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zepelin [54]
2 years ago
8

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 requ

ired 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.

Engineering
1 answer:
dimulka [17.4K]2 years ago
3 0

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

<em>To Find tension in AC and magnitude R, use sine rule</em>.

\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

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