Final answer:
The tension in each cable suspending a loudspeaker can be found using trigonometry and Newton's second law. By calculating the vertical force due to gravity on the loudspeaker and the vertical component of the tension, we can determine the tension in each symmetrically angled cable.
Step-by-step explanation:
The question is asking to find the tension in each of the cables that suspend a loudspeaker. To solve this problem, we first need to recognize that the system is in equilibrium, meaning that the sum of the forces in both the vertical and horizontal directions is zero. We can use trigonometry to determine the angles involved and then apply Newton's second law to find the tensions.
To find the tension, we start by calculating the angles that the cables make with the ceiling. Since the loudspeaker is located 2.40 m below the ceiling and the cables are 3.30 m long, we can use trigonometry to find that the angle θ, with respect to the vertical, is cosine^{-1}(2.40/3.30). The vertical force due to gravity on the loudspeaker is the weight, which is the mass (23.0 kg) multiplied by the acceleration due to gravity (9.8 m/s²). This force must be balanced by the vertical component of the tension in the two cables. Since there are two cables and they are symmetrical, the tension in each cable is the same. We can then set up an equation with the vertical component of tension (T cos(θ)) equal to half of the loudspeaker's weight and solve for T, which is the tension in each cable.