Alright, let's analyze the scenario in detail to determine which objects will begin to move.
We are provided with data for four objects, and each object's forces are given in terms of Leftward force (L), Rightward force (R), Upward force (U), and Downward force (D). The focus is on determining the net forces acting on each object and analyzing if they will begin to move based on these net forces.
### Step-by-Step Solution:
#### 1. Calculate Net Horizontal Force:
The net horizontal force for each object is calculated by subtracting the Leftward force from the Rightward force:
[tex]\[ \text{Net Horizontal Force} = R - L \][/tex]
Object 1:
[tex]\[ \text{Net Horizontal Force} = 0 - 9 = -9 \, \text{N} \][/tex]
Object 2:
[tex]\[ \text{Net Horizontal Force} = 0 - 9 = -9 \, \text{N} \][/tex]
Object 3:
[tex]\[ \text{Net Horizontal Force} = 25 - 10 = 15 \, \text{N} \][/tex]
Object 4:
[tex]\[ \text{Net Horizontal Force} = 30 - 30 = 0 \, \text{N} \][/tex]
#### 2. Calculate Net Vertical Force:
The net vertical force for each object is calculated by subtracting the Downward force from the Upward force:
[tex]\[ \text{Net Vertical Force} = U - D \][/tex]
Object 1:
[tex]\[ \text{Net Vertical Force} = 50 - 45 = 5 \, \text{N} \][/tex]
Object 2:
[tex]\[ \text{Net Vertical Force} = 65 - 65 = 0 \, \text{N} \][/tex]
Object 3:
[tex]\[ \text{Net Vertical Force} = 0 - 0 = 0 \, \text{N} \][/tex]
Object 4:
[tex]\[ \text{Net Vertical Force} = 0 - 0 = 0 \, \text{N} \][/tex]
#### 3. Determine Movement:
An object will begin to move if there is a non-zero net force acting on it in either the horizontal or vertical direction.
Object 1:
- Net Horizontal Force: [tex]\(-9 \, \text{N}\)[/tex]
- Net Vertical Force: [tex]\(5 \, \text{N}\)[/tex]
- Since both forces are non-zero, Object 1 will begin to move.
Object 2:
- Net Horizontal Force: [tex]\(-9 \, \text{N}\)[/tex]
- Net Vertical Force: [tex]\(0 \, \text{N}\)[/tex]
- Since the net horizontal force is non-zero, Object 2 will begin to move.
Object 3:
- Net Horizontal Force: [tex]\(15 \, \text{N}\)[/tex]
- Net Vertical Force: [tex]\(0 \, \text{N}\)[/tex]
- Since the net horizontal force is non-zero, Object 3 will begin to move.
Object 4:
- Net Horizontal Force: [tex]\(0 \, \text{N}\)[/tex]
- Net Vertical Force: [tex]\(0 \, \text{N}\)[/tex]
- Since both forces are zero, Object 4 will not begin to move.
### Conclusion:
- Object 1 will begin to move.
- Object 2 will begin to move.
- Object 3 will begin to move.
- Object 4 will not begin to move.
Thus, the objects that will begin to move are Objects 1, 2, and 3.
