Statics: CE Nov. 2010 - Two tension wires are supported by a concrete block
Two tension wires are supported by a concrete block attached to an anchor ring as shown in the figure.
1. Which of the following most nearly gives the resultant force in the anchor ring?
a. 7.28 KN c. 9.07 KN
b. 10.42 KN d. 5.16 KN
2. Which of the following most nearly gives the angle that the resultant force makes with the horizontal?
a. 43.67° c. 39.55°
b. 53.17° d. 48.72
For #1
→+ΣFx (horizontal)
Rx = -7cos15° + 3.5cos30° = -3.7304 = -3.73 KN
↑+ΣFy (vertical)
Ry = 7sin15° + 3.5sin30° = 3.5617 = 3.562 KN
Use the Pythagorean Theorem
R² = Rx² + Ry²
R² = (-3.73)² + (3.562)²
R = 5.16 KN
For #2
tan θ = |Ry/Rx|
tan θ = |3.562/-3.73|
θ = 43.67°
θ = |tan-1(3.562/-3.73)|
θ = 43.67°
