http://www.elab.tecnico.ulisboa.pt/wwwelab/wiki/index.php?title=Inclined_Plane&feed=atom&action=historyInclined Plane - Revision history2024-03-28T23:01:08ZRevision history for this page on the wikiMediaWiki 1.34.2http://www.elab.tecnico.ulisboa.pt/wiki/index.php?title=Inclined_Plane&diff=4075&oldid=prevIst428984 at 19:03, 17 May 20212021-05-17T19:03:36Z<p></p>
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<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Revision as of 19:03, 17 May 2021</td>
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<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Initially the chute tilts to a position with a negative angle in order to collect and park the car at the origin, about 1.3 m from the spring that will absorb the energy of its movement. The electromagnet immobilizes the car and, subsequently, the rail is raised to the pre-selected height. When it reaches that point, the electromagnet releases the car and it moves freely on the rail until it hits the spring. An ultrasonic detector then collects position samples as a function of the elapsed time, allowing to trace the vehicle's trajectory during the fall and in its final damping.</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Initially the chute tilts to a position with a negative angle in order to collect and park the car at the origin, about 1.3 m from the spring that will absorb the energy of its movement. The electromagnet immobilizes the car and, subsequently, the rail is raised to the pre-selected height. When it reaches that point, the electromagnet releases the car and it moves freely on the rail until it hits the spring. An ultrasonic detector then collects position samples as a function of the elapsed time, allowing to trace the vehicle's trajectory during the fall and in its final damping.</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;"></del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">(Um detector ultrasónico colhe, então, amostras da posição em função do tempo decorrido, permitindo traçar a trajectória do veículo durante a queda e no seu amortecimento final.)</del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Protocol==</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Protocol==</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>When performing this multivariate analysis, we are considering an independent association between the parameters, a necessary condition for these parameters to be part of a numerical model that will prove correct by the outcome of the adjustment. For this purpose, a numerical solver should be used, interactively adjusting the various covariates, such as that of the MSExcel.</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>When performing this multivariate analysis, we are considering an independent association between the parameters, a necessary condition for these parameters to be part of a numerical model that will prove correct by the outcome of the adjustment. For this purpose, a numerical solver should be used, interactively adjusting the various covariates, such as that of the MSExcel.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>====<del class="diffchange diffchange-inline">Determinação rigorosa da constante de restituição da mola</del>====</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>====<ins class="diffchange diffchange-inline">Strict determination of the spring restitution constant</ins>====</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">A brief analysis makes it possible to conclude that the spring restitution constant for the various strikes is affected by an appreciable error, which increases with the distance traveled, since the work carried out by the frictional force affects the calculation of the mechanical energy in each section of the movement. However, by calculating the work performed by the frictional force based on the frictional force equation determined by the previously described process, it is possible to correctly infer the mechanical energy before and after each impact, allowing to correctly calculate the spring restitution constant.</ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">Uma análise breve permite concluir que a constante de restituição da mola para os vários embates vem ferida de um erro apreciável, tanto maior quanto o percurso percorrido, uma vez que o trabalho realizado pela força de atrito prejudica o cálculo da energia mecânica em cada troço do movimento</del>. <del class="diffchange diffchange-inline">No entanto, calculando o trabalho efetuado pela força de atrito com base na equação da força de atrito determinada pelo processo anteriormente descrito, é possível inferir corretamente </del>a <del class="diffchange diffchange-inline">energia mecânica antes e depois de cada embate, permitindo calcular corretamente </del>a <del class="diffchange diffchange-inline">constante de restituição da mola.</del></div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">==Construction details==</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">[[File:ElectroIma.png||thumb| Car mooring electromagnet.|right|border|120px]]</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">The most curious component of this experience is the electromagnet who keeps the car safe in the launch position</ins>. <ins class="diffchange diffchange-inline">This electromagnet can be built by wrapping enameled wire over </ins>a <ins class="diffchange diffchange-inline">soft iron core or using an electromagnet extracted from </ins>a <ins class="diffchange diffchange-inline">simple toaster! </ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">==Pormenores da construção==</del></div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">Another innovation is the fact that the assembly is carried out on a tilting chute that simplifies the return of the car to the launch position</ins>. <ins class="diffchange diffchange-inline">As it is necessary a reasonable inclination to overcome static friction</ins>, <ins class="diffchange diffchange-inline">the impact on the fixing electromagnet is significant but can be resolved by placing </ins>a <ins class="diffchange diffchange-inline">self-adhesive foam on both sides</ins>, <ins class="diffchange diffchange-inline">between the mooring iron and the car</ins>.</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">[[File:ElectroIma</del>.<del class="diffchange diffchange-inline">png||thumb|Eletroiman de atracação do carrinho.