A 150-N bird feeder is supported by three cables as shown in Figure P4.13. Find the tension in each cable.
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To find the tension in each cable, we need to analyze the forces acting on the bird feeder.
Step 1: Analyze the forces
In this case, the bird feeder is in equilibrium, which means that the sum of all the forces acting on it is zero. We need to break down the tension in each cable into its vertical and horizontal components.
Step 2: Resolve the force vectors
Let's label the cables as Cable A, Cable B, and Cable C.
Cable A: Vertical component (A_y) opposes the weight of the bird feeder, so A_y = 150 N.
Cable A: Horizontal component (A_x) is balanced by the horizontal components of the other cables, so A_x = 0.
Cable B: Vertical component (B_y) opposes the weight of the bird feeder, so B_y = 150 N.
Cable B: Horizontal component (B_x) is balanced by the horizontal components of the other cables, so B_x = 0.
Cable C: Vertical component (C_y) opposes the weight of the bird feeder, so C_y = 150 N.
Cable C: Horizontal component (C_x) is balanced by the horizontal components of the other cables, so C_x = 0.
Step 3: Find the tensions
The tension in each cable is equal to the magnitude of its total force (tension = √(tension_x^2 + tension_y^2)).
For Cable A:
Tension_A = √(A_x^2 + A_y^2) = √(0^2 + 150^2) = √(0 + 22,500) = 150 N
For Cable B:
Tension_B = √(B_x^2 + B_y^2) = √(0^2 + 150^2) = √(0 + 22,500) = 150 N
For Cable C:
Tension_C = √(C_x^2 + C_y^2) = √(0^2 + 150^2) = √(0 + 22,500) = 150 N
So, the tension in each cable is 150 N.