{ "cells": [ { "cell_type": "markdown", "id": "a92e028d-9c9e-45ac-a8c2-77b0a5597dbc", "metadata": { "tags": [] }, "source": [ "# Experimento: midiendo la aceleración de la gravedad con un péndulo\n", "\n", "## Un poco de historia: reloj de péndulo\n", "\n", "> From its invention in 1656 by Christiaan Huygens until the 1930s, the **pendulum clock** was the world's **most precise timekeeper**.\n", "\n", "> **The introduction of the pendulum**, the first harmonic oscillator used in timekeeping, **increased the accuracy** of clocks enormously, from about **15 minutes per day to 15 seconds per day**.\n", "\n", "> The increased accuracy resulting from these developments **caused the minute hand**, previously rare, **to be added** to clock faces beginning **around 1690**.\n", "\n", "> Pendulum clocks remained the world standard for accurate timekeeping for 270 years, until the invention of the quartz clock in 1927.\n", "\n", "*Nota: Extractos de Wikipedia que citaban diversos libros y fuentes.*\n", "\n", "## Isocronismo\n", "\n", "> Huygens was inspired by investigations of pendulums by Galileo Galilei beginning around 1602. Galileo discovered **the key property that makes pendulums useful timekeepers: isochronism**, which means that the period of swing of a pendulum is approximately the same for different sized swings.\n", "\n", "El periodo del péndulo es aproximadamente igual para diferentes amplitudes de la oscilación.\n", "\n", "> Clockmakers' realization that only **pendulums with small swings are isochronous** motivated the invention of the anchor escapement by Robert Hooke around 1658." ] }, { "attachments": { "732d060a-d3d9-4ba8-94ec-e296b7d157a2.png": { "image/png": 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" } }, "cell_type": "markdown", "id": "4b99ddbc-dfec-494d-a673-973567e6876c", "metadata": {}, "source": [ "## Esquema de un péndulo ideal\n", "\n", "![image.png](attachment:732d060a-d3d9-4ba8-94ec-e296b7d157a2.png)\n", "\n", "Variables del diagrama:\n", "- $g$: aceleración de la gravedad\n", "- $m$: masa del péndulo\n", "- $N$: fuerza de tensión de la cuerda\n", "- $\\theta$: coordenada angular\n", "- $\\Theta$: ángulo máximo\n", "- $A, A^\\prime$: puntos de ángulo máximos\n", "- $C$: posición de reposo\n", "\n", "Falta en el diagrama:\n", "- $L$: largo del péndulo" ] }, { "cell_type": "markdown", "id": "2dc4fb68-93d2-43dd-9452-eb1896e50a02", "metadata": {}, "source": [ "**Pregunta:** ¿cómo determinamos la aceleración de la gravedad a partir de un péndulo?" ] }, { "cell_type": "markdown", "id": "b4f96c37-ea47-408f-aac3-6d2cbf6e11cd", "metadata": {}, "source": [ "**Analogía con $\\pi$**: ¿Qué es $\\pi$?" ] }, { "cell_type": "markdown", "id": "c5dc2973-1d78-4334-8457-9261c045fada", "metadata": { "tags": [] }, "source": [ "## Ecuaciones de Newton\n", "\n", "Como el péndulo hace un movimiento circular, es más cómodo resolver las ecuaciones de Newton en coordenadas polares." ] }, { "cell_type": "markdown", "id": "cb64e2bd-6828-4836-a9f3-a391f6b5bc1f", "metadata": { "jp-MarkdownHeadingCollapsed": true, "tags": [] }, "source": [ "### Opción A: ecuación radial\n", "\n", "$$ m a_r = N - mg \\cos\\theta$$" ] }, { "cell_type": "markdown", "id": "048cf26a-f8a1-4ae9-86d6-d4c83008e6dc", "metadata": {}, "source": [ "Como $a_r=0$, entonces $N = mg \\cos\\theta$.\n", "\n", "Si pudiesemos medir la fuerza de tensión $N$ y la masa $m$, podríamos determinar $g$... " ] }, { "cell_type": "markdown", "id": "baaf510d-2cdd-431b-88aa-5b2502263843", "metadata": {}, "source": [ "### Opción B: ecuación tangencial\n", "\n", "$$ ma_t = L\\ddot{\\theta} = -mg \\sin\\theta $$" ] }, { "cell_type": "markdown", "id": "c0086b93-8335-489d-bf3c-6f8621b1c5a3", "metadata": {}, "source": [ "Reescribiendo,\n", "\n", "$$ \\ddot{\\theta} + \\frac{g}{L} \\sin\\theta = 0$$\n", "\n", "ya no depende de la masa." ] }, { "cell_type": "markdown", "id": "ee9a64e6-f6ac-40f5-ac41-582230df8c54", "metadata": { "tags": [] }, "source": [ "#### Aproximación de ángulos pequeños\n", "\n", "Si la oscilación se da en ángulos pequeños, $\\theta << 1$, podemos podemos aproximar $\\sin \\theta \\approx \\theta$, y tenemos:\n", "\n", "$$ \\ddot{\\theta} + \\frac{g}{L} \\theta = 0 $$\n", "\n", "que es la ecuación de un oscilador armónico." ] }, { "cell_type": "markdown", "id": "d3fb0482-4c2e-4ef3-9190-2f9e29c2c5f7", "metadata": {}, "source": [ "La solución del oscilador armónico es:\n", "\n", "$$ \\theta(t) = \\theta_0 \\cos(\\omega t) $$\n", "\n", "donde la frecuencia angular $\\omega = \\sqrt{\\frac{g}{L}}$,\n", "\n", "y se asumió que se suelta el péndulo del ángulo $\\theta_0$ a $t=0$." ] }, { "cell_type": "markdown", "id": "6aaa66e7-18cb-47e8-9609-17d322feb4fc", "metadata": {}, "source": [ "Podemos relacionar la frecuencia angular $\\omega$ con el periodo $T$:\n", "\n", "$$ \\omega = \\frac{2\\pi}{T} $$\n", "\n", "y llegar entonces a:\n", "\n", "$$ T = 2\\pi \\sqrt{\\frac{L}{g}} $$" ] }, { "cell_type": "markdown", "id": "703e2f9a-44f5-4bb0-9cc8-cec566108f23", "metadata": {}, "source": [ "Entonces, midiendo el periodo $T$ y la longitud $L$, podemos determinar la aceleración de la gravedad $g$." ] }, { "cell_type": "markdown", "id": "e52bf533-565a-4602-890d-1660f03b7d18", "metadata": {}, "source": [ "## Hipótesis del péndulo\n", "\n", "Este experimento supone varias hipótesis sobre el péndulo.\n", "\n", "Es importante tener en cuenta cuales son para:\n", "\n", "1. hacer un experimento acorde a lo que esperamos\n", "2. poder entender donde tenemos que corregir nuestro experimento o modelo si falla\n", "\n", "En el segundo caso, podemos corregir:\n", "\n", "- el experimento acercandonos más a las hipótesis, por ejemplo, ángulos más pequeños\n", "- el modelo agregandole complejidad para que represente mejor el experimento, por ejemplo, no haciendo la aproximación de ángulos pequeñós ($\\sin \\theta \\approx \\theta$).\n", "\n", "Ya mencionamos:\n", "\n", "1. ángulos pequeños\n", "\n", "> Clockmakers' realization that only pendulums with small swings of a few degrees are isochronous motivated the invention of the anchor escapement by Robert Hooke around 1658, which reduced the pendulum's swing to 4–6. [7]\n", "\n", "¿Qué otras se les ocurre?" ] }, { "cell_type": "markdown", "id": "c27c6797-7084-4756-960d-e983bcba6eac", "metadata": {}, "source": [ "2. masa puntual" ] }, { "cell_type": "markdown", "id": "aea410e3-7a17-4827-b148-50f503f663da", "metadata": {}, "source": [ "3. cuerda ideal: sin masa e inextensible\n", "\n", " El material de la cuerda puede sufrir expansión térmica.\n", "\n", "> Older quality clocks used wooden pendulum rods to reduce this error, as wood expands less than metal.\n", "\n", "> The first pendulum to correct for this error was the mercury pendulum invented by Graham in 1721.\n", "\n", "> Beginning around 1900, some of the highest precision scientific clocks had pendulums made of ultra-low-expansion materials such as the nickel steel alloy Invar or fused silica, which required very little compensation for the effects of temperature.\n" ] }, { "cell_type": "markdown", "id": "187668ce-2bbc-4189-ba8d-da12467f142c", "metadata": {}, "source": [ "4. sin resistencia del aire\n", "\n", "> In the late 19th century and early 20th century, pendulums for precision regulator clocks in astronomical observatories were often operated in a chamber that had been pumped to a low pressure to reduce drag." ] }, { "cell_type": "markdown", "id": "9cab51c1-d86b-4473-a222-95005d2c5597", "metadata": {}, "source": [ "¿Cómo podemos testar si son importantes estas hipótesis?" ] }, { "attachments": { "7083f07e-8072-4215-99ee-deb6843b7cf6.png": { "image/png": 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" } }, "cell_type": "markdown", "id": "4972fa6d-a490-46f2-9e52-8de1e1dffd0d", "metadata": {}, "source": [ "## Metodología\n", "\n", "¿Cómo medimos el periodo?\n", "\n", "Es importante medir correctamente el periodo: cuando vuelve al mismo punto con la misma velocidad (y dirección).\n", "\n", "![image.png](attachment:7083f07e-8072-4215-99ee-deb6843b7cf6.png)" ] }, { "cell_type": "markdown", "id": "a5422a15-9c27-408b-acd7-1315adc744ca", "metadata": { "tags": [] }, "source": [ "### Opción A\n", "\n", "Cuando pasa por un extremo o ángulo máximo.\n", "\n", "### Opción B\n", "\n", "Cuando pasa por el centro o ángulo mínimo." ] }, { "cell_type": "markdown", "id": "80c937e5-0766-49eb-9f2d-71825431aefd", "metadata": {}, "source": [ "### Opción C\n", "\n", "Se podría medir medio periodo y multiplicar por 2, con lo que se obtendrían más mediciones en menos tiempo.\n", "\n", "¿Es esta opción válida?" ] }, { "cell_type": "markdown", "id": "17fbb15c-11e7-4ceb-919e-eaba2bc3fe19", "metadata": {}, "source": [ "## Preguntas\n", "\n", "**Responder encuestas en canal #general de Discord.**\n", "\n", "1. ¿Es más precisa la opción A o la B?\n", "\n", "2. ¿Es válida la opción C?\n", "\n", "3. ¿Pueden detectar diferencias de periodo por medir a distintos ángulos?\n", "\n", "4. ¿Da consistente con la aceleración de la gravedad esperada? $g = 9.79688239 \\, m/s^2$ [1]\n", "\n", "5. ¿Pueden contestar todas estas preguntas o les faltan herramientas que veremos en la parte 2?\n", "\n", "[1] https://www.ign.gob.ar/NuestrasActividades/Geodesia/Gravimetria/RAGA" ] } ], "metadata": { "kernelspec": { "display_name": "book", "language": "python", "name": "book" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.9.2" } }, "nbformat": 4, "nbformat_minor": 5 }