The table represents the forces on four objects, with directions. a 5-column table with 4 rows. the first column labeled object has entries w, x, y, z. the second column labeled f subscript 1 arrow pointing up has entries 30 newtons, 15 newtons, 60 newtons, 45 newtons. the third column labeled f subscript 2 arrow pointing right has entries 20 newtons, 35 newtons, 0 newtons, 0 newtons. the fourth column labeled f subscript 3 arrow pointing left has entries 20 newtons, 25 newtons, 0 newtons, 22 newtons. the fifth column labeled f subscript 4 arrow pointing down has entries 30 newtons, 15 newtons, 60 newtons, 45 newtons. which best explains the forces acting on the objects? objects w and x have balanced forces, and objects y and z have unbalanced forces. objects w and y have balanced forces, and objects x and z have unbalanced forces. objects x and y have balanced forces, and objects w and z have unbalanced forces. objects x and z have balanced forces, and objects w and y have unbalanced forces.

Objects W and Y have balanced forces, and objects X and Z have unbalanced forces.

Explanation:

We represent the table below and study which forces are balanced in the vertical and horizontal directions separately:

Study of the balance of vertical forces (we study the Up and Down forces (Columns and   . e notice that the magnitudes we read for object W are 30N and 30N respectively, therefore this object is vertically balanced. Object X is also vertically balanced since the magnitude of the force pointing up equals the magnitude of force pointing down (15N in both cases). Objects Y and Z are also balanced vertically, since for object Y the force up is 60N and equal in magnitude to the downward force of 60N; and object Z has 45N pointing up and also 45N pointing down. Then vertically, all objects are balanced.

Now the horizontal analysis of forces:

Object W shows 20N to the right and 20N to the left, so this object is balanced also horizontally.

Object X is NOT balanced because the force to the right 35N is 10N larger than the force to the left (25N)

Object Y is horizontally balanced since it has 0N both left and right.

Object Z is NOT balanced horizontally, since the force to the left is 22N while there is a zero force to the right.

In summary: the only objects that are completely balanced (vertically and horizontally) are: object W and object Y. While objects X and Z have unbalanced forces

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