Forces in Equilibrium: Finding Balance in the Universe

How can we determine the force F in rope A and the corresponding angle θ in a system?

If the resultant force acting on the support is to be 1200 lb, directed horizontally to the right.

Answer:

In order to determine the force F in rope A and the corresponding angle θ, we must analyze the system and consider the concept of forces in equilibrium.

When dealing with forces in equilibrium, it means that the system is balanced and there is no acceleration. This allows us to use the principles of vector resolution to find the components of the given resultant force.

The horizontal component of the force, labeled as Fx, is known to be 1200 lb in this scenario. As there is no vertical movement indicated, the vertical component, Fy, will be 0 lb.

By resolving Fx into its components using trigonometry, we can determine that the force F in rope A is equivalent to 1200 lb. The angle θ, in this case, is calculated to be 0°.

This analysis demonstrates that the system is in equilibrium, and the force F in rope A acts in the direction and magnitude necessary to maintain this balance. Understanding forces in equilibrium is crucial in various fields, from physics to engineering, where balance is essential for stability and safety.