Question

part d complete previous part(s) submit request answer there are two remaining tensions, f_ab and f_bc. which equilibrium equation depends on only one of them? the sum of the forces in the z - direction. the sum of the forces in the y - direction. both equilibrium equations depend on both forces. both equilibrium equations depend on only one of the forces

Explanation:

Step1: Analyze force - equilibrium concept

In a static - equilibrium situation, the sum of forces in each direction (x, y, z) must be zero. If we consider the y - direction or z - direction forces acting on point B where tensions \(F_{AB}\) and \(F_{BC}\) are present, the equilibrium equations \(\sum F_y = 0\) and \(\sum F_z=0\) usually depend on multiple forces acting in those directions. However, if we consider a situation where one of the forces has no component in a particular direction, the equilibrium equation for that direction may depend on only one of the forces. For example, if \(F_{AB}\) has no z - component and \(F_{BC}\) has a non - zero z - component, the \(\sum F_z = 0\) equation may depend only on \(F_{BC}\).

Answer:

The sum of the forces in the z - direction.