To determine the force $F_{T,1}$ in the cord required to hold the frame in position, we'll analyze the system using equilibrium conditions for both forces and torques.

Step 1: Identify the forces acting on the frame

The forces involved are:

1. The weight of the frame, $W = 11.3 \, \text{N}$, acting vertically downward at the center of the frame.
2. The force $F_{T,1}$ in the cord making an angle of $50^\circ$ with the horizontal.
3. The vertical force $F_{T,2}$ acting upward at the left corner of the frame.
4. The horizontal force $F$ acting at point P on the right side of the frame.

Step 2: Write the equations of equilibrium

Force Equilibrium

For the frame to be in equilibrium, the sum of all horizontal and vertical forces must be zero:

• Horizontal forces: $F_{T,1} \cos(50^\circ) = F$

• Vertical forces: $F_{T,1} \sin(50^\circ) + F_{T,2} = 11.3 \, \text{N}$

Torque Equilibrium

Let's take the torque about the point where $F_{T,2}$ is applied (top-left corner of the frame). Assuming counterclockwise torque as positive:

• The torque due to $W = 11.3 \, \text{N}$ (acting downward at the center of the frame, 14 cm below the top and 14 cm horizontally from the left): $\tau_W = 11.3 \, \text{N} \times 14 \, \text{cm} = 158.2 \, \text{N} \cdot \text{cm} \quad (\text{clockwise, negative})$

• The torque due to $F_{T,1}$ (at 28 cm from the left corner): $\tau_{F_{T,1}} = F_{T,1} \sin(50^\circ) \times 28 \, \text{cm} \quad (\text{counterclockwise, positive})$

• The torque due to $F$ at point P (which does not produce torque about the top-left corner).

Setting the sum of the torques equal to zero: $F_{T,1} \sin(50^\circ) \times 28 \, \text{cm} = 158.2 \, \text{N} \cdot \text{cm}$

Step 3: Solve for $F_{T,1}$

Solving the torque equation for $F_{T,1}$: $F_{T,1} = \frac{158.2 \, \text{N} \cdot \text{cm}}{28 \, \text{cm} \times \sin(50^\circ)}$

Calculating the value: $F_{T,1} = \frac{158.2}{28 \times 0.766} \approx 7.35 \, \text{N}$

Final Answer

The force $F_{T,1}$ in the cord required to hold the frame in position is approximately: $F_{T,1} \approx 7.35 \, \text{N}$

Would you like a more detailed breakdown or have any questions?

Related Questions:

1. How do you determine the value of $F_{T,2}$ in the system?
2. What would change in the calculations if the angle of $F_{T,1}$ were different?
3. How would you find the horizontal force $F$ acting at point P?
4. What are the conditions for equilibrium in terms of forces and torques?
5. How does changing the weight of the frame affect the forces in the cords?

Tip:

Always choose a point with multiple unknown forces as the pivot for calculating torque to simplify your equations!