coordenadas normales y tangenciales
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The document describes an experiment to determine the normal and tangential components of motion for a particle moving in a circular trajectory. The objectives are to develop a model to demonstrate these components, relate experimental errors to theory, and calculate the normal and tangential components. Graphs and calculations from two trials are presented, finding values for velocity, acceleration, angular velocity, and more. The conclusions state that the experiment successfully applied theoretical knowledge and represented the normal and tangential motions with a circular model.
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El documento describe diferentes tipos de movimiento en cinemática, incluyendo movimiento rectilíneo uniforme, movimiento rectilíneo uniformemente variado, movimiento circular, tiro parabólico, tiro vertical y movimiento armónico simple. Explica conceptos como posición, velocidad, aceleración y fuerza centrípeta. También proporciona fórmulas para calcular distancia, velocidad, aceleración y fuerza para diferentes tipos de movimiento.
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Proyecto dinamica en coordenadas normales y tangenciales primer parcial_alex ...
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LEON_ERICK_DISEÑO_Y_CONSTRUCCION_DE_UNA_MAQUINA_DE_MOVIMENTO_PERPETUO
UNIVERSIDAD DE LAS FUERZAS ARMADAS ESPE SEDE LATACUNGA
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NRC: 5994
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Introduction to objective, scope and outcome the subject
Chapter 2
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coordenadas normales y tangenciales
- 1. COMPONETES NORMAL Y TANGENCIAL Practica realizada para evidenciar las componetes
- 2. Objetivos 1. Objetivo General: Determinar los componentes normales y tangenciales del movimiento de una partícula que se encuentra moviéndose en una trayectoria circular. 2. Objetivos Específicos: Desarrollar una maqueta para evidenciar y representar el comportamiento de dichas componentes. Relacionar la teoría de errores con los datos obtenidos en la práctica. Determinar los cálculos para las componentes normales y tangenciales.
- 3. Introduccion al tema ● Cuando se conoce la trayectoria a lo largo de la cual viaja una partícula, entonces a menudo conviene describir el movimiento por medio de los ejes de coordenadas n y t, los cuales actúan de manera normal y tangente a la trayectoria, respectivamente, y en el instante considerado tienen su origen localizado en la partícula. ● ● El eje tangente positivo actúa en la dirección del movimiento y el eje normal positivo está dirigido hacia el centro de curvatura de la trayectoria.
- 7. Radio de cruvatura 02 Es la diferencia entre el cambio de curvas, es decir, que en una curva es más cerrada o más abierta que otra generando un cambio de velocidades en el móvil y a la suma de dicho cambio es menos al cambio de dirección dado por ∆𝜃.
- 8. —Materiales
- 9. Parámetro físico Símbolo Valor promedio error abs Revolución 1 rpm 46 47,8 1,8 Revolución 2 rpm 48 47,8 0,2 Revolución 3 rpm 49 47,8 1,2 Revolución 4 rpm 47 47,8 0,8 Revolución 5 rpm 48 47,8 0,2 Revolución 6 rpm 47 47,8 0,8 Revolución 7 rpm 49 47,8 1,2 Revolución 8 rpm 48 47,8 0,2 Revolución 9 rpm 49 47,8 1,2 Revolución 10 rpm 47 47,8 0,8 Rev. Promedio rpm 47,80 promedio error abs. 0,840
