Final answer:
In the analysis of structures like trusses, identifying forces and creating a free-body diagram assist in determining if members are in tension or compression. Using this strategy, one can use equilibrium conditions and trigonometry to solve for the forces within the system.
Step-by-step explanation:
To determine the force in each member of the truss in terms of the external loading and to state if the members are in tension or compression, one needs to understand how forces function on a truss system.
The given scenario involves a tightrope walker, for which we must consider their weight and the tension on either side of the person. By using a free-body diagram and applying trigonometry, we can conclude that the horizontal components of the tension forces T₁ (left tension) and TR (right tension) acting on the wire must be equal to maintain a state of equilibrium, as there is no horizontal acceleration.
When analyzing a rigid body, all acting forces and their lever arms should be identified, and a free-body diagram should be constructed. The free-body diagram helps us set up the equilibrium conditions for forces and torques. For members in tension or compression, the deforming force acts along the length of the member and causes a change from the original length L₀ to a new length L, with tension causing elongation and compression causing contraction.