Answer :
To analyze the forces acting on the objects and determine whether they are balanced or unbalanced, we need to calculate the net force on each object. The net force is the sum of all individual forces acting on an object.
1. Object [tex]\( W \)[/tex]:
- Forces: [tex]\( F_1 = 30 \, \text{N} \)[/tex], [tex]\( F_2 = -20 \, \text{N} \)[/tex], [tex]\( F_3 = -20 \, \text{N} \)[/tex], [tex]\( F_4 = 30 \, \text{N} \)[/tex]
- Net Force: [tex]\( 30 - 20 - 20 + 30 = 20 \, \text{N} \)[/tex]
- Since the net force is not zero, the forces on [tex]\( W \)[/tex] are unbalanced.
2. Object [tex]\( X \)[/tex]:
- Forces: [tex]\( F_1 = 15 \, \text{N} \)[/tex], [tex]\( F_2 = -35 \, \text{N} \)[/tex], [tex]\( F_3 = -25 \, \text{N} \)[/tex], [tex]\( F_4 = 15 \, \text{N} \)[/tex]
- Net Force: [tex]\( 15 - 35 - 25 + 15 = -30 \, \text{N} \)[/tex]
- Since the net force is not zero, the forces on [tex]\( X \)[/tex] are unbalanced.
3. Object [tex]\( Y \)[/tex]:
- Forces: [tex]\( F_1 = 60 \, \text{N} \)[/tex], [tex]\( F_2 = 0 \, \text{N} \)[/tex], [tex]\( F_3 = 0 \, \text{N} \)[/tex], [tex]\( F_4 = 60 \, \text{N} \)[/tex]
- Net Force: [tex]\( 60 + 0 + 0 + 60 = 120 \, \text{N} \)[/tex]
- Since the net force is not zero, the forces on [tex]\( Y \)[/tex] are unbalanced.
4. Object [tex]\( Z \)[/tex]:
- Forces: [tex]\( F_1 = 45 \, \text{N} \)[/tex], [tex]\( F_2 = 0 \, \text{N} \)[/tex], [tex]\( F_3 = -22 \, \text{N} \)[/tex], [tex]\( F_4 = 45 \, \text{N} \)[/tex]
- Net Force: [tex]\( 45 + 0 - 22 + 45 = 68 \, \text{N} \)[/tex]
- Since the net force is not zero, the forces on [tex]\( Z \)[/tex] are unbalanced.
After calculating the net forces, we determine the states of balance for these objects:
- Objects [tex]\( W \)[/tex], [tex]\( X \)[/tex], [tex]\( Y \)[/tex], and [tex]\( Z \)[/tex] all have unbalanced forces (net forces are non-zero).
Therefore, the best explanation for the forces acting on the objects is:
- [tex]\( \textbf{Objects W, X, Y, and Z all have unbalanced forces.} \)[/tex]
This situation does not match any of the options that describe specific pairs of objects as balanced or unbalanced. Therefore, none of the provided answer choices (A, B, C, or D) accurately explain the given scenario based on our calculations.
1. Object [tex]\( W \)[/tex]:
- Forces: [tex]\( F_1 = 30 \, \text{N} \)[/tex], [tex]\( F_2 = -20 \, \text{N} \)[/tex], [tex]\( F_3 = -20 \, \text{N} \)[/tex], [tex]\( F_4 = 30 \, \text{N} \)[/tex]
- Net Force: [tex]\( 30 - 20 - 20 + 30 = 20 \, \text{N} \)[/tex]
- Since the net force is not zero, the forces on [tex]\( W \)[/tex] are unbalanced.
2. Object [tex]\( X \)[/tex]:
- Forces: [tex]\( F_1 = 15 \, \text{N} \)[/tex], [tex]\( F_2 = -35 \, \text{N} \)[/tex], [tex]\( F_3 = -25 \, \text{N} \)[/tex], [tex]\( F_4 = 15 \, \text{N} \)[/tex]
- Net Force: [tex]\( 15 - 35 - 25 + 15 = -30 \, \text{N} \)[/tex]
- Since the net force is not zero, the forces on [tex]\( X \)[/tex] are unbalanced.
3. Object [tex]\( Y \)[/tex]:
- Forces: [tex]\( F_1 = 60 \, \text{N} \)[/tex], [tex]\( F_2 = 0 \, \text{N} \)[/tex], [tex]\( F_3 = 0 \, \text{N} \)[/tex], [tex]\( F_4 = 60 \, \text{N} \)[/tex]
- Net Force: [tex]\( 60 + 0 + 0 + 60 = 120 \, \text{N} \)[/tex]
- Since the net force is not zero, the forces on [tex]\( Y \)[/tex] are unbalanced.
4. Object [tex]\( Z \)[/tex]:
- Forces: [tex]\( F_1 = 45 \, \text{N} \)[/tex], [tex]\( F_2 = 0 \, \text{N} \)[/tex], [tex]\( F_3 = -22 \, \text{N} \)[/tex], [tex]\( F_4 = 45 \, \text{N} \)[/tex]
- Net Force: [tex]\( 45 + 0 - 22 + 45 = 68 \, \text{N} \)[/tex]
- Since the net force is not zero, the forces on [tex]\( Z \)[/tex] are unbalanced.
After calculating the net forces, we determine the states of balance for these objects:
- Objects [tex]\( W \)[/tex], [tex]\( X \)[/tex], [tex]\( Y \)[/tex], and [tex]\( Z \)[/tex] all have unbalanced forces (net forces are non-zero).
Therefore, the best explanation for the forces acting on the objects is:
- [tex]\( \textbf{Objects W, X, Y, and Z all have unbalanced forces.} \)[/tex]
This situation does not match any of the options that describe specific pairs of objects as balanced or unbalanced. Therefore, none of the provided answer choices (A, B, C, or D) accurately explain the given scenario based on our calculations.