|right|border|120px]]</del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">O componente mais curioso desta experiência é o eletroiman que mantém o carrinho seguro na posição de lançamento. Com efeito</del>, <del class="diffchange diffchange-inline">este eletroiman pode ser construído enrolando fio esmaltado sobre um núcleo de ferro mole ou usando um eletroiman extraído duma simples torradeira!</del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">Outra inovação é </del>a <del class="diffchange diffchange-inline">montagem ser efetuada sobre uma calha basculante que simplifica o recolher do carrinho à posição de lançamento. Como é necessário uma inclinação razoável para vencer o atrito estático, o embate no eletroiman de fixação é significativo mas pode ser resolvido colocando uma espuma autocolante em ambas as faces</del>, <del class="diffchange diffchange-inline">entre o ferro de atracação e o carro</del>.</div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>==<del class="diffchange diffchange-inline">Ligações</del>==</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>==<ins class="diffchange diffchange-inline">Links</ins>==</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*[[Plano inclinado | Portuguese version (Versão em Português)]]</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*[[Plano inclinado | Portuguese version (Versão em Português)]]</div></td></tr>
</table>Ist428984http://www.elab.tecnico.ulisboa.pt/wiki/index.php?title=Inclined_Plane&diff=4074&oldid=prevIst428984 at 18:47, 17 May 20212021-05-17T18:47:20Z<p></p>
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<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Revision as of 18:47, 17 May 2021</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l50" >Line 50:</td>
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<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>====Multivariate model====</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>====Multivariate model====</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>The multivariate analysis used serves to build a model of numerical adjustment for various angles to the various characteristics of the movement obtained. The variation of the angle makes it possible to distinguish the effect of gravity from the effect of rolling friction force, since this is considered independent of the angle. Thus, by making a ''a = b + c*v + d*v<sup>2</sup>'' type adjustment, the parameter ''b'' which implicitly deters the gravity and friction of the bearing (related to the mechanics of the vehicle) can be solved by separating it into ''b =g*sin(θ)+b<sub> friction </sub>''. The remaining parameters result from a model of the dependence of friction with speed. For high values of this (typically greater than 7-10 ms<sup>-1</sup>), friction has a strong quadratic dependence on speed - aerodynamic friction - but, in our case, we also have to consider the dependence on mechanical friction (''b<sub>atrito</sub>+c*v''), since the car departs from rest.</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>The multivariate analysis used serves to build a model of numerical adjustment for various angles to the various characteristics of the movement obtained. The variation of the angle makes it possible to distinguish the effect of gravity from the effect of rolling friction force, since this is considered independent of the angle. Thus, by making a ''a=b+c*v+d*v<sup>2</sup>'' type adjustment, the parameter ''b'' which implicitly deters the gravity and friction of the bearing (related to the mechanics of the vehicle) can be solved by separating it into ''b =g*sin(θ)+b<sub> friction </sub>''. The remaining parameters result from a model of the dependence of friction with speed. For high values of this (typically greater than 7-10 ms<sup>-1</sup>), friction has a strong quadratic dependence on speed - aerodynamic friction - but, in our case, we also have to consider the dependence on mechanical friction (''b<sub>atrito</sub>+c*v''), since the car departs from rest.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>When performing this multivariate analysis, we are considering an independent association between the parameters, a necessary condition for these parameters to be part of a numerical model that will prove correct by the outcome of the adjustment. For this purpose, a numerical solver should be used, interactively adjusting the various covariates, such as that of the MSExcel.</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>When performing this multivariate analysis, we are considering an independent association between the parameters, a necessary condition for these parameters to be part of a numerical model that will prove correct by the outcome of the adjustment. For this purpose, a numerical solver should be used, interactively adjusting the various covariates, such as that of the MSExcel.</div></td></tr>
</table>Ist428984http://www.elab.tecnico.ulisboa.pt/wiki/index.php?title=Inclined_Plane&diff=4073&oldid=prevIst428984 at 18:46, 17 May 20212021-05-17T18:46:42Z<p></p>
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<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Revision as of 18:46, 17 May 2021</td>
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<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>====Multivariate model====</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>====Multivariate model====</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>The multivariate analysis used serves to build a model of numerical adjustment for various angles to the various characteristics of the movement obtained. The variation of the angle makes it possible to distinguish the effect of gravity from the effect of rolling friction force, since this is considered independent of the angle. Thus, by making a ''a = b + c*v + d*v<sup>2</sup>'' type adjustment, the parameter ''b'' which implicitly deters the gravity and friction of the bearing (related to the mechanics of the vehicle) can be solved by separating it into ''b = g * sin (θ) + b <sub> friction </sub>''. The remaining parameters result from a model of the dependence of friction with speed. For high values of this (typically greater than 7-10 ms<sup>-1</sup>), friction has a strong quadratic dependence on speed - aerodynamic friction - but, in our case, we also have to consider the dependence on mechanical friction (''b<sub>atrito</sub>+c*v''), since the car departs from rest.