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We are tasked with finding the magnitudes of tensions \( T_1 \) and \( T_2 \) in the system, where a 20 N block is suspended by two strings. 

### Key information:
- Weight of the block \( W = 20 \, \text{N} \)
- The angle between \( T_1 \) and the vertical is \( 60^\circ \)
- \( T_2 \) is horizontal, pulling the block to the right.

### Step-by-step solution:

1. **Vertical force balance:**
   The vertical forces must sum to zero for the block to be in equilibrium. The weight is acting downward, and only the vertical component of \( T_1 \) is balancing it. Thus:
   \[
   T_{1y} = T_1 \cos(60^\circ)
   \]
   Since this balances the weight:
   \[
   T_1 \cos(60^\circ) = W = 20 \, \text{N}
   \]
   Solving for \( T_1 \):
   \[
   T_1 \cos(60^\circ) = 20 \, \text{N}
   \]
   \[
   T_1 (0.5) = 20 \, \text{N}
   \]
   \[
   T_1 = 40 \, \text{N}
   \]

2. **Horizontal force balance:**
   The horizontal forces must also sum to zero. The horizontal component of \( T_1 \) must be equal and opposite to \( T_2 \):
   \[
   T_1 \sin(60^\circ) = T_2
   \]
   Substituting \( T_1 = 40 \, \text{N} \) and \( \sin(60^\circ) = \frac{\sqrt{3}}{2} \):
   \[
   40 \times \frac{\sqrt{3}}{2} = T_2
   \]
   \[
   T_2 = 20 \sqrt{3} \, \text{N}
   \]
   \[
   T_2 \approx 34.64 \, \text{N}
   \]

### Final Answer:
- \( T_1 = 40 \, \text{N} \)
- \( T_2 \approx 34.64 \, \text{N} \)

Would you like further details or clarifications on any step?

Here are 5 related questions you could explore:
1. What happens to \( T_1 \) and \( T_2 \) if the angle changes to \( 45^\circ \)?
2. How would the tensions change if the weight of the block increases?
3. What is the role of equilibrium conditions in such problems?
4. Can you express the tensions as functions of the angle?
5. What would happen if \( T_2 \) had a slight slope instead of being horizontal?

**Tip:** For equilibrium problems, always ensure you resolve forces into vertical and horizontal components to balance the system effectively.

Un bloque de 20 N se suspende por medio de una cuerda sin peso, que se mantiene formando un ángulo de 60º con la vertical, mediante una cuerda horizontal. Hallar la magnitud de las tensiones T1 y T2.

Find the tensions T1 and T2 in a system where a 20 N block is suspended by a string forming a 60º angle with the vertical. Learn to apply static equilibrium and trigonometric functions to solve this problem, suitable for high school physics students.

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