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To solve this problem, we need to find the tensions in the two cables supporting the 200 kg mass. Let’s break it down.

### Step 1: Understanding the Forces
1. **Mass**: The object has a mass of 200 kg.
2. **Gravitational Force** (\( W \)): The weight can be calculated using \( W = m \cdot g \), where \( g = 9.81 \, \text{m/s}^2 \).
   \[
   W = 200 \times 9.81 = 1962 \, \text{N}
   \]

### Step 2: Defining the Tensions
Let's denote:
- \( T_1 \) as the tension in the cable angled at 30° to the vertical.
- \( T_2 \) as the tension in the horizontal cable.

### Step 3: Setting Up Equilibrium Equations
Since the system is in static equilibrium, the sum of forces in both the \( x \)- and \( y \)-directions must be zero.

1. **Vertical Force Balance ( \( y \)-direction)**:
   \[
   T_1 \sin(30^\circ) = W
   \]
   Substitute \( W = 1962 \, \text{N} \):
   \[
   T_1 \times 0.5 = 1962
   \]
   \[
   T_1 = \frac{1962}{0.5} = 3924 \, \text{N}
   \]

2. **Horizontal Force Balance ( \( x \)-direction)**:
   \[
   T_1 \cos(30^\circ) = T_2
   \]
   Substituting \( T_1 = 3924 \, \text{N} \):
   \[
   T_2 = 3924 \times \cos(30^\circ)
   \]
   \[
   T_2 = 3924 \times 0.866 \approx 3397 \, \text{N}
   \]

### Answer
The tensions in the cables are:
- \( T_1 = 3924 \, \text{N} \)
- \( T_2 = 3397 \, \text{N} \)

Would you like further explanation on any of these steps, or have any additional questions?

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Here are some additional questions to expand on this topic:
1. How would the tensions change if the angle were different?
2. What if the mass was increased to 300 kg—how would \( T_1 \) and \( T_2 \) change?
3. How can we determine if the cable can withstand these tensions?
4. What would be the effect of changing the angle to 45° on \( T_2 \)?
5. Why is it important to analyze forces in both \( x \)- and \( y \)-directions for equilibrium?

**Tip**: Always double-check angle measurements, as they significantly impact tension calculations.

Hallar las tensiones 2266 y 1137 N en un sistema donde un objeto de 200 kg está sostenido por dos cables, uno inclinado a 30° con la vertical.

Solve for the tensions in a system where a 200 kg mass is suspended by two cables, one at a 30° angle to the vertical. Includes step-by-step solution, force balance equations, and equilibrium conditions for a static system.

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