Answer:
T_ac = 6.586 KN
R = 10.51 KN
Explanation:
Given:
- Tension in cable T_ab = 9.1 KN
Find:
- 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.
Solution:
- Compute the three angles as shown in figure attached, a, B , y:
a = arctan (40/50) = 38.36 degrees
B = arctan (50/30) = 59.04 degrees
y = 180 - 38.36 = 82.6 degrees
- Use cosine rule to calculate R and F_ac as follows:
sin(a) / T_ac = sin(B) / T_ab = sin(y) / R
sin(38.36) / T_ac = sin(59.04) / 9.1 = sin(82.06) / R
T_ac = 9.1 * ( sin(38.36) / sin(59.04) )
T_ac = 6.586 KN
R = 9.1 * ( sin(82.06) / sin(59.04) )
R = 10.51 KN
