Question

Un semáforo de 80N cuelga del punto medio de un cable de 30m tendido entre 2 postes. Halle la tensión en cada segmento del cable si éste tiene un pandeo que lo hace descender una distancia vertical de 1m

Answer 1

Answer:

T1 = T2 = 602.33 N

Explanation:

I attached an image of the forces diagram below.

The x component of the forces for this cases is:

$\Sigma F_x=T_1cos\theta-T_2cos\theta=0\\\\T_1cos\theta=T_2cos\theta\\\\T_1=T_2$

And the y components:

$\Sigma F_y=T_1sin\theta+T_2sin\theta-W=0\\\\T_1=T_2=T\\\\\Sigma F_y=2Tsin\theta=W\\\\T=\frac{W}{2sin\theta}$

The angle is calculated by using the information about the length of the cable and the vertical distance of the traffic light:

$\theta=tan^{-1}(\frac{1}{15})=3.81\°$

Thus, you obtain:

$T=\frac{80N}{2(sin3.81\°)}=601.33N$

hence, the tension in both segments of the cable is 602.33 N