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Movimiento Rectilineo Uniforme

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Clasificación del movimiento, MRU, MRUV. Características del MRU. Gráficas del MRU.

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Movimiento Rectilineo Uniforme

  1. 1. FÍSICA 1º curso BGU Ing. EDGAR JACINTO ESPINOZA BERNAL 1
  2. 2. CLASIFICACIÓN DEL MOVIMIENTO 2 TRAYECTORIA RECTILÍNEO CIRCULAR CURVILÍNEO VELOCIDAD UNIFORME velocidad es constante UNIFORMEMENTE VARIADO velocidad varía uniformemente VARIADO velocidad es variable ACELERACIÓN UNIFORME aceleración nula UNIFORMEMENTE VARIADO aceleración es constante VARIADO aceleración es variable
  3. 3. CLASIFICACIÓN DEL MOVIMIENTO Estos movimientos por sí solos no existen en la naturaleza, son el resultado de combinar la clasificación anterior, así tendremos: Movimiento Rectilíneo Uniforme: MRU Movimiento Rectilíneo Uniformemente Variado: MRUV Movimiento Circular Uniforme: MCU Movimiento Circular Uniformemente Variado: MCUV En este capítulo aprenderemos a describir EL MOVIMIENTO RECTILÍNEO EN UNA DIMENSIÓN. 3
  4. 4. MOVIMIENTO RECTILÍNEO Si la velocidad es constante (v = cte) Entonces, la aceleración es cero (a = 0) Movimiento Rectilíneo Uniforme Se clasifica en: Si la velocidad varía uniformemente Entonces, la aceleración es constante (a = cte) Movimiento Rectilíneo Uniformemente Variado 4
  5. 5. MOVIMIENTO RECTILÍNEO Posición en función del tiempo: X = f (t) Todo movimiento se define por una de sus ecuaciones cinemáticas, nuestra tarea es deducir las otras dos por medio de las definiciones de posición, velocidad y aceleración. ECUACIONES CINEMÁTICAS Velocidad en función del tiempo: V = f (t) Aceleración en función del tiempo: a = f (t) 5
  6. 6. Movimiento Rectilíneo Uniforme MRU 6 • Es decir, recorre distancias iguales en intervalos iguales de tiempo Un móvil está animado de MRU cuando: • La TRAYECTORIA que describe es una LÍNEA RECTA • La VELOCIDAD permanece CONSTANTE, por tanto a = 0 0 V=30 km/h 1 5 30 150 0 2 60 3 90 4 120 t (h) X (km) Por ejemplo: el automóvil recorre 30 km (ΔX=30 km) en cada hora (Δt=1 h). Es decir, se mueve con una velocidad de 30 km/h, la cual permanece constante durante el movimiento.
  7. 7. Movimiento Rectilíneo Uniforme MRU 7 La VELOCIDAD permanece CONSTANTE, significa que: los cambios de posición (ΔX) respecto al tiempo (Δt) son UNIFORMES (o CONSTANTES) 0 V=30 km/h 1 5 30 150 0 2 60 3 90 4 120 t (h) X (km)
  8. 8. Movimiento Rectilíneo Uniforme MRU 8 ECUACIONES CINEMÁTICAS Posición Velocidad Aceleración
  9. 9. 9 ANÁLISIS DEL MRU En el desplazamiento: Si xf > x0 entonces Δx > 0 (se mueve hacia la derecha) Si xf < x0 entonces Δx < 0 (se mueve hacia la izquierda) Si xf = x0 entonces Δx = 0 (está en reposo o regresó al punto de partida) La distancia recorrida por un cuerpo es el valor del módulo del desplazamiento (siempre y cuando no exista un regreso o cambio de sentido) 0 X0 =5 m Ejemplo 1: un móvil parte de la posición X=5 m hacia la posición X=12 m, determine el vector desplazamiento y la distancia recorrida. X=12 m X=X – X0 X=12 m – 5 m X=7 m Respuesta: el desplazamiento del móvil es 7 m hacia la derecha. La distancia recorrida es 7 m. d = |x| = |7 m| = 7 m X d
  10. 10. 10 0 X=5 m Ejemplo 3: un hombre parte de la posición X=8 m hacia la posición X=5 m, determine el vector desplazamiento y la distancia recorrida. X0 =8 m X=X – X0 X=5 m – 8 m X= – 3 m ANÁLISIS DEL MRU Respuesta: el automóvil se desplaza 15 m hacia la derecha y la distancia que recorre es 15 m. Ejemplo 2: un automóvil parte de la posición X=–5 m hacia la posición X=10 m, determine el vector desplazamiento y la distancia recorrida. 0X0 = – 5 m X=10 m X=X – X0 X=10 m – (– 5 m) X=15 m d = |x| = |15 m| = 15 m X d Respuesta: el hombre se desplaza 3 m hacia la izquierda y la distancia que recorre es 3 m. d = |x| = | – 3 m| = 3 m X d
  11. 11. Distancia recorrida sobre la trayectoria En un movimiento rectilíneo sin cambios de sentido, la distancia recorrida sobre la trayectoria coincide con el módulo del vector desplazamiento El módulo del vector desplazamiento y la distancia recorrida sobre la trayectoria, en general no coinciden La distancia recorrida sobre la trayectoria por un móvil durante su movimiento es la longitud medida sobre la trayectoria que recorre. 11
