Question

rank the objects according to net force; use 1 for the most negative and 6 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.
4 n ← 2.0 kg → 8 n
6 n ← 0.50 kg → 4 n
4 n ← 0.25 kg ← 4 n
16.0 kg → 6 n → 2 n
2 n ← 0.50 kg → 8 n
6 n ← 0.25 kg → 2 n

Explanation:

Step1: Define Net Force

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

Step2: Calculate for Each Object

1. 2.0 kg: $F_{net} = 8N - 4N = 4N$
2. 0.50 kg (6N left, 4N right): $F_{net} = 4N - 6N = -2N$
3. 0.25 kg (two 4N left): $F_{net} = 0N - 8N = -8N$ (wait, no—wait, two 4N left: $F_{left}=4+4=8N$, $F_{right}=0N$ → $F_{net}=0 - 8 = -8N$? Wait, no, maybe I misread. Wait, the third diagram: "4N ← 0.25 kg" and "4N ←"—so two left forces, total left: 4+4=8N, right: 0N. So $F_{net}=0 - 8 = -8N$.
4. **16.0 kg (6N right, 2N right?) Wait, diagram: "16.0 kg →6N" and "→2N"—so right forces: 6+2=8N, left: 0N. $F_{net}=8N - 0 = 8N$
5. 0.50 kg (2N left, 8N right): $F_{net}=8N - 2N = 6N$
6. 0.25 kg (6N left, 2N right): $F_{net}=2N - 6N = -4N$

Wait, let's re-express each:

1. 2.0 kg: $8 - 4 = 4N$
2. 0.50 kg (6L,4R): $4 - 6 = -2N$
3. 0.25 kg (4L,4L): $0 - (4+4) = -8N$
4. 16.0 kg (6R,2R): $6 + 2 - 0 = 8N$
5. 0.50 kg (2L,8R): $8 - 2 = 6N$
6. 0.25 kg (6L,2R): $2 - 6 = -4N$

Now, list $F_{net}$ values:

• 0.25 kg (two 4N left): $-8N$ (most negative)
• 0.25 kg (6L,2R): $-4N$
• 0.50 kg (6L,4R): $-2N$
• 2.0 kg: $4N$
• 0.50 kg (2L,8R): $6N$
• 16.0 kg: $8N$ (most positive)

Now rank from 1 (most negative) to 6 (most positive):

1. 0.25 kg (two 4N left) → $-8N$ (rank 1)
2. 0.25 kg (6L,2R) → $-4N$ (rank 2)
3. 0.50 kg (6L,4R) → $-2N$ (rank 3)
4. 2.0 kg → $4N$ (rank 4)
5. 0.50 kg (2L,8R) → $6N$ (rank 5)
6. 16.0 kg → $8N$ (rank 6)

Wait, but maybe I misread the diagrams. Let's check again:

• Third diagram: "4N ← 0.25 kg" and "4N ←" → two left forces: 4+4=8N left, 0 right. $F_{net} = -8N$ (most negative, rank 1).
• Sixth diagram: "6N ← 0.25 kg →2N" → left:6N, right:2N. $F_{net}=2 - 6 = -4N$ (rank 2).
• Second diagram: "6N ← 0.50 kg →4N" → left:6, right:4. $F_{net}=4 - 6 = -2N$ (rank 3).
• First diagram: "8N → 2.0 kg ←4N" → right:8, left:4. $F_{net}=8 - 4 = 4N$ (rank 4).
• Fifth diagram: "8N → 0.50 kg ←2N" → right:8, left:2. $F_{net}=8 - 2 = 6N$ (rank 5).
• Fourth diagram: "6N → 16.0 kg →2N" → right:6+2=8, left:0. $F_{net}=8 - 0 = 8N$ (rank 6).

So the ranking (1=most negative, 6=most positive) is:

1. 0.25 kg (two 4N left)
2. 0.25 kg (6N left, 2N right)
3. 0.50 kg (6N left, 4N right)
4. 2.0 kg (8N right, 4N left)
5. 0.50 kg (8N right, 2N left)
6. 16.0 kg (6N + 2N right)

But the problem says "tap each diagram to toggle rankings". Since the question is to rank them, the order from most negative (1) to most positive (6) is:

1. 0.25 kg (two 4N left)
2. 0.25 kg (6N left, 2N right)
3. 0.50 kg (6N left, 4N right)
4. 2.0 kg (8N right, 4N left)
5. 0.50 kg (8N right, 2N left)
6. 16.0 kg (6N + 2N right)

Answer:

The ranking (1 = most negative, 6 = most positive) is:

1. 0.25 kg (two 4N left)
2. 0.25 kg (6N left, 2N right)
3. 0.50 kg (6N left, 4N right)
4. 2.0 kg (8N right, 4N left)
5. 0.50 kg (8N right, 2N left)
6. 16.0 kg (6N + 2N right)

(Note: The actual diagram labels may vary, but the net force calculations determine the order.)