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My name is Ann [436]
3 years ago
7

Una bola de 1 kg gira alrededor de un circulovrtical en el extremo de un cuerda. El otro extremo de la cuerda esta fijo en el ce

ntro del circulo. Calcular la diferencia entre las tensiones (de la cuerda) maxima y minima
Physics
1 answer:
Vladimir79 [104]3 years ago
5 0

Answer:

La diferencia entre las tensiones máxima y mínima es de 19.614 newtons.

Explanation:

Puesto que la bola gira en un círculo vertical, existe claramente una diferencia entre las tensiones debido a la influencia de la gravedad y la tensión que resulta de la aceleración centrípeta experimentada por la masa. La máxima tensión ocurre cuando la bola se encuentra en el nadir (o la sima) del trayecto circular, la cual se describe por la Segunda Ley de Newton:

T_{max} - m\cdot g = m\cdot \frac{v^{2}}{L}

En cambio, la mínima tensión aparece cuando la bola se encuentra en el cénit (o la cima) del trayecto circular, descrita por la misma ley de Newton:

T_{min} + m\cdot g = m\cdot \frac{v^{2}}{L}

Donde:

T_{min}, T_{max} - Tensiones mínima y máxima, medidas en newtons.

m - Masa de la bola, medida en kilogramos.

g - Constante gravitacional, medida en metros por segundo al cuadrado.

L - Distancia con respecto al eje de rotación, medida en metros.

v - Rapidez tangencial, medido en metros por segundo.

Se elimina la aceleración centrípeta de ambas expresiones por igualación:

T_{min} + m\cdot g = T_{max} - m\cdot g

Ahora, la diferencia entre las tensiones máxima y mínima es:

T_{max} - T_{min} = 2\cdot m \cdot g

Si m = 1\,kg y g = 9.807\,\frac{m}{s^{2}}, entonces:

T_{max} - T_{min} = 2\cdot (1\,kg)\cdot \left(9.807\,\frac{m}{s^{2}} \right)

T_{max}-T_{min} = 19.614\,N

La diferencia entre las tensiones máxima y mínima es de 19.614 newtons.

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