To find the tension in each cable, we can use the principle of equilibrium. According to this principle, the sum of all forces in both the horizontal and vertical directions is equal to zero.
In this case, we can assume that the vertical direction is positive upward and the horizontal direction is positive to the right.
Let's label the tension in the left cable as T1, the tension in the right cable as T2, and the tension in the bottom cable as T3.
Looking at the image, we can see that the bird feeder is in equilibrium vertically. This means that the sum of the vertical forces is equal to zero.
We have:
T1 + T2 - T3 - 165.8 N = 0 (Equation 1)
Next, let's consider the equilibrium horizontally. Since there are no external horizontal forces acting on the bird feeder, the sum of the horizontal forces is also equal to zero.
We have:
T2 - T1 = 0 (Equation 2)
Now we can solve these two equations simultaneously to find the tension in each cable.
From Equation 2, we can rewrite it as T2 = T1.
Substituting T2 = T1 into Equation 1, we get:
T1 + T1 - T3 - 165.8 N = 0
2T1 - T3 - 165.8 N = 0
Now, let's solve for T1 and T3 using this equation.
To find T1, we need to solve for it in terms of T3:
2T1 = T3 + 165.8 N
T1 = (T3 + 165.8 N) / 2
Now, substitute this value of T1 back into the equation T2 = T1:
T2 = (T3 + 165.8 N) / 2
So, the tension in the left cable (T1) is (T3 + 165.8 N) / 2, the tension in the right cable (T2) is (T3 + 165.8 N) / 2, and the tension in the bottom cable (T3) is T3.
However, to fully solve the problem, we need additional information about the angles at which the cables are attached. Without this information, we cannot determine the exact values of T1, T2, and T3.