The basis for hanging object problems is the same for ALL of our forces problems:

If an object experiences unbalanced forces in the "x" or "horizontal" direction, it will accelerate in the direction of the unbalanced force.

If an object experiences unbalanced forces in the "y" or " vertical" direction, it will accelerate in the direction of the unbalanced force.

If an object is at rest in the "x" or "horizontal" direction the forces in that direction MUST be balanced or absent.

If an object is at rest in the "y" or "vertical" direction the forces in that direction MUST be balanced or absent.
Mathematically we express those situations as:
∑F_{x} = ma_{x}
∑F_{y}= ma_{y}
THEREFORE
Our job is to
(1) determine if the forces acting in the horizontal ("x") direction are balanced or unbalanced
(2) determine if the forces acting in the vertical ("y") direction are balanced or unbalanced
TO WIT:
HANGING PROBLEMS REVIEW
► For a recap on the basics of hanging object problems see forces01 and forces02
► For an explanation of how to componentize hanging forces please see forces03
HANGING PROBLEMS (With annotated solutions)
► For a worked example of a basic hanger problem is HERE.
► A somewhat more difficult (but still very doable) hanger problem is HERE
► A rather bigleague (and kinda NASTY) hanger problem is HERE: