A 184 N bird feeder is supported by three cables. angle 1 is 60 degrees and angle 2 is 30 degrees Find the tension in each cable.
To find the tension in each cable, we need to use trigonometry and resolve the forces into their components.
Let's denote the tension in the first cable as T1, the tension in the second cable as T2, and the tension in the third cable as T3.
First, let's consider the horizontal components of the forces. The horizontal component of T1 is T1 * cos(angle 1), and the horizontal component of T2 is T2 * cos(angle 2). Since there is no horizontal force acting on the bird feeder, these components must cancel each other out:
T1 * cos(60) + T2 * cos(30) = 0
Next, let's consider the vertical components of the forces. The vertical component of T1 is T1 * sin(angle 1), the vertical component of T2 is T2 * sin(angle 2), and the vertical component of T3 is T3. These forces should add up to balance the weight of the bird feeder, which is 184 N:
T1 * sin(60) + T2 * sin(30) + T3 = 184
We now have a system of equations:
1) T1 * cos(60) + T2 * cos(30) = 0
2) T1 * sin(60) + T2 * sin(30) + T3 = 184
To solve this system, we can use substitution or elimination. Let's start by solving equation 1) for T2:
T2 = -T1 * cos(60) / cos(30)
Now substitute this value of T2 into equation 2):
T1 * sin(60) - T1 * cos(60) * tan(30) + T3 = 184
Now simplify the equation:
(T1 * sin(60) - T1 * cos(60) * tan(30)) + T3 = 184
We can simplify further:
T1 * (sin(60) - cos(60) * tan(30)) + T3 = 184
Now, we can solve this equation for T3:
T3 = 184 - T1 * (sin(60) - cos(60) * tan(30))
With the values of T1 and T3, we can substitute them back into equation 1) to find T2:
T2 = -T1 * cos(60) / cos(30)
Now you can use a calculator to evaluate the equations and find the values of T1, T2, and T3.