To determine which objects have balanced and unbalanced forces, we need to analyze the net forces acting on each object in both the vertical and horizontal directions. The forces acting on the objects are given in the table:
[tex]\[
\begin{array}{|c|c|c|c|c|}
\hline
\text{Object} & F_1 \uparrow & F_2 \rightarrow & F_3 \leftarrow & F_4 \downarrow \\
\hline
W & 30\,\text{N} & 20\,\text{N} & 20\,\text{N} & 30\,\text{N} \\
\hline
X & 15\,\text{N} & 35\,\text{N} & 25\,\text{N} & 15\,\text{N} \\
\hline
Y & 60\,\text{N} & 0\,\text{N} & 0\,\text{N} & 60\,\text{N} \\
\hline
Z & 45\,\text{N} & 0\,\text{N} & 22\,\text{N} & 45\,\text{N} \\
\hline
\end{array}
\][/tex]
Next, we calculate the net forces for each object:
- Object W:
- Net vertical force = [tex]\(F_1 - F_4 = 30\,\text{N} - 30\,\text{N} = 0\,\text{N}\)[/tex]
- Net horizontal force = [tex]\(F_2 - F_3 = 20\,\text{N} - 20\,\text{N} = 0\,\text{N}\)[/tex]
- Since both net forces are [tex]\(0\,\text{N}\)[/tex], the forces on W are balanced.
- Object X:
- Net vertical force = [tex]\(F_1 - F_4 = 15\,\text{N} - 15\,\text{N} = 0\,\text{N}\)[/tex]
- Net horizontal force = [tex]\(F_2 - F_3 = 35\,\text{N} - 25\,\text{N} = 10\,\text{N}\)[/tex]
- Since the net horizontal force is not [tex]\(0\,\text{N}\)[/tex], the forces on X are unbalanced.
- Object Y:
- Net vertical force = [tex]\(F_1 - F_4 = 60\,\text{N} - 60\,\text{N} = 0\,\text{N}\)[/tex]
- Net horizontal force = [tex]\(F_2 - F_3 = 0\,\text{N} - 0\,\text{N} = 0\,\text{N}\)[/tex]
- Since both net forces are [tex]\(0\,\text{N}\)[/tex], the forces on Y are balanced.
- Object Z:
- Net vertical force = [tex]\(F_1 - F_4 = 45\,\text{N} - 45\,\text{N} = 0\,\text{N}\)[/tex]
- Net horizontal force = [tex]\(F_2 - F_3 = 0\,\text{N} - 22\,\text{N} = -22\,\text{N}\)[/tex]
- Since the net horizontal force is not [tex]\(0\,\text{N}\)[/tex], the forces on Z are unbalanced.
Based on these calculations, we see that objects W and Y have balanced forces, while objects X and Z have unbalanced forces.
Thus, the best explanation for the forces acting on the objects is:
- Objects [tex]$W$[/tex] and [tex]$Y$[/tex] have balanced forces, and objects [tex]$X$[/tex] and [tex]$Z$[/tex] have unbalanced forces.