- 10. Cálculos Error relativo 𝐸. 𝑅 = 𝑃𝑟𝑜𝑚. 𝐸𝑟𝑟. 𝐴𝑏𝑠 𝑃𝑟𝑜𝑚. 𝑣𝑎𝑙𝑜𝑟 𝐸. 𝑅 = 0.840 47.80 𝐸. 𝑅 = 0.0176 Error relativo porcentual %𝐸. 𝑅 = 𝐸. 𝑅 ∗ 100% %𝐸. 𝑅 = 0.0176 ∗ 100 % %𝐸. 𝑅 = 1,76%
- 11. Cálculos Velocidad angular final 𝜔𝑓 = 48𝑟𝑝𝑚 𝜔𝑓 = 0,8𝑟𝑒𝑣/𝑠𝑒𝑔 𝜔𝑓 = 0,8 ∗ 2𝜋 𝜔𝑓 = 5.027𝑟𝑎𝑑/𝑠𝑒𝑔 Aceleración angular 𝑟 = 7.5𝑐𝑚 = 0.075𝑚 𝛼 = 𝜔𝑓 − 𝜔𝑜 𝑡 𝛼 = 5.027 − 0 60𝑠𝑒𝑔 𝛼 = 0.08378𝑟𝑎𝑑 Aceleración tangencial 𝑎𝑡 = 𝛼 ∗ 𝑟 𝑎𝑡 = 0.08378 ∗ 0.075 𝑎𝑡 = 0,006284𝑚/𝑠2 Velocidad angular 𝜔 = 𝜃 𝑡 𝜔 = 25 60𝑠𝑒𝑔 𝜔 = 0.4167𝑟𝑎𝑑/𝑠𝑒𝑔
- 12. Parámetro físico Símbolo Valor Promedio Error abs Revolución 1 rpm 150 149,5 0,5 Revolución 2 rpm 148 149,5 1,5 Revolución 3 rpm 152 149,5 2,5 Revolución 4 rpm 151 149,5 1,5 Revolución 5 rpm 150 149,5 0,5 Revolución 6 rpm 148 149,5 1,5 Revolución 7 rpm 147 149,5 2,5 Revolución 8 rpm 148 149,5 1,5 Revolución 9 rpm 151 149,5 1,5 Revolución 10 rpm 150 149,5 0,5 Rev. Promedio rpm 149,5 promedio error abs. 1,40
- 13. Cálculos Error relativo 𝐸. 𝑅 = 𝑃𝑟𝑜𝑚. 𝐸𝑟𝑟. 𝐴𝑏𝑠 𝑃𝑟𝑜𝑚. 𝑣𝑎𝑙𝑜𝑟 𝐸. 𝑅 = 1.40 149.5 𝐸. 𝑅 = 0.009364 Error relativo porcentual %𝐸. 𝑅 = 𝐸. 𝑅 ∗ 100% %𝐸. 𝑅 = 0.009364 ∗ 100 % %𝐸. 𝑅 = 0.936%
- 14. Cálculos Velocidad angular final 𝜔𝑓 = 149𝑟𝑝𝑚 𝜔𝑓 = 2.4833𝑟𝑒𝑣/𝑠𝑒𝑔 𝜔𝑓 = 2.4833 ∗ 2𝜋 𝜔𝑓 = 15.6032𝑟𝑎𝑑/𝑠𝑒𝑔 Aceleración angular 𝑟 = 12𝑐𝑚 = 0.12𝑚 𝛼 = 𝜔𝑓 − 𝜔𝑜 𝑡 𝛼 = 15.6032 − 5.027 60𝑠𝑒𝑔 𝛼 = 0.17627𝑟𝑎𝑑 Aceleración tangencial 𝑎𝑡 = 𝛼 ∗ 𝑟 𝑎𝑡 = 0.17627 ∗ 0.12 𝑎𝑡 = 0.0212𝑚/𝑠2 Velocidad angular 𝜔 = 𝜃 𝑡 𝜔 = 25 60𝑠𝑒𝑔 𝜔 = 0.4167𝑟𝑎𝑑/𝑠𝑒𝑔
- 15. Cálculos Aceleración normal 𝑎𝑁 = 𝜔2 ∗ 𝑟 𝑎𝑁 = 0.41672 ∗ 0.12 𝑎𝑁 = 0.02084 Velocidad 𝑣 = 𝜔 ∗ 𝑅 𝑣 = 0.4167 ∗ 0.12 𝑣 = 0.050004𝑚/𝑠
- 16. Agrupación de datos Parámetro físico Valor Unidad Velocidad 1 Velocidad angular final 5.027 𝑟𝑎𝑑 𝑠𝑒𝑔 Aceleración angular 0.08378 𝑟𝑎𝑑 Aceleración tangencial 0,006284 𝑚 𝑠2 Velocidad angular 0.4167 𝑟𝑎𝑑 𝑠𝑒𝑔 Aceleración normal 0.01302 𝑚 𝑠2 Velocidad 0.03125 𝑚 𝑠 Velocidad 2 Velocidad angular final 15.6032 𝑟𝑎𝑑 𝑠𝑒𝑔 Aceleración angular 0.17627 𝑟𝑎𝑑 Aceleración tangencial 0.0212 𝑚 𝑠2 Velocidad angular 0.4167 𝑟𝑎𝑑 𝑠𝑒𝑔 Aceleración normal 0.02084 𝑚 𝑠2
- 17. Concluciónes Se aplico todos los conocimientos adquiridos ya sea por medio de la teoría o trabajo preparatorio y se comprobó esta misma teoría al realizar y culminar con éxito cada uno de las ejercicios y problemas plateados con ayuda de las formulas definidas para la determinación del error experimental. 01 Se consiguió representar mediante una maqueta las componentes normales y tangenciales, se vieron reflejadas la ejecución de la maqueta desarrollada, misma que generaba un movimiento circular con una circunferencia inicial menor a la circunferencia de la velocidad final. 03 Entre cuanto mas se ejerce una aceleración mas alta la velocidad aumenta por lo tanto el numero de vueltas que dan en un minuto, haciendo que el resorte se expanda mas allá del limite de la plataforma realizada para el desplazamiento de la masa 02 Aún que la trayectoria está expresada en función de sus coordenadas 𝑥 y 𝑦, aún así podemos establecer el origen de los ejes n, t en el punto fijo A de la trayectoria y determinar las componentes de 𝑣 y 𝑎 a lo largo de los ejes. 04
- 18. Gracias por su atención