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The problem shows a setup with two tensions, \( T_1 \) and \( T_2 \), connected to a 1 kg mass. The mass is hanging vertically, while \( T_1 \) forms an angle of 45° with the horizontal. Based on this diagram, we need to calculate the tensions \( T_1 \) and \( T_2 \).

### Let's analyze the situation:

1. **Forces acting on the mass:**
   - The weight of the mass is \( W = mg = 1 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 9.8 \, \text{N} \) (acting downwards).
   - There are two tension forces, \( T_1 \) (angled at 45°) and \( T_2 \) (acting horizontally).

2. **Vertical forces:**
   - The vertical component of \( T_1 \), which balances the weight of the mass, is \( T_1 \sin(45^\circ) \).
   - The sum of the vertical forces must equal zero for equilibrium: 
     \[
     T_1 \sin(45^\circ) = W
     \]
     Substituting the known values:
     \[
     T_1 \times \frac{\sqrt{2}}{2} = 9.8 \, \text{N}
     \]
     Solving for \( T_1 \):
     \[
     T_1 = \frac{9.8}{\frac{\sqrt{2}}{2}} = 9.8 \times \frac{2}{\sqrt{2}} = 13.86 \, \text{N}
     \]

3. **Horizontal forces:**
   - The horizontal component of \( T_1 \) is \( T_1 \cos(45^\circ) \).
   - Since \( T_2 \) balances this horizontal component, we have:
     \[
     T_2 = T_1 \cos(45^\circ) = T_1 \times \frac{\sqrt{2}}{2}
     \]
     Substituting \( T_1 = 13.86 \, \text{N} \):
     \[
     T_2 = 13.86 \times \frac{\sqrt{2}}{2} = 9.8 \, \text{N}
     \]

### Final Results:
- \( T_1 = 13.86 \, \text{N} \)
- \( T_2 = 9.8 \, \text{N} \)

Let me know if you'd like further clarification or more details!

### Relative Questions:
1. How would the tensions change if the mass were heavier?
2. What if the angle of \( T_1 \) was 30° instead of 45°? How would that affect the tensions?
3. How does the system behave if \( T_2 \) were removed?
4. What are the real-life examples of such force systems?
5. How does the force diagram change for a different angle or mass?

### Tip:
Always start by resolving the forces into horizontal and vertical components when dealing with inclined tension problems.

Perhatikan gambar 1. Hitunglah besar T1 dan T2 untuk sebuah benda 1 kg yang tergantung dengan sudut 45°.

Learn how to calculate the tension forces T1 and T2 in a system where a 1 kg mass hangs vertically with a rope at a 45° angle. This problem covers key concepts in Newton's Laws, trigonometry, and equilibrium of forces.

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