  12. 12. 12 ANÁLISIS DEL MRU En la velocidad: La velocidad media es igual a la velocidad instantánea Si la velocidad es positiva el cuerpo se mueve hacia la derecha Si la velocidad es negativa el cuerpo se mueve hacia la izquierda. La rapidez es el valor del módulo de la velocidad (no siempre)
  13. 13. 0 20 40 60 80 100 X (m) t (s)2 4 6 8 10 Gráficos del MRU 0 1 2 3 4 5 6 7 8 9 10 0 10 20 30 40 50 60 70 80 90 100 El móvil recorre distancias iguales en intervalos de tiempo iguales La distancia recorrida sobre la trayectoria es proporcional al tiempo empleado en recorrerla. La constante de proporcionalidad es la velocidad t X vvm    tvX  . t (s) X (m) 13
  14. 14. Gráficos del MRU 14 La gráfica posición en función del tiempo [X = f(t)] es una línea recta que puede o no pasar por el origen. La pendiente de la recta representa a la velocidad. X0 = 0; X = v . Δt X0 ≠ 0; X = X0 + v .Δt
  15. 15. Corresponde a la ecuación X = X0 + v. Δt X t X t Corresponde a la ecuación X = v. Δt Gráficos del MRU Gráficas X = f (t) X t El móvil A es más rápido que el B y éste más rápido que el C A B C 15
  16. 16. Gráficos del MRU 16 Si la aceleración es nula (a=0), la gráfica aceleración en función del tiempo [a = f(t)] no existe. Si v = constante, la gráfica velocidad en función del tiempo [v = f(t)] es una línea recta horizontal paralela al eje de los tiempos. El área bajo esta línea, representa la distancia recorrida en el intervalo de tiempo correspondiente. A = d
  17. 17. 17 ANÁLISIS DEL MRU Los cuerpos con MRU se mueven sobre una carretera horizontal (o trayectoria horizontal). 0 30 15060 90 120 X (km) Las gráficas de posición en función del tiempo, NO SON LAS TRAYECTORIAS de los cuerpos, las gráficas son las HISTORIAS DEL MOVIMIENTO. 0 1 52 3 4 t (h) 30 60 90 120 150 X (km) A B C 6 8
  18. 18. 18 ANÁLISIS DEL MRU Al analizar la gráfica X=f(t), se tiene que: El móvil parte del origen. 0 1 52 3 4 t (h) 30 60 90 120 150 X (km) 6 8 Entre t = 0 h y t = 2 h, se desplaza hacia la derecha y recorre 60 km, llegando a la posición 60 km Entre t = 2 h y t = 3 h, se detiene en la posición 60 km Entre t = 3 h y t = 6 h, se desplaza hacia la derecha y recorre 90 km, llegando a la posición 150 km Entre t = 6 h y t = 8 h, se desplaza hacia la izquierda y recorre 90 km, llegando finalmente a la posición 60 km
  19. 19. 19 ANÁLISIS DEL MRU En una gráfica de x = f (t) si la pendiente de la recta es: Positiva, el cuerpo se mueve hacia la derecha. Negativa, el cuerpo se mueve hacia la izquierda. Cero, el cuerpo no se mueve o permanece en reposo. De t = 0 h hasta t = 2 h De t = 2 h hasta t = 3 h De t = 3 h hasta t = 6 h De t = 6 h hasta t = 8 h h/km30 h)02( km)060( v1     h/km0 h)23( km)6060( v2     h/km30 h)36( km)60150( v3     h/km45 h)68( km)15060( v4    
  20. 20. 20 ANÁLISIS DEL MRU A1 0 1 52 3 4 t (h)6 7 8 A3 A4 A2 30 – 45 V (km/h) En una gráfica de v = f (t) Distancia = suma geométrica de las áreas: d = A1 + A2 + A3 + A4 d = v1.Δt1 + v2.Δt2 + v3.Δt3 + v4.Δt4 d = 30 km/h.2 h + 0 km/h.1 h + 30 km/h.3 h + 45 km/h.2 h d = 60 km + 0 km + 90 km + 90 km d = 240 km Δt1 Δt2 Δt3 Δt4
  21. 21. 21 ANÁLISIS DEL MRU A1 0 1 52 3 4 t (h)6 7 8 A3 A4 A2 30 – 45 V (km/h) En una gráfica de v = f (t) Desplazamiento = suma algebraica de las áreas: ΔX = A1 + A2 + A3 – A4 ΔX = v1.Δt1 + v2.Δt2 + v3.Δt3 – v4.Δt4 ΔX = 30 km/h.2 h + 0 km/h.1 h + 30 km/h.3 h – 45 km/h.2 h ΔX = 60 km + 0 km + 90 km – 90 km ΔX = 60 km ΔX = 60 km hacia la derecha Δt1 Δt2 Δt3 Δt4
  22. 22. Movimiento Rectilíneo Uniforme MRU 22 1. Establecer el sistema de referencia: PASOS PARA RESOLVER EJERCICIOS DE CINEMÁTICA 0 20 10040 60 80 X (km) 2. Dibujar un esquema con la situación propuesta. 3. Establecer el signo de aceleración, velocidad y posición. 0 20 10040 60 80 X (km) V ΔX
  23. 23. Movimiento Rectilíneo Uniforme MRU 23 4. Identificar las magnitudes conocidas y desconocidas: DATOS: V=____ ΔX=____ Δt=____ PASOS PARA RESOLVER EJERCICIOS DE CINEMÁTICA 5. Asegurarse que todas las unidades son homogéneas. 6. Identificar las ecuaciones del movimiento que servirán para obtener los resultados. 7. Sustituya los valores en las ecuaciones y realice los cálculos necesarios.
  24. 24. Movimiento Rectilíneo Uniforme MRU 24 8. Compruebe que el resultado sea correcto matemáticamente y que sea razonable desde el punto de vista físico. PASOS PARA RESOLVER EJERCICIOS DE CINEMÁTICA Desde este momento, aplicaremos los conocimientos adquiridos, para resolver los ejercicios propuestos en el Módulo del Movimiento Rectilíneo Uniforme – MRU. GRACIAS POR SU ATENCIÓN

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