Question

The guy wires AB and AC are attached to the top of the transmission tower. The tension in cable AB is 8.7 kN. Determine the required tension T in cable AC such that the net effect of the two cables is a downward force at point A. Determine the magnitude R of this downward force.

Answer 1

Answer:

$T_A_C = 6.296 kN$

$R = 10.06 kN$

Explanation:

Given:

$T_A_B = 8.7 kN$

Required:

Find the tension TAC and magnitude R of this downward force.

First calculate $\alpha, \beta, \gamma$

$\alpha = tan^-^1 =\frac{40}{50} = 38. 36$

$\beta = tan^-^1 =\frac{50}{30} = 59.04$

$\gamma = 180 - 38.36 - 59.04 = 82.6$

To Find tension in AC and magnitude R, use sine rule.

$\frac{sin a}{T_A_C} = \frac{sin b}{T_A_B} = \frac{sin c}{R}$

Substitute values:

$\frac{sin 38.36}{T_A_C} = \frac{sin 59.04}{8.7} = \frac{82.6}{R}$

Solve for T_A_C:

$T_A_C = 8.7 * \frac{sin 38.36}{sin 59.04} =$

$T_A_C = 8.7 * 0.724 = 6.296 kN$

Solve for R.

$R = 8.7 * \frac{sin 82.6}{sin 59.04} =$

$R = 8.7 * 1.156$

R = 10.06 kN

Tension AC = 6.296kN

Magnitude,R = 10.06 kN