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We are asked to find the force \( F_{T,1} \) in the cord that supports the picture frame. Let's break down the forces and torques acting on the system.

### Step 1: Define forces and torques
- The system is in equilibrium, so the sum of forces and the sum of torques must both be zero.
- Forces acting on the frame:
  1. \( F_{T,1} \) at an angle of 50°, acting along the cord on the right.
  2. \( F_{T,2} \), the tension force acting vertically on the left cord.
  3. The weight of the picture frame, which is 11.4 N, acting downwards at the center of the frame.

### Step 2: Force equilibrium
In the horizontal and vertical directions, the sum of forces must be zero.

#### Horizontal direction:
\[
\sum F_x = 0 \quad \Rightarrow \quad F_{T,1} \cos(50^\circ) - F = 0
\]
So, 
\[
F = F_{T,1} \cos(50^\circ)
\]

#### Vertical direction:
\[
\sum F_y = 0 \quad \Rightarrow \quad F_{T,1} \sin(50^\circ) + F_{T,2} - 11.4 = 0
\]
\[
F_{T,2} = 11.4 - F_{T,1} \sin(50^\circ)
\]

### Step 3: Torque equilibrium
We can take torques about point P (the lower-right corner) to avoid needing to include the unknown horizontal force \( F \).

The sum of torques must be zero:
\[
\sum \tau_P = 0
\]
Torque contributions:
- The weight (11.4 N) creates a counterclockwise torque:
  \[
  \tau_{\text{weight}} = 11.4 \, \text{N} \times 10 \, \text{cm} = 1.14 \, \text{N}\cdot\text{m}
  \]
- \( F_{T,2} \) creates a counterclockwise torque:
  \[
  \tau_{F_{T,2}} = F_{T,2} \times 20 \, \text{cm} = F_{T,2} \times 0.2 \, \text{m}
  \]
- \( F_{T,1} \) creates a clockwise torque, and the vertical component of \( F_{T,1} \) contributes to this:
  \[
  \tau_{F_{T,1}} = F_{T,1} \sin(50^\circ) \times 20 \, \text{cm} = F_{T,1} \sin(50^\circ) \times 0.2 \, \text{m}
  \]

Setting the sum of torques to zero:
\[
1.14 = F_{T,1} \sin(50^\circ) \times 0.2
\]
\[
F_{T,1} = \frac{1.14}{0.2 \times \sin(50^\circ)}
\]
\[
F_{T,1} = \frac{1.14}{0.153} \approx 7.45 \, \text{N}
\]

### Final Answer:
The force in the cord \( F_{T,1} \) is approximately **7.45 N**.

Would you like further details or clarification on this solution?

### Related Questions:
1. How do we calculate the force \( F \) based on the value of \( F_{T,1} \)?
2. How does changing the angle of the cord affect the tension force \( F_{T,1} \)?
3. What is the value of \( F_{T,2} \) using the equilibrium conditions?
4. How would the torque balance change if the picture frame's weight increased?
5. What is the significance of choosing point P for the torque calculation?

### Tip:
Always select a pivot point where unknown forces pass through, simplifying your torque calculations!

A uniform 11.4 N picture frame is supported as shown. Find the force FT,1 in the cord that is required to hold the frame in this position. Answer in units of N.

Learn how to find the force FT,1 in a cord supporting a uniform 11.4 N picture frame using equilibrium conditions. This problem involves trigonometry and torque calculations, suitable for advanced physics students.

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