</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>The multivariate analysis used serves to build a model of numerical adjustment for various angles to the various characteristics of the movement obtained. The variation of the angle makes it possible to distinguish the effect of gravity from the effect of rolling friction force, since this is considered independent of the angle. Thus, by making a ''a = b + c*v + d*v<sup>2</sup>'' type adjustment, the parameter ''b'' which implicitly deters the gravity and friction of the bearing (related to the mechanics of the vehicle) can be solved by separating it into ''b =g*sin(θ)+b<sub> friction </sub>''. The remaining parameters result from a model of the dependence of friction with speed. For high values of this (typically greater than 7-10 ms<sup>-1</sup>), friction has a strong quadratic dependence on speed - aerodynamic friction - but, in our case, we also have to consider the dependence on mechanical friction (''b<sub>atrito</sub>+c*v''), since the car departs from rest.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>When performing this multivariate analysis, we are considering an independent association between the parameters, a necessary condition for these parameters to be part of a numerical model that will prove correct by the outcome of the adjustment. For this purpose, a numerical solver should be used, interactively adjusting the various covariates, such as that of the MSExcel.</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>When performing this multivariate analysis, we are considering an independent association between the parameters, a necessary condition for these parameters to be part of a numerical model that will prove correct by the outcome of the adjustment. For this purpose, a numerical solver should be used, interactively adjusting the various covariates, such as that of the MSExcel.</div></td></tr>
</table>Ist428984http://www.elab.tecnico.ulisboa.pt/wiki/index.php?title=Inclined_Plane&diff=4072&oldid=prevIst428984: /* Multivariate model */2021-05-17T18:45:20Z<p><span dir="auto"><span class="autocomment">Multivariate model</span></span></p>
<table class="diff diff-contentalign-left" data-mw="interface">
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<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Revision as of 18:45, 17 May 2021</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l50" >Line 50:</td>
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<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>====Multivariate model====</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>====Multivariate model====</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">A análise multivariada utilizada serve para construir um modelo de ajuste numérido para vários ângulos às várias características do movimento obtido</del>. <del class="diffchange diffchange-inline">A variação do ângulo permite distinguir o efeito da gravidade do da força de atrito de rolamento</del>, <del class="diffchange diffchange-inline">já que este é considerado independente do ângulo</del>. <del class="diffchange diffchange-inline">Deste modo</del>, <del class="diffchange diffchange-inline">ao fazer um ajuste do tipo </del>''a = b + c*v + d*v<sup>2</sup>'', <del class="diffchange diffchange-inline">o parâmetro </del>''b'' <del class="diffchange diffchange-inline">que detém implicitamente a gravidade e o atrito de rolamento </del>(<del class="diffchange diffchange-inline">relacionado com a mecânica do veículo</del>) <del class="diffchange diffchange-inline">pode ser resolvido separando-o em </del>''b=g*sin(θ) + b<sub><del class="diffchange diffchange-inline">atrito</del></sub>''. <del class="diffchange diffchange-inline">Os restantes parâmetros resultam de um modelo da dependência do atrito com </del>a <del class="diffchange diffchange-inline">velocidade</del>. <del class="diffchange diffchange-inline">Para valores elevados desta </del>(<del class="diffchange diffchange-inline">tipicamente superior a </del>7-10 ms<sup>-1</sup>), <del class="diffchange diffchange-inline">o atrito tem uma forte dependência quadrática com </del>a <del class="diffchange diffchange-inline">velocidade – atrito aerodinâmico – mas</del>, <del class="diffchange diffchange-inline">no nosso caso</del>, <del class="diffchange diffchange-inline">também temos de considerar a dependência de atrito mecânico </del>(''b<sub>atrito</sub>+c*v''), <del class="diffchange diffchange-inline">uma vez que o carro parte do repouso</del>.</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">The multivariate analysis used serves to build a model of numerical adjustment for various angles to the various characteristics of the movement obtained</ins>. <ins class="diffchange diffchange-inline">The variation of the angle makes it possible to distinguish the effect of gravity from the effect of rolling friction force</ins>, <ins class="diffchange diffchange-inline">since this is considered independent of the angle</ins>. <ins class="diffchange diffchange-inline">Thus</ins>, <ins class="diffchange diffchange-inline">by making a </ins>''a = b + c*v + d*v<sup>2</sup>'' <ins class="diffchange diffchange-inline">type adjustment</ins>, <ins class="diffchange diffchange-inline">the parameter </ins>''b'' <ins class="diffchange diffchange-inline">which implicitly deters the gravity and friction of the bearing </ins>(<ins class="diffchange diffchange-inline">related to the mechanics of the vehicle</ins>) <ins class="diffchange diffchange-inline">can be solved by separating it into </ins>''b = g * sin (θ) + b <sub> <ins class="diffchange diffchange-inline">friction </ins></sub>''. <ins class="diffchange diffchange-inline">The remaining parameters result from </ins>a <ins class="diffchange diffchange-inline">model of the dependence of friction with speed</ins>. <ins class="diffchange diffchange-inline">For high values of this </ins>(<ins class="diffchange diffchange-inline">typically greater than </ins>7-10 ms<sup>-1</sup>), <ins class="diffchange diffchange-inline">friction has </ins>a <ins class="diffchange diffchange-inline">strong quadratic dependence on speed - aerodynamic friction - but</ins>, <ins class="diffchange diffchange-inline">in our case</ins>, <ins class="diffchange diffchange-inline">we also have to consider the dependence on mechanical friction </ins>(''b<sub>atrito</sub>+c*v''), <ins class="diffchange diffchange-inline">since the car departs from rest</ins>.