27 mayo 2011

Actividad 6: Galileo. La caída libre de los cuerpos


En primer lugar y tras haber tomado nota de los datos
que nos describen en el vídeo, hemos realizado una tabla donde colocarlos.

A partir de esa tabla, hemos realizado esta gráfica que relaciona los datos del tiempo en segundos (eje X) con los de desplazamiento en metros (eje Y).


Sabemos que:

v (t) = incremento de y/incremento de t

Nota: el incremento de t es siempre 0,08

V1 = 0,025-0/0,08-0=0,31 m/s
V2 = 0,12-0,025/0,16-0,08 = 1,187 m/s
V3 = 0,27-0,12/0,24-0,16 = 1,87 m/s
V4 = 0,49-0,27/0,32-0,24 = 2,75 m/s
V5 = 0,78-0,49/0,4-0,32 = 3,62 m/s
V6 = 1,13-0,78/0,48-0,4 = 4,37 m/s

Hemos obtenido la velocidad de la bola en función del tiempo para cada intervalo.

3. A partir de los datos obtenidos hemos representado la velocidad (Y) de cada intervalo respecto al tiempo(X). Como ya sabemos este movimiento es de tipo MRUA (Movimiento rectilíneo y uniformemente acelerado). Como se puede observar debajo, nos sale una recta cuya pendiente es el valor de la aceleración.


Si observamos detenidamente la gráfica se puede ver la linea de los resultados obtenidos y la de los resultados que esperábamos obtener, el error del experimento es casi inapreciable.

4. Hemos representado en una tabla a partir de la gráfica anterior los resultados que esperamos obtener y los que obtuvimos:

5. La aceleración en nuestro caso nos ha dado 10,16 m/s 2. Esta aceleración en este experimento es la gravedad, que es la aceleración con la que la tierra atrae a los cuerpos, ya que se trata de una caída libre. Pero al comparar nuestro dato (10,16 m/s 2) con el real (9,8 m/s 2), observamos que presentan una ligera variación. Esto es debido a errores como la resistencia del aire, o simplemente errores en la medida, ya que esta es una experiencia muy difícil de reproducir.

Solamente en el hipotético caso de que no hubiera rozamiento y de que nuestros cálculos y mediciones fueran del todo exactas podríamos obtener el modelo teórico de resultado.
Dado que esta tarea es imposible, hemos decidido calcular los datos que obtendríamos en el supuesto caso de que se cumplieran las condiciones ideales.

Para ello nos hemos ayudado de las ecuaciones cinematicas para la caída libre:

h=1/2 9,8m/s 2 t2

h (m) t (s)
Posición 1 0,031 0,080
Posición 2 0,125 0,160
Posición 3 0,282 0,240
Posición 4 0,501 0,320
Posición 5 0,784 0,400
Posición 6 1,120 0,480

A partir de aqui obtenemos la velocidad, sabiendo que velocidad= espacio/tiempo

1) v=0,031/0,080=0,387 m/s 2
2)v=0,125/0,160= 0,78 m/s 2
3)v=0,282/0,240=1,175 m/s 2
4)v=0,501/0,320=1,5 m/s 2
5)v=0,784/0,4=1,96 m/s 2
6)v=1,120/0,480=2,3 m/s 2

Por último para verlo más claro representaremos estos datos en una gráfica v-t:

La pendiente en esta recta tendría que ser la aceleración producida (a=v/t) es decir 9,8 m/s 2

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