-decoration: none;">: </ins><math> <ins style="color: red; font-weight: bold; text-decoration: none;">\rho_</ins>{<ins style="color: red; font-weight: bold; text-decoration: none;">\mathrm{lera}</ins>} = <ins style="color: red; font-weight: bold; text-decoration: none;">\displaystyle\frac{V_{\mathrm{vatten}}\cdot \rho_{\mathrm{vatten}}}{V_{\mathrm{lera}}} </math> <br/><br/> När båten flyter undantränger den <math>\mathrm{</ins>0,100<ins style="color: red; font-weight: bold; text-decoration: none;">\, l}</ins></math> <ins style="color: red; font-weight: bold; text-decoration: none;">vatten, vilket </ins>är <ins style="color: red; font-weight: bold; text-decoration: none;">den volym </ins><math><ins style="color: red; font-weight: bold; text-decoration: none;">V_{\mathrm{vatten}} </math> som ger upphov till lyftkraften <math> F_{\mathrm{lyft}}</math> <br/> När båten sänks undantränger den <math>\mathrm{</ins>0,050<ins style="color: red; font-weight: bold; text-decoration: none;">\, </ins>l<ins style="color: red; font-weight: bold; text-decoration: none;">}</math> vatten, vilket är lerans faktiska volym <math>V_{\mathrm{lera}}</math> <br/><br/> <math>V_{\mathrm{lera}} </ins>= 0,050 \cdot 10^{-3}<ins style="color: red; font-weight: bold; text-decoration: none;">\, </ins>m^3</math> <ins style="color: red; font-weight: bold; text-decoration: none;">och </ins><math><ins style="color: red; font-weight: bold; text-decoration: none;">V_{</ins>\<ins style="color: red; font-weight: bold; text-decoration: none;">mathrm{vatten}} </ins>= <ins style="color: red; font-weight: bold; text-decoration: none;">0,100 \cdot 10^{-3}\, </ins>m<ins style="color: red; font-weight: bold; text-decoration: none;">^3<</ins>/<ins style="color: red; font-weight: bold; text-decoration: none;">math> <br/><br/> <math> \rho_{\mathrm{lera}} </ins>= <ins style="color: red; font-weight: bold; text-decoration: none;">\displaystyle</ins>\frac{<ins style="color: red; font-weight: bold; text-decoration: none;">V_{\mathrm{vatten</ins>}<ins style="color: red; font-weight: bold; text-decoration: none;">}\cdot \rho_{\mathrm{vatten}}}{V_{\mathrm{lera}}} = \displaystyle\frac</ins>{0,<ins style="color: red; font-weight: bold; text-decoration: none;">1</ins>\cdot <ins style="color: red; font-weight: bold; text-decoration: none;">\mathrm</ins>{<ins style="color: red; font-weight: bold; text-decoration: none;">999,7\, kg/m^</ins>3}<ins style="color: red; font-weight: bold; text-decoration: none;">}{0,05} = 1999,4\, \mathrm {kg/</ins>m^3<ins style="color: red; font-weight: bold; text-decoration: none;">} </math> <br/><br/> <math>\rho_{\mathrm{lera}</ins>} = 2000<ins style="color: red; font-weight: bold; text-decoration: none;">\, \mathrm {</ins>kg/m^3<ins style="color: red; font-weight: bold; text-decoration: none;">} </ins></math></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><math> m_{vatten}\cdot g\cdot \<del style="color: red; font-weight: bold; text-decoration: none;">rho </del>= <del style="color: red; font-weight: bold; text-decoration: none;">(0,100 kg </del>\<del style="color: red; font-weight: bold; text-decoration: none;">cdot 9,82 m</del>/<del style="color: red; font-weight: bold; text-decoration: none;">s^2 </del>\cdot <del style="color: red; font-weight: bold; text-decoration: none;">999,7 kg</del>/<del style="color: red; font-weight: bold; text-decoration: none;">m^3 </del>= <del style="color: red; font-weight: bold; text-decoration: none;">0,988 N </del></math></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div> </div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;">medför </del>att <math><del style="color: red; font-weight: bold; text-decoration: none;">m_</del>{<del style="color: red; font-weight: bold; text-decoration: none;">modellera</del>} = 0,100 <del style="color: red; font-weight: bold; text-decoration: none;">kg</del></math><del style="color: red; font-weight: bold; text-decoration: none;">.</del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div> </div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;">Volymen </del>är <math>0,050 l = 0,050\cdot 10^{-3} m^3</math> <del style="color: red; font-weight: bold; text-decoration: none;"> ger</del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div> </div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><math>\<del style="color: red; font-weight: bold; text-decoration: none;">rho </del>= m/<del style="color: red; font-weight: bold; text-decoration: none;">V</del>= \frac{<del style="color: red; font-weight: bold; text-decoration: none;">0,100 kg</del>}{0,<del style="color: red; font-weight: bold; text-decoration: none;">050</del>\cdot <del style="color: red; font-weight: bold; text-decoration: none;">10^</del>{<del style="color: red; font-weight: bold; text-decoration: none;">-</del>3} m^3}= 2000 kg/m^3</math></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></div></td></tr>
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Louwah
http://wiki.math.se/wikis/forberedandefysik/index.php?title=L%C3%B6sning_1.5:6&diff=563&oldid=prev
Lena Chytraeus: Ny sida: Båten undantränger <math>0,100 l</math> vatten, lyftkraften blir då <math> m_{vatten}\cdot g\cdot \rho = (0,100 kg \cdot 9,82 m/s^2 \cdot 999,7 kg/m^3 = 0,988 N </math> medför att <ma...
2009-12-09T10:37:46Z
<p>Ny sida: Båten undantränger <math>0,100 l</math> vatten, lyftkraften blir då <math> m_{vatten}\cdot g\cdot \rho = (0,100 kg \cdot 9,82 m/s^2 \cdot 999,7 kg/m^3 = 0,988 N </math> medför att <ma...</p>
<p><b>Ny sida</b></p><div>Båten undantränger <math>0,100 l</math> vatten, lyftkraften blir då<br />
<math> m_{vatten}\cdot g\cdot \rho = (0,100 kg \cdot 9,82 m/s^2 \cdot 999,7 kg/m^3 = 0,988 N </math><br />
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medför att <math>m_{modellera} = 0,100 kg</math>.<br />
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Volymen är <math>0,050 l = 0,050\cdot 10^{-3} m^3</math> ger<br />
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<math>\rho = m/V= \frac{0,100 kg}{0,050\cdot 10^{-3} m^3}= 2000 kg/m^3</math></div>
Lena Chytraeus