Final answer:
The weight of the sign, supported by two cables at a 30-degree angle with equal tension of 50 N each, is 50 N. This is derived by adding the vertical components of the tension from both cables, which must equal the weight of the sign for it to be in static equilibrium.
Step-by-step explanation:
The weight of the sign can be determined using principles of static equilibrium, where the sum of the forces in any direction equals zero. Each cable exerts a vertical force component that is a function of its tension and the angle it makes with the horizontal. Given that the tension in both cables is 50 N and the angle is 30 degrees, the vertical component of tension can be found using trigonometry (Tension × sin(angle)).
For each cable: Vertical force = 50 N × sin(30°) = 50 N × 0.5 = 25 N.
Since there are two cables with the same tension and the same angle, their vertical components will add up to support the weight of the sign. Therefore, the total vertical force supporting the sign is 25 N + 25 N = 50 N. Consequently, the weight of the sign must be 50 N, assuming equilibrium conditions where the vertical forces balance the weight of the sign.