Final answer:
To calculate the tension in the two cables holding the gold nugget, we can use trigonometric functions to find the vertical and horizontal components of the tension. By balancing the vertical components with the weight of the nugget and setting the horizontal components equal to each other, we can solve for the tensions in the cables. The tension in the two cables is approximately 9,820 N.
Step-by-step explanation:
To calculate the tension in the two cables, we need to find the vertical and horizontal components of the tension. We can do this by using trigonometric functions. Let's denote the tension in the left cable as T1 and the tension in the right cable as T2. From the given angles, we can determine the vertical components of the tension: T1v = T1sin(45°) and T2v = T2sin(60°). The sum of these vertical components must balance the weight of the gold nugget, so we have T1v + T2v = mg, where m is the mass of the nugget and g is the acceleration due to gravity. We're given that the mass is 2,350 kg. The horizontal components of the tension, T1h and T2h, must cancel out to keep the nugget in equilibrium. Therefore, T1h = T2h. We can now use these equations to find T1 and T2:
T1v + T2v = mg
T1sin(45°) + T2sin(60°) = (2,350 kg)(9.8 m/s²)
T1h = T2h
T1cos(45°) = T2cos(60°)
Solving these equations, we find T1 ≈ 9,820 N and T2 ≈ 9,820 N. Therefore, the tension in the two cables is approximately 9,820 N.