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">Ao realizar esta análise multivariada estamos </del>a <del class="diffchange diffchange-inline">considerar uma associação independente entre os parâmetros, condição necessária para esses parâmetros fazerem parte de um modelo numérico que se provará correto pelo desfecho do ajuste</del>. <del class="diffchange diffchange-inline">Para o efeito</del>, <del class="diffchange diffchange-inline">deverá ser utilizado um ''</del>solver<del class="diffchange diffchange-inline">'' numérico ajustando interativamente </del>as <del class="diffchange diffchange-inline">várias co-variáveis, tal como o do </del>MSExcel.</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">When performing this multivariate analysis, we are considering an independent association between the parameters, a necessary condition for these parameters to be part of </ins>a <ins class="diffchange diffchange-inline">numerical model that will prove correct by the outcome of the adjustment</ins>. <ins class="diffchange diffchange-inline">For this purpose</ins>, <ins class="diffchange diffchange-inline">a numerical </ins>solver <ins class="diffchange diffchange-inline">should be used, interactively adjusting the various covariates, such </ins>as <ins class="diffchange diffchange-inline">that of the </ins>MSExcel.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>====Determinação rigorosa da constante de restituição da mola====</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>====Determinação rigorosa da constante de restituição da mola====</div></td></tr>
</table>Ist428984http://www.elab.tecnico.ulisboa.pt/wiki/index.php?title=Inclined_Plane&diff=4070&oldid=prevIst428984 at 18:29, 17 May 20212021-05-17T18:29:01Z<p></p>
<table class="diff diff-contentalign-left" data-mw="interface">
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<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Revision as of 18:29, 17 May 2021</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l65" >Line 65:</td>
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<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Ligações==</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Ligações==</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>*[[<del class="diffchange diffchange-inline">Inclined Plane </del>| Versão em <del class="diffchange diffchange-inline">Inglês (English Version</del>)]]</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>*[[<ins class="diffchange diffchange-inline">Plano inclinado </ins>| <ins class="diffchange diffchange-inline">Portuguese version (</ins>Versão em <ins class="diffchange diffchange-inline">Português</ins>)]]</div></td></tr>
</table>Ist428984http://www.elab.tecnico.ulisboa.pt/wiki/index.php?title=Inclined_Plane&diff=4069&oldid=prevIst428984 at 18:27, 17 May 20212021-05-17T18:27:51Z<p></p>
<table class="diff diff-contentalign-left" data-mw="interface">
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<col class="diff-marker" />
<col class="diff-content" />
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<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Revision as of 18:27, 17 May 2021</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l38" >Line 38:</td>
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<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Based on the pre-selected data in the experiment, obtain a graph of the position as a function of the elapsed time. Based on this data, determine the speed and acceleration graphs. Compare the acceleration obtained value with gravity.</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Based on the pre-selected data in the experiment, obtain a graph of the position as a function of the elapsed time. Based on this data, determine the speed and acceleration graphs. Compare the acceleration obtained value with gravity.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>====<del class="diffchange diffchange-inline">Determinação da velocidade em função da distância percorrida</del>====</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>====<ins class="diffchange diffchange-inline">Determination of speed as a function of distance traveled</ins>====</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">Com base nos dados anteriores</del>, determine a <del class="diffchange diffchange-inline">velocidade em função da distância percorrida</del>, <del class="diffchange diffchange-inline">eliminando o tempo nos gráficos anteriores</del>, <del class="diffchange diffchange-inline">ou seja, traçando a curva desenhada pelos pares velocidade</del>, <del class="diffchange diffchange-inline">distância para cada tempo disponível</del>.</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">Based on the previous data</ins>, determine <ins class="diffchange diffchange-inline">the speed as </ins>a <ins class="diffchange diffchange-inline">function of the distance traveled eliminating the time in the previous graphs</ins>, <ins class="diffchange diffchange-inline">that is</ins>, <ins class="diffchange diffchange-inline">tracing the curve drawn by the speed pairs</ins>, <ins class="diffchange diffchange-inline">distance for each available time</ins>.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>====<del class="diffchange diffchange-inline">Determinação da constante de restituição da mola</del>====</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>====<ins class="diffchange diffchange-inline">Determination of the spring restitution constant</ins>====</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">Depending on the various parables obtained in the vehicle's damping, determine the relative energy loss in each collision with the spring and determine the spring restitution constant.</ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">Em função das várias parábolas obtidas no amortecimento do veículo</del>, <del class="diffchange diffchange-inline">determine </del>a <del class="diffchange diffchange-inline">perda relativa de energia em cada embate com </del>a <del class="diffchange diffchange-inline">mola e determine </del>a <del class="diffchange diffchange-inline">constante de restituição da mola</del>.