Question

rank the objects according to net force; use 1 for the most negative and 8 for the most positive.
directions: tap each diagram in order to toggle though the possible net force rankings. once each object has a unique ranking, a check answer button will appear.
2 n ← 0.25 kg → 6 n; 6 n ← 0.50 kg → 4 n; 6 n ← 0.50 kg → 6 n; 0.25 kg → 6 n, → 2 n; 6 n ← 0.25 kg → 2 n; 8 n ← 2.0 kg → 2 n; 6 n ← 2.0 kg, 4 n ←; 2 n ← 0.25 kg → 4 n

Explanation:

Step1: Define Net Force Calculation

Net force ($F_{net}$) for horizontal forces: $F_{net} = F_{right} - F_{left}$ (right is positive, left is negative).

Step2: Calculate Net Force for Each Object

1. First Object (0.25 kg, 2 N left, 6 N right):

$F_{net} = 6 - 2 = 4\ N$

1. Second Object (0.50 kg, 6 N left, 4 N right):

$F_{net} = 4 - 6 = -2\ N$

1. Third Object (0.50 kg, 6 N left, 6 N right):

$F_{net} = 6 - 6 = 0\ N$

1. **Fourth Object (0.25 kg, 2 N right, 6 N right? Wait, diagram: 0.25 kg, 2 N right? Wait, original: "0.25 kg →2 N" and "→6 N"? Wait, re-express: Let's parse the diagrams correctly.

Wait, fourth diagram: "0.25 kg" with two right forces? Wait, no—probably:
Wait, first row, first: 2 N ←, 6 N → (0.25 kg).
First row, second: 6 N ←, 4 N → (0.50 kg).
Second row, first: 6 N ←, 6 N → (0.50 kg).
Second row, second: 0.25 kg, 2 N →, 6 N →? Wait, no—maybe "0.25 kg" with →2 N and →6 N? So total right: 2 + 6 = 8 N? Wait, no, maybe the arrows: if two right arrows, sum them. Wait, maybe I misread. Let's re-express each:

• Object 1 (Top-Left): Left: 2 N, Right: 6 N. $F_{net} = 6 - 2 = 4\ N$.
• Object 2 (Top-Right): Left: 6 N, Right: 4 N. $F_{net} = 4 - 6 = -2\ N$.
• Object 3 (Middle-Left): Left: 6 N, Right: 6 N. $F_{net} = 6 - 6 = 0\ N$.
• Object 4 (Middle-Right): 0.25 kg, Right: 2 N and 6 N? Wait, "0.25 kg →2 N" and "→6 N"—so total right: 2 + 6 = 8 N? Wait, no, maybe the diagram is: two right forces? So $F_{net} = 2 + 6 = 8\ N$ (since no left force). Wait, that makes sense.
• Object 5 (Bottom-Left): 0.25 kg, Left: 6 N, Right: 2 N. $F_{net} = 2 - 6 = -4\ N$.
• Object 6 (Bottom-Middle): 2.0 kg, Left: 8 N, Right: 2 N. $F_{net} = 2 - 8 = -6\ N$.
• **Object 7 (Bottom-Left? Wait, seventh: "6 N ←, 4 N ←, 2.0 kg"? Wait, "6 N ←, 4 N ←, 2.0 kg"—so total left: 6 + 4 = 10 N? Wait, no, original: "6 N ←, 4 N ←, 2.0 kg"—so $F_{net} = 0 - (6 + 4) = -10\ N$? Wait, no, right force? Wait, no—if two left forces, net force is negative (left). Wait, maybe I misread. Let's list all 8 objects (since rank 1–8):

Wait, the problem says "rank the objects" (8 objects? Let's count the diagrams:

1. Top-Left: 0.25 kg, 2 N ←, 6 N →
2. Top-Right: 0.50 kg, 6 N ←, 4 N →
3. Middle-Left: 0.50 kg, 6 N ←, 6 N →
4. Middle-Right: 0.25 kg, 2 N →, 6 N → (two right forces)
5. Bottom-Left: 0.25 kg, 6 N ←, 2 N →
6. Bottom-Middle: 2.0 kg, 8 N ←, 2 N →
7. Bottom-Left (second row? Wait, seventh: "6 N ←, 4 N ←, 2.0 kg" (two left forces)
8. Bottom-Right: 0.25 kg, 2 N ←, 4 N →

Wait, let's recalculate all 8:

1. Object 1 (0.25 kg, 2←, 6→): $F_{net} = 6 - 2 = 4\ N$
2. Object 2 (0.50 kg, 6←, 4→): $F_{net} = 4 - 6 = -2\ N$
3. Object 3 (0.50 kg, 6←, 6→): $F_{net} = 6 - 6 = 0\ N$
4. Object 4 (0.25 kg, 2→, 6→): $F_{net} = 2 + 6 = 8\ N$ (both right, sum)
5. Object 5 (0.25 kg, 6←, 2→): $F_{net} = 2 - 6 = -4\ N$
6. Object 6 (2.0 kg, 8←, 2→): $F_{net} = 2 - 8 = -6\ N$
7. Object 7 (2.0 kg, 6←, 4←): $F_{net} = 0 - (6 + 4) = -10\ N$ (both left, net left)
8. Object 8 (0.25 kg, 2←, 4→): $F_{net} = 4 - 2 = 2\ N$

Step3: Rank by Net Force (1 = most negative, 8 = most positive)

Sort net forces from most negative to most positive:

• Object 7: -10 N (most negative, rank 1)
• Object 6: -6 N (rank 2)
• Object 5: -4 N (rank 3)
• Object 2: -2 N (rank 4)
• Object 3: 0 N (rank 5)
• Object 8: 2 N (rank 6)
• Object 1: 4 N (rank 7)
• Object 4: 8 N (most positive, rank 8)

Answer:

To rank:

1. Object 7 (2.0 kg, 6 N ←, 4 N ←)
2. Object 6 (2.0 kg, 8 N ←, 2 N →)
3. Object 5 (0.25 kg, 6 N ←, 2 N →)
4. Object 2 (0.50 kg, 6 N ←, 4 N →)
5. Object 3 (0.50 kg, 6 N ←, 6 N →)
6. Object 8 (0.25 kg, 2 N ←, 4 N →)
7. Object 1 (0.25 kg, 2 N ←, 6 N →)
8. Object 4 (0.25 kg, 2 N →, 6 N →)

(Note: The exact diagram labels may vary, but the key is calculating $F_{net} = F_{right} - F_{left}$ and sorting from most negative to most positive.)