Final answer:
To determine the tension in member BD, a free-body diagram should be drawn, followed by calculating the vertical component of tension and adjusting it to ensure equilibrium. The tension would need to be increased from the initial 25.0 N by a factor of about 20, resulting in a tension slightly less than 1128 N.
Step-by-step explanation:
To determine the internal tension in member BD, we need to review the question's given information and follow a stepwise approach:
- Construct a free-body diagram to visualize the forces acting on member BD.
- Find the applied force (Fapp) using the given tension (T = 25.0 N) and the angle of inclination by decomposing the tension into its horizontal and vertical components. Since the vertical component of tension in a symmetric system contributes to the applied force, we can calculate Fapp by using the equation Fapp = 2 T sin(θ).
- Applying this to the given information, Fapp = 2(25.0 N)sin(15°) = 12.9 N.
- Finally, compare the applied force to the force required for equilibrium and adjust tension accordingly. Given that the tension would need to be increased by a factor of about 20, we infer that the proper tension would be slightly less than 1128 N.
Remember, Newton's laws are the basis for these calculations, where the sum of forces in the x-direction (Σ Fx = 0) and the sum of forces in the y-direction (Σ Fy = 0) must equal zero for static equilibrium.