Two identical strings making an angle of 𝜃 = 26.3° with respect to the vertical support a block of mass *m* = 19.7 kg (see the figure below). What is the tension in each of the strings? (Enter your answer in N.)

To find the tension in each string, we can approach this problem using equilibrium conditions and basic trigonometry.

### Step 1: Identify Forces
The block is in equilibrium, so the forces acting on it must sum to zero. The forces involved are:

- The **weight** of the block, \( W = mg \), acting vertically downward, where \( m = 19.7 \, \text{kg} \) and \( g = 9.8 \, \text{m/s}^2 \).
- The **tension** \( T \) in each string. Since there are two identical strings and they make an angle \( \theta = 26.3^\circ \) with the vertical, the vertical components of the tension forces must balance the weight.

### Step 2: Vertical and Horizontal Components of Tension
Each tension force can be broken down into two components:

- The vertical component of tension in each string is \( T \cos(\theta) \).
- The horizontal component is \( T \sin(\theta) \).

Since the block is in equilibrium, the vertical components of the two tensions must balance the block's weight:

\[
2T \cos(\theta) = mg
\]

### Step 3: Solve for the Tension \( T \)
Now, we can solve for \( T \):

\[
T = \frac{mg}{2 \cos(\theta)}
\]

### Step 4: Plug in the Given Values
We are given:
- \( m = 19.7 \, \text{kg} \)
- \( g = 9.8 \, \text{m/s}^2 \)
- \( \theta = 26.3^\circ \)

First, calculate the weight of the block:

\[
mg = 19.7 \times 9.8 = 193.06 \, \text{N}
\]

Next, substitute the values into the tension equation:

\[
T = \frac{193.06}{2 \cos(26.3^\circ)}
\]

We can now calculate the cosine of 26.3° and the tension.

\[
T = \frac{193.06}{2 \times 0.895} = \frac{193.06}{1.79} \approx 107.91 \, \text{N}
\]

So, the tension in each string is approximately \( T = 107.91 \, \text{N} \).

### Final Answer:
The tension in each string is \( 107.91 \, \text{N} \).

---

Would you like more details, or do you have any further questions?

Here are 5 related questions to expand on this concept:
1. How would the tension change if the angle \( \theta \) increased?
2. What would happen to the tension if the mass of the block were doubled?
3. How does the horizontal component of tension affect the stability of the block?
4. How can we determine the total force on the block if the system were not in equilibrium?
5. What role does the angle play in determining the force distribution on the strings?

**Tip:** Always break forces into components when dealing with inclined forces, as it simplifies calculations!

Two identical strings making an angle of 𝜃 = 26.3° with respect to the vertical support a block of mass m = 19.7 kg (see the figure below). What is the tension in each of the strings? (Enter your answer in N.)

Find the tension in two strings supporting a 19.7 kg block at an angle of 26.3° using equilibrium and trigonometry. This step-by-step solution covers key concepts such as weight, tension, and vertical equilibrium, suitable for high school and college physics students.

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