</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">===Advanced protocol===</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">As can be quickly inferred</ins>, <ins class="diffchange diffchange-inline">the adjustment of the parabolic model to the movement produces </ins>a <ins class="diffchange diffchange-inline">deviation that is only possible to understand with the inclusion of </ins>a <ins class="diffchange diffchange-inline">friction term. In effect, the car has a front flap designed to induce a certain aerodynamic friction. By adapting the equations to include a rolling friction term (linear with velocity) and aerodynamic (Cx, quadratic dependence with velocity), </ins>a <ins class="diffchange diffchange-inline">more accurate value for the acceleration of the vehicle can finally be determined. Usually the ''Cx'' only significantly influences the movement after 25 km/h</ins>.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">===Protocolo avançado===</del></div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">The adjustment of </ins>a <ins class="diffchange diffchange-inline">friction function for the acceleration in the form </ins>''<ins class="diffchange diffchange-inline">a = b + c*v + d*v<sup>2</sup></ins>'' <ins class="diffchange diffchange-inline">allows to extract the local acceleration of gravity when using several sets of data for various angles</ins>.</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">Como pode ser inferido rapidamente, o ajuste do modelo parabólico ao movimento produz um desvio que só é possivel de entender com a inclusão de um termo de fricção. Com efeito, o carrinho dispõe duma pala frontal destinada a induzir um certo atrito aerodinâmico. Adaptando as equações de modo a incluir um termo de atrito de rolamento (linear com a velocidade) e aerodinâmico (Cx, dependência quadrática com a velocidade), pode-se determinar finalmente um valor mais preciso para </del>a <del class="diffchange diffchange-inline">aceleração do veículo.</del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">Normalmente o </del>''<del class="diffchange diffchange-inline">Cx</del>'' <del class="diffchange diffchange-inline">só influencia significativamente o movimento a partir dos 25 km/h</del>. </div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">O ajuste duma função de atrito para a aceleração na forma ''a </del>= <del class="diffchange diffchange-inline">b + c*v + d*v<sup>2</sup>'' permite extrair a aceleração local da gravidade ao serem utilizadas várias séries de dados para ângulos variados.</del></div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>====<ins class="diffchange diffchange-inline">Multivariate model</ins>====</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> </div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>===<del class="diffchange diffchange-inline">=Modelo multivariado</del>====</div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>A análise multivariada utilizada serve para construir um modelo de ajuste numérido para vários ângulos às várias características do movimento obtido. A variação do ângulo permite distinguir o efeito da gravidade do da força de atrito de rolamento, já que este é considerado independente do ângulo. Deste modo, ao fazer um ajuste do tipo ''a = b + c*v + d*v<sup>2</sup>'', o parâmetro ''b'' que detém implicitamente a gravidade e o atrito de rolamento (relacionado com a mecânica do veículo) pode ser resolvido separando-o em ''b=g*sin(θ) + b<sub>atrito</sub>''. Os restantes parâmetros resultam de um modelo da dependência do atrito com a velocidade. Para valores elevados desta (tipicamente superior a 7-10 ms<sup>-1</sup>), o atrito tem uma forte dependência quadrática com a velocidade – atrito aerodinâmico – mas, no nosso caso, também temos de considerar a dependência de atrito mecânico (''b<sub>atrito</sub>+c*v''), uma vez que o carro parte do repouso.</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>A análise multivariada utilizada serve para construir um modelo de ajuste numérido para vários ângulos às várias características do movimento obtido. A variação do ângulo permite distinguir o efeito da gravidade do da força de atrito de rolamento, já que este é considerado independente do ângulo. Deste modo, ao fazer um ajuste do tipo ''a = b + c*v + d*v<sup>2</sup>'', o parâmetro ''b'' que detém implicitamente a gravidade e o atrito de rolamento (relacionado com a mecânica do veículo) pode ser resolvido separando-o em ''b=g*sin(θ) + b<sub>atrito</sub>''. Os restantes parâmetros resultam de um modelo da dependência do atrito com a velocidade. Para valores elevados desta (tipicamente superior a 7-10 ms<sup>-1</sup>), o atrito tem uma forte dependência quadrática com a velocidade – atrito aerodinâmico – mas, no nosso caso, também temos de considerar a dependência de atrito mecânico (''b<sub>atrito</sub>+c*v''), uma vez que o carro parte do repouso.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
</table>Ist428984http://www.elab.tecnico.ulisboa.pt/wiki/index.php?title=Inclined_Plane&diff=4068&oldid=prevIst428984 at 17:05, 17 May 20212021-05-17T17:05:50Z<p></p>
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<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Revision as of 17:05, 17 May 2021</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l7" >Line 7:</td>
<td colspan="2" class="diff-lineno">Line 7:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>In laboratory experiments that recreate this machine, when an air chute is not used in order to almost eliminate the rolling friction, the plane must have a significant slope so that the gravitational acceleration can be much higher than the friction, making it impossible for this experience to be carried out in a long time, perceptible to human senses.</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>In laboratory experiments that recreate this machine, when an air chute is not used in order to almost eliminate the rolling friction, the plane must have a significant slope so that the gravitational acceleration can be much higher than the friction, making it impossible for this experience to be carried out in a long time, perceptible to human senses.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">Contudo</del>, <del class="diffchange diffchange-inline">o atrito é parte integrante da mecânica do problema</del>. <del class="diffchange diffchange-inline">Esta experiência permite determinar </del>a <del class="diffchange diffchange-inline">função de atrito através duma análise multivariada</del>, <del class="diffchange diffchange-inline">ajustando uma função que dependa da inclinação da calha</del>. <del class="diffchange diffchange-inline">A experiência</del>, <del class="diffchange diffchange-inline">para esse efeito</del>, <del class="diffchange diffchange-inline">permite alterar o ângulo de descida e</del>, <del class="diffchange diffchange-inline">através deste</del>, <del class="diffchange diffchange-inline">separar as forças de atrito da força gravítica, obtendo-se um valor muito próximo de </del>9,8 ms<sup>-2</sup>.