Physics, 10.06.2021 19:00 anme3c9

Una cuerda de 20 pies se estira entre dos arboles. Un peso W cuelga del centro de la cuerda hace que el punto medio de la misma y baja 2 pies. Si la tensión resultante en la cuerda es de 200 lb,¿cual es la manigtud de la masa?

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Answer from: maddieberridgeowud2s

La magnitud de la masa del peso es 78.447 libras-masa.

Explanation:

La tensión es una fuerza de reacción de la cuerda causada por la acción de una fuerza externa. En este caso, esa fuerza externa es el peso que cuelga en el centro de la cuerda. Abajo hemos adjuntado una representación simplificada del enunciado.

Por las leyes de Newton, tenemos la siguiente ecuación de equilibrio conformada por tres fuerzas:

$\vec T_{1} + \vec T_{2} + \vec W = (0, 0)\, [N]$ (1)

Donde:

$\vec T_{1}$ , $\vec T_{2}$ - Tensiones a cada lado de la cuerda, en newtons.

$\vec W$ - Peso, en newtons.

Si sabemos que $\vec T_{1} = T\cdot (\cos \alpha, \sin \alpha)$ , $\vec T_{2} = T\cdot (-\cos \alpha, \sin \alpha)$ y $\vec W = W\cdot (0, -1)$ , entonces tenemos la siguiente ecuación vectorial:

$T\cdot (\cos \alpha, \sin \alpha) + T\cdot (-\cos\alpha, \sin \alpha) + W\cdot (0, -1) = (0,0)$

$T\cdot (0, 2\cdot \sin \alpha) = W\cdot (0, 1)$

Esto permite reducir la anterior expresión a una fórmula escalar:

$2\cdot T\cdot \sin \alpha = W$

Donde $\alpha$ es el ángulo de inclinación de la cuerda, medido en grados sexagesimales.

El ángulo de inclinación de la cuerda se determina mediante la siguiente fórmula trigonométrica inversa es:

$\alpha = \tan^{-1} \left(\frac{2\,ft}{10\,ft}\right)$

$\alpha \approx 11.310^{\circ}$

Si conocemos que $\alpha \approx 11.310^{\circ}$ y $T = 200\,lbf$ , entonces la magnitud del peso es:

$W = 2\cdot (200\,lb)\cdot \sin 11.310^{\circ}$

$W \approx 78.447\,lbf$

En el Sistema Imperial, las fuerzas son medidas en forma gravitacional, entonces la magnitud de la fuerza gravitacional del peso equivale a la magnitud de su masa. En síntesis, la magnitud de la masa es $78.447\,lbm$ .

La magnitud de la masa del peso es 78.447 libras-masa.

Una cuerda de 20 pies se estira entre dos arboles. Un peso W cuelga del centro de la cuerda hace que

Answer from: Quest

force is based upon mass and acceleration.the statement is not always true.

it can be explained from newton's second law of motion.

as per newton's second law of motion the rate of change of momentum is directly proportional to the applied force and takes place along the direction of force.

mathematically it can be written as -

$f\alpha \frac{dp}{dt}$

⇒ $f= k \frac{dp}{dt}$

here k is the proportionality constant whose value is 1.

$f=\frac{dp}{dt}$

$f= \frac{d[mv]}{dt}$

$f= m\frac{dv}{dt} +v\frac{dm}{dt}$

$f=ma+v\frac{dm}{dt}$ [a is the acceleration=dv/dt]

hence we see that force not only depends on mass and acceleration but also on velocity and rate of change of mass. force f will depend on mass and acceleration only when mass is constant.

hence the statement that force is based upon mass and acceleration is false.

Answer from: Quest

Ibelieve that the correct answer is: c. along plate boundaries

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