Inclined Plane - Revision history

Ist1106345 at 16:03, 15 November 2025

2025-11-15T16:03:08Z

Ist12916: /* Advanced protocol */

2025-11-05T20:55:16Z

Advanced protocol

Ist12916: /* Experiment description */

2025-11-05T20:46:14Z

Experiment description

Ist12916: /* Experiment description */

2025-11-05T20:43:13Z

Experiment description

Ist428984 at 19:03, 17 May 2021

2021-05-17T19:03:36Z

Ist428984 at 18:47, 17 May 2021

2021-05-17T18:47:20Z

Ist428984 at 18:46, 17 May 2021

2021-05-17T18:46:42Z

Ist428984: /* Multivariate model */

2021-05-17T18:45:20Z

Multivariate model

Ist428984 at 18:29, 17 May 2021

2021-05-17T18:29:01Z

Ist428984 at 18:27, 17 May 2021

2021-05-17T18:27:51Z

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 [[File:Promenor_Sonar.jpeg||thumb|General view of the experiment with the sonar at one end, after the collision collector spring. |right|border|288px]]
-The inclined plane of this experiment recreates this "reduction of gravity". It consists of a vehicle that moves on a track with adjustable inclination and that tilts at its midpoint. The height of the chute is measured at 1003 mm from the axis of the experiment.
+The inclined plane of this experiment recreates this "reduction of gravity". It consists of a vehicle, with mass 67.37 g, that moves on a track with adjustable inclination and that tilts at its midpoint. The height of the chute is measured at 1003 mm from the axis of the experiment.
 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 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.

@@ Line 42: / Line 42: @@
 ===Advanced protocol===
-As can be quickly inferred, the adjustment of the parabolic model to the movement produces a deviation that is only possible to understand with the inclusion of a 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), a 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.
+As can be quickly inferred, the adjustment of the parabolic model to the movement produces a deviation that is only possible to understand with the inclusion of a 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 (Cv, viscous, linear with velocity) and aerodynamic (Cx, quadratic dependence with velocity), a 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.
-The adjustment of a friction function for the acceleration in the form ''a = b + c*v + d*v<sup>2</sup>'' allows to extract the local acceleration of gravity when using several sets of data for various angles.
+The adjustment of a friction function for the acceleration in the form ''a = b + c*v + d*v<sup>2</sup>'' allows to extract the local acceleration of gravity when using several sets of data for various angles as the ''b'' term from the Coulomb friction as the same dimensions as gravity.
 ====Multivariate model====

@@ Line 20: / Line 20: @@
 </div>
-Purposely, this experiment uses a car equipped with a frontal windshield in order to exacerbate the effect of friction and demonstrate that its equation can be determined by multivariate analysis of several rides, for different inclinations.
+On purpose, this experiment uses a car equipped with a frontal windshield in order to exacerbate the effect of friction and demonstrate that its motion equation can be determined by multivariate analysis over several rides, for different inclinations.
 [[File:PlanoInclinado.png|thumb| 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 sonar.|center|720px]]
@@ Line 30: / Line 30: @@
 The inclined plane of this experiment recreates this "reduction of gravity". It consists of a vehicle that moves on a track with adjustable inclination and that tilts at its midpoint. The height of the chute is measured at 1003 mm from the axis of the experiment.
-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.
+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 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.
 ==Protocol==

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 <div class="mw-collapsible-content">
 *Laboratory: [http://elab.tecnico.ulisboa.pt Básico]
 *Control Room: Inclined Plane

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 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.
 ==Protocol==
@@ Line 54: / Line 52: @@
 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.
-====Determinação rigorosa da constante de restituição da mola====
+====Strict determination of the spring restitution constant====
-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.
+==Construction details==
-==Pormenores da construção==
+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. As it is necessary a reasonable inclination to overcome static friction, the impact on the fixing electromagnet is significant but can be resolved by placing a self-adhesive foam on both sides, between the mooring iron and the car.
-==Ligações==
+==Links==
 *[[Plano inclinado | Portuguese version (Versão em Português)]]

@@ Line 50: / Line 50: @@
 ====Multivariate model====
-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.
+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.
 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.

← Older revision		Revision as of 18:29, 17 May 2021
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	==Ligações==		==Ligações==

−	*[[~~Inclined Plane~~ \| Versão em ~~Inglês (English Version~~)]]	+	*[[Plano inclinado \| Portuguese version (Versão em Português)]]

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 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.
-====Determinação da velocidade em função da distância percorrida====
+====Determination of speed as a function of distance traveled====
-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.
+Based on the previous data, determine the speed as a function of the distance traveled eliminating the time in the previous graphs, that is, tracing the curve drawn by the speed pairs, distance for each available time.
-====Determinação da constante de restituição da mola====
+====Determination of the spring restitution constant====
-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.
+===Advanced protocol===
-===Protocolo avançado===
+The adjustment of a friction function for the acceleration in the form ''a = b + c*v + d*v<sup>2</sup>'' allows to extract the local acceleration of gravity when using several sets of data for various angles.
-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.
+====Multivariate model====
 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.