</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">However</ins>, <ins class="diffchange diffchange-inline">friction is an integral part of the mechanics of the problem</ins>. <ins class="diffchange diffchange-inline">With this experiment, it is possible to determine the friction function through </ins>a <ins class="diffchange diffchange-inline">multivariate analysis</ins>, <ins class="diffchange diffchange-inline">adjusting a function that depends on the inclination of the rail</ins>. <ins class="diffchange diffchange-inline">For this purpose</ins>, <ins class="diffchange diffchange-inline">the experiment allows changing the descent angle and</ins>, <ins class="diffchange diffchange-inline">through this</ins>, <ins class="diffchange diffchange-inline">separating the frictional forces from the gravitational force</ins>, <ins class="diffchange diffchange-inline">obtaining a value very close to </ins>9,8 ms<sup>-2</sup>.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><div class="toccolours mw-collapsible mw-collapsed" style="width:420px"></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><div class="toccolours mw-collapsible mw-collapsed" style="width:420px"></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>'''<del class="diffchange diffchange-inline">Ligações</del>'''</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>'''<ins class="diffchange diffchange-inline">Links</ins>'''</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><div class="mw-collapsible-content"></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><div class="mw-collapsible-content"></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>*<del class="diffchange diffchange-inline">Vídeo</del>: rtsp://elabmc.ist.utl.pt/plinc.sdp</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>*<ins class="diffchange diffchange-inline">Video</ins>: rtsp://elabmc.ist.utl.pt/plinc.sdp</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>*<del class="diffchange diffchange-inline">Laboratório</del>: [http://elab.tecnico.ulisboa.pt Básico]</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>*<ins class="diffchange diffchange-inline">Laboratory</ins>: [http://elab.tecnico.ulisboa.pt Básico]</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>*<del class="diffchange diffchange-inline">Sala de Controlo</del>: <del class="diffchange diffchange-inline">Plano inclinado</del></div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>*<ins class="diffchange diffchange-inline">Control Room</ins>: <ins class="diffchange diffchange-inline">Inclined Plane</ins></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>*<del class="diffchange diffchange-inline">Nível</del>: *</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>*<ins class="diffchange diffchange-inline">Level</ins>: *</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div></div></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div></div></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div></div></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div></div></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">Propositadamente</del>, <del class="diffchange diffchange-inline">nesta experiência é usado um carro equipado com um pára-vento frontal de modo </del>a <del class="diffchange diffchange-inline">exacerbar o efeito do atrito e demonstrar que </del>a <del class="diffchange diffchange-inline">sua equação pode ser determinada pela análise multivariada de vários percursos</del>, <del class="diffchange diffchange-inline">para inclinações diferentes</del>.</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">Purposely</ins>, <ins class="diffchange diffchange-inline">this experiment uses </ins>a <ins class="diffchange diffchange-inline">car equipped with </ins>a <ins class="diffchange diffchange-inline">frontal windshield in order to exacerbate the effect of friction and demonstrate that its equation can be determined by multivariate analysis of several rides</ins>, <ins class="diffchange diffchange-inline">for different inclinations</ins>.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>[[File:PlanoInclinado.png|thumb|<del class="diffchange diffchange-inline">Montagem da experiência do plano inclinado onde se identifica facilmente o isolamento acústico necessário a evitar ecos espúrios que dificultam a detecção da posição pelo </del>sonar.|center|720px]]</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>[[File:PlanoInclinado.png|thumb| <ins class="diffchange diffchange-inline">Inclined plane experience assembly where is easy to identify the necessary acoustic insulation to avoid spurious echoes that difficult the detection of the position by the </ins>sonar.|center|720px]]</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>===<del class="diffchange diffchange-inline">Aparato experimental</del>===</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>===<ins class="diffchange diffchange-inline">Experimental apparatus</ins>===</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>[[File:Promenor_Sonar.jpeg||thumb|<del class="diffchange diffchange-inline">Vista geral da experiência com o </del>sonar <del class="diffchange diffchange-inline">numa das extremidades</del>, <del class="diffchange diffchange-inline">após a mola coletora do embate</del>. |right|border|288px]]</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>[[File:Promenor_Sonar.jpeg||thumb|<ins class="diffchange diffchange-inline">General view of the experiment with the </ins>sonar <ins class="diffchange diffchange-inline">at one end</ins>, <ins class="diffchange diffchange-inline">after the collision collector spring</ins>. |right|border|288px]]</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">O plano inclinado desta experiência recria essa </del>"<del class="diffchange diffchange-inline">desmultiplicação da gravidade</del>". <del class="diffchange diffchange-inline">Consiste num veículo que se desloca numa calha com inclinação regulável e que bascula no seu ponto médio</del>. <del class="diffchange diffchange-inline">A altura da calha é medida a </del>1003 mm <del class="diffchange diffchange-inline">do eixo da experiência</del>.