MY VIDEO Introduction to Hanging Object Problems is HERE
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
MY Video Introduction to Hanging Problems is HERE
► For one of OUR worked examples of a basic hanger problem go HERE.
► For a basic hanger practice problem try #14 & 16 on the Physics Classroom HERE (Hint: it is easier to visualize those problems as 2 dimensional hanging problems with half of the ropes/cables pulling up to the left and the other half pulling up to the right).
► A somewhat more difficult (but still very doable) hanger problem is HERE
► For a video/worked example, take a look at this (skip to 3:55)
► A rather bigleague (and kinda NASTY) hanger problem is HERE: