In this problem, we are asked to find the tension in each of two identical strings that support a block of mass $m = 13.7 \, \text{kg}$. The strings make an angle $\theta = 25.3^\circ$ with the vertical.

Step 1: Analyze the forces on the block

Since the block is in equilibrium (not moving), the forces acting on it must balance. The forces involved are:

• The gravitational force ($F_g$) acting downward due to the block's weight, given by: $F_g = mg$ where $g = 9.81 \, \text{m/s}^2$ is the acceleration due to gravity and $m$ is the mass of the block.

• The tension forces in the two strings, which we will call $T$. Each string pulls upward at an angle $\theta = 25.3^\circ$ from the vertical.

Step 2: Set up the force balance equations

Since the block is in equilibrium, the sum of the forces in both the vertical and horizontal directions must be zero.

Vertical direction:

In the vertical direction, the upward components of the tension forces must balance the downward gravitational force: $2T \cos \theta = mg$ where $T$ is the tension in each string, and the factor of 2 accounts for the two strings.

Horizontal direction:

In the horizontal direction, the leftward and rightward components of the tensions cancel each other, so we don't need to consider them for finding the tension.

Step 3: Solve for $T$

Rearranging the equation for the vertical force balance to solve for $T$: $T = \frac{mg}{2 \cos \theta}$ Substituting the given values:

• $m = 13.7 \, \text{kg}$
• $g = 9.81 \, \text{m/s}^2$
• $\theta = 25.3^\circ$

Now, calculate $T$.The tension in each of the two strings is approximately $74.33 \, \text{N}$.

Would you like further details on any of the steps, or do you have any other questions?

Here are 5 related questions to further explore this concept:

1. How would the tension change if the angle $\theta$ were increased?
2. What would the tension be if the block's mass were doubled?
3. How does the tension vary if only one string were used to support the block?
4. What happens to the system if the angle $\theta$ approaches 90°?
5. How can we calculate the horizontal components of the tension forces?

Tip: When solving equilibrium problems, always check both the vertical and horizontal force balances.