</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">The inclined plane of this experiment recreates this </ins>"<ins class="diffchange diffchange-inline">reduction of gravity</ins>". <ins class="diffchange diffchange-inline">It consists of a vehicle that moves on a track with adjustable inclination and that tilts at its midpoint</ins>. <ins class="diffchange diffchange-inline">The height of the chute is measured at </ins>1003 mm <ins class="diffchange diffchange-inline">from the axis of the experiment</ins>.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">Inicialmente </del>a <del class="diffchange diffchange-inline">calha bascula para uma posição com um ângulo negativo de modo </del>a <del class="diffchange diffchange-inline">recolher e a parquear o carro na origem</del>, <del class="diffchange diffchange-inline">a cerca de </del>1<del class="diffchange diffchange-inline">,3m da mola que irá absorver a energia do seu movimento</del>. <del class="diffchange diffchange-inline">Este é imobilizado através de um eletroíman e</del>, <del class="diffchange diffchange-inline">posteriormente</del>, <del class="diffchange diffchange-inline">a calha é elevada até à altura pré</del>-<del class="diffchange diffchange-inline">selecionada</del>. <del class="diffchange diffchange-inline">Quando atinge esse ponto</del>, <del class="diffchange diffchange-inline">o eletroíman liberta o carrinho e este desloca-se livremente sobre a calha até embater na mola</del>.</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">Initially the chute tilts to </ins>a <ins class="diffchange diffchange-inline">position with </ins>a <ins class="diffchange diffchange-inline">negative angle in order to collect and park the car at the origin</ins>, <ins class="diffchange diffchange-inline">about </ins>1.<ins class="diffchange diffchange-inline">3 m from the spring that will absorb the energy of its movement. The electromagnet immobilizes the car and</ins>, <ins class="diffchange diffchange-inline">subsequently</ins>, <ins class="diffchange diffchange-inline">the rail is raised to the pre</ins>-<ins class="diffchange diffchange-inline">selected height</ins>. <ins class="diffchange diffchange-inline">When it reaches that point</ins>, <ins class="diffchange diffchange-inline">the electromagnet releases the car and it moves freely on the rail until it hits the spring</ins>. <ins class="diffchange diffchange-inline">An ultrasonic </ins>detector <ins class="diffchange diffchange-inline">then collects position samples as a function of the elapsed time</ins>, <ins class="diffchange diffchange-inline">allowing to trace the vehicle's trajectory during the fall and in its </ins>final <ins class="diffchange diffchange-inline">damping</ins>.</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">Um </del>detector <del class="diffchange diffchange-inline">ultra-sónico colhe</del>, <del class="diffchange diffchange-inline">então, amostras da posição em função do tempo decorrido, permitindo traçar a trajectória do veículo durante a queda e no seu amortecimento </del>final.</div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">==Protocolo==</del></div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">(Um detector ultrasónico colhe, então</ins>, <ins class="diffchange diffchange-inline">amostras </ins>da posição em função do tempo decorrido<ins class="diffchange diffchange-inline">, permitindo traçar a trajectória do veículo durante a queda e no seu amortecimento final</ins>.<ins class="diffchange diffchange-inline">)</ins></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">Com base nos dados pré-seleccionados na experiência</del>, <del class="diffchange diffchange-inline">obtenha um gráfico </del>da posição em função do tempo decorrido. <del class="diffchange diffchange-inline">Com base nestes dados</del>, determine <del class="diffchange diffchange-inline">ainda os gráficos da velocidade e da aceleração</del>. Compare <del class="diffchange diffchange-inline">o valor obtido da aceleração com a gravidade</del>.</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">==Protocol==</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">Based on the pre-selected data in the experiment, obtain a graph of the position as a function of the elapsed time. Based on this data</ins>, determine <ins class="diffchange diffchange-inline">the speed and acceleration graphs</ins>. Compare <ins class="diffchange diffchange-inline">the acceleration obtained value with gravity</ins>.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>====Determinação da velocidade em função da distância percorrida====</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>====Determinação da velocidade em função da distância percorrida====</div></td></tr>
</table>Ist428984http://www.elab.tecnico.ulisboa.pt/wiki/index.php?title=Inclined_Plane&diff=4067&oldid=prevIst428984: Created page with "==Experiment description== The inclined plane is one of the six [https://pt.wikipedia.org/wiki/M%C3%A1quina_simples classic simple machines]. Inclined planes are generally us..."2021-05-17T15:21:43Z<p>Created page with "==Experiment description== The inclined plane is one of the six [https://pt.wikipedia.org/wiki/M%C3%A1quina_simples classic simple machines]. Inclined planes are generally us..."</p>
<p><b>New page</b></p><div>==Experiment description==<br />
<br />
The inclined plane is one of the six [https://pt.wikipedia.org/wiki/M%C3%A1quina_simples classic simple machines]. Inclined planes are generally used to move heavy loads over vertical obstacles, such as ramps to move cargo.<br />
<br />
Moving an object up on an inclined plane requires less force than lifting it vertically, as if we reduced gravity! This mechanical advantage, by which the force is reduced, is equal to the ratio between the length of the inclined surface and the height of the plane.<br />
<br />
In laboratory experiments that recreate this machine, when an air chute is not used in order to almost eliminate the rolling friction, the plane must have a significant slope so that the gravitational acceleration can be much higher than the friction, making it impossible for this experience to be carried out in a long time, perceptible to human senses.<br />
<br />
Contudo, o atrito é parte integrante da mecânica do problema. Esta experiência permite determinar a função de atrito através duma análise multivariada, ajustando uma função que dependa da inclinação da calha. A experiência, para esse efeito, permite alterar o ângulo de descida e, através deste, separar as forças de atrito da força gravítica, obtendo-se um valor muito próximo de 9,8 ms<sup>-2</sup>.<br />
<br />
<div class="toccolours mw-collapsible mw-collapsed" style="width:420px"><br />
