To determine whether the forces acting on each object are balanced or unbalanced, we need to sum all the forces applied to each object and check if the total net force is zero (balanced) or not (unbalanced).
Let's examine each object step-by-step:
### Object W:
[tex]\[ F_1 = 30\,N, \, F_2 = -20\,N, \, F_3 = -20\,N, \, F_4 = 30\,N \][/tex]
The net force on [tex]\( W \)[/tex] is:
[tex]\[ 30 + (-20) + (-20) + 30 = 30 - 20 - 20 + 30 = 20 \][/tex]
Since the net force on [tex]\( W \)[/tex] is not zero, the forces on [tex]\( W \)[/tex] are unbalanced.
### Object X:
[tex]\[ F_1 = 15\,N, \, F_2 = -35\,N, \, F_3 = -25\,N, \, F_4 = 15\,N \][/tex]
The net force on [tex]\( X \)[/tex] is:
[tex]\[ 15 + (-35) + (-25) + 15 = 15 - 35 - 25 + 15 = -30 \][/tex]
Since the net force on [tex]\( X \)[/tex] is not zero, the forces on [tex]\( X \)[/tex] are unbalanced.
### Object Y:
[tex]\[ F_1 = 60\,N, \, F_2 = 0\,N, \, F_3 = 0\,N, \, F_4 = 60\,N \][/tex]
The net force on [tex]\( Y \)[/tex] is:
[tex]\[ 60 + 0 + 0 + 60 = 120 \][/tex]
Since the net force on [tex]\( Y \)[/tex] is not zero, the forces on [tex]\( Y \)[/tex] are unbalanced.
### Object Z:
[tex]\[ F_1 = 45\,N, \, F_2 = 0\,N, \, F_3 = -22\,N, \, F_4 = 45\,N \][/tex]
The net force on [tex]\( Z \)[/tex] is:
[tex]\[ 45 + 0 + (-22) + 45 = 45 - 22 + 45 = 68 \][/tex]
Since the net force on [tex]\( Z \)[/tex] is not zero, the forces on [tex]\( Z \)[/tex] are unbalanced.
From our calculations, we see that the forces on all four objects [tex]\( W, X, Y, \)[/tex] and [tex]\( Z \)[/tex] are unbalanced. Therefore, the correct explanation of the forces acting on the objects based on the given options is:
None of the options are correct because all the objects [tex]\( W, X, Y, \)[/tex] and [tex]\( Z \)[/tex] have unbalanced forces.