'''Ligações'''<br />
<div class="mw-collapsible-content"><br />
<br />
*Vídeo: rtsp://elabmc.ist.utl.pt/plinc.sdp<br />
*Laboratório: [http://elab.tecnico.ulisboa.pt Básico]<br />
*Sala de Controlo: Plano inclinado<br />
*Nível: *<br />
<br />
</div><br />
</div><br />
<br />
Propositadamente, nesta experiência é usado um carro equipado com um pára-vento frontal de modo a exacerbar o efeito do atrito e demonstrar que a sua equação pode ser determinada pela análise multivariada de vários percursos, para inclinações diferentes.<br />
<br />
[[File:PlanoInclinado.png|thumb|Montagem da experiência do plano inclinado onde se identifica facilmente o isolamento acústico necessário a evitar ecos espúrios que dificultam a detecção da posição pelo sonar.|center|720px]]<br />
<br />
===Aparato experimental===<br />
<br />
[[File:Promenor_Sonar.jpeg||thumb|Vista geral da experiência com o sonar numa das extremidades, após a mola coletora do embate. |right|border|288px]]<br />
<br />
O plano inclinado desta experiência recria essa "desmultiplicação da gravidade". Consiste num veículo que se desloca numa calha com inclinação regulável e que bascula no seu ponto médio. A altura da calha é medida a 1003 mm do eixo da experiência.<br />
<br />
Inicialmente a calha bascula para uma posição com um ângulo negativo de modo a recolher e a parquear o carro na origem, a cerca de 1,3m da mola que irá absorver a energia do seu movimento. Este é imobilizado através de um eletroíman e, posteriormente, a calha é elevada até à altura pré-selecionada. Quando atinge esse ponto, o eletroíman liberta o carrinho e este desloca-se livremente sobre a calha até embater na mola.<br />
Um detector ultra-sónico colhe, então, amostras da posição em função do tempo decorrido, permitindo traçar a trajectória do veículo durante a queda e no seu amortecimento final.<br />
<br />
==Protocolo==<br />
Com base nos dados pré-seleccionados na experiência, obtenha um gráfico da posição em função do tempo decorrido. Com base nestes dados, determine ainda os gráficos da velocidade e da aceleração. Compare o valor obtido da aceleração com a gravidade.<br />
<br />
====Determinação da velocidade em função da distância percorrida====<br />
Com base nos dados anteriores, determine a velocidade em função da distância percorrida, eliminando o tempo nos gráficos anteriores, ou seja, traçando a curva desenhada pelos pares velocidade, distância para cada tempo disponível.<br />
<br />
====Determinação da constante de restituição da mola====<br />
<br />
Em função das várias parábolas obtidas no amortecimento do veículo, determine a perda relativa de energia em cada embate com a mola e determine a constante de restituição da mola.<br />
<br />
===Protocolo avançado===<br />
Como pode ser inferido rapidamente, o ajuste do modelo parabólico ao movimento produz um desvio que só é possivel de entender com a inclusão de um termo de fricção. Com efeito, o carrinho dispõe duma pala frontal destinada a induzir um certo atrito aerodinâmico. Adaptando as equações de modo a incluir um termo de atrito de rolamento (linear com a velocidade) e aerodinâmico (Cx, dependência quadrática com a velocidade), pode-se determinar finalmente um valor mais preciso para a aceleração do veículo.<br />
Normalmente o ''Cx'' só influencia significativamente o movimento a partir dos 25 km/h. <br />
<br />
O ajuste duma função de atrito para a aceleração na forma ''a = b + c*v + d*v<sup>2</sup>'' permite extrair a aceleração local da gravidade ao serem utilizadas várias séries de dados para ângulos variados.<br />
<br />
====Modelo multivariado====<br />
A análise multivariada utilizada serve para construir um modelo de ajuste numérido para vários ângulos às várias características do movimento obtido. A variação do ângulo permite distinguir o efeito da gravidade do da força de atrito de rolamento, já que este é considerado independente do ângulo. Deste modo, ao fazer um ajuste do tipo ''a = b + c*v + d*v<sup>2</sup>'', o parâmetro ''b'' que detém implicitamente a gravidade e o atrito de rolamento (relacionado com a mecânica do veículo) pode ser resolvido separando-o em ''b=g*sin(θ) + b<sub>atrito</sub>''. Os restantes parâmetros resultam de um modelo da dependência do atrito com a velocidade. Para valores elevados desta (tipicamente superior a 7-10 ms<sup>-1</sup>), o atrito tem uma forte dependência quadrática com a velocidade – atrito aerodinâmico – mas, no nosso caso, também temos de considerar a dependência de atrito mecânico (''b<sub>atrito</sub>+c*v''), uma vez que o carro parte do repouso.<br />
<br />
Ao realizar esta análise multivariada estamos a considerar uma associação independente entre os parâmetros, condição necessária para esses parâmetros fazerem parte de um modelo numérico que se provará correto pelo desfecho do ajuste. Para o efeito, deverá ser utilizado um ''solver'' numérico ajustando interativamente as várias co-variáveis, tal como o do MSExcel.<br />
<br />
====Determinação rigorosa da constante de restituição da mola====<br />
<br />
Uma análise breve permite concluir que a constante de restituição da mola para os vários embates vem ferida de um erro apreciável, tanto maior quanto o percurso percorrido, uma vez que o trabalho realizado pela força de atrito prejudica o cálculo da energia mecânica em cada troço do movimento. No entanto, calculando o trabalho efetuado pela força de atrito com base na equação da força de atrito determinada pelo processo anteriormente descrito, é possível inferir corretamente a energia mecânica antes e depois de cada embate, permitindo calcular corretamente a constante de restituição da mola.<br />
<br />
==Pormenores da construção==<br />
[[File:ElectroIma.png||thumb|Eletroiman de atracação do carrinho.|right|border|120px]]<br />
O componente mais curioso desta experiência é o eletroiman que mantém o carrinho seguro na posição de lançamento. Com efeito, este eletroiman pode ser construído enrolando fio esmaltado sobre um núcleo de ferro mole ou usando um eletroiman extraído duma simples torradeira!<br />
Outra inovação é a montagem ser efetuada sobre uma calha basculante que simplifica o recolher do carrinho à posição de lançamento. Como é necessário uma inclinação razoável para vencer o atrito estático, o embate no eletroiman de fixação é significativo mas pode ser resolvido colocando uma espuma autocolante em ambas as faces, entre o ferro de atracação e o carro.<br />
<br />
==Ligações==<br />
<br />
*[[Inclined Plane | Versão em Inglês (English Version)]]</div>Ist428984