Question

rank the objects according to acceleration; use 1 for the most negative and 4 for the most positive.
directions: tap each diagram in order to toggle though the possible acceleration rankings. once each object has a unique ranking, a check answer button will appear.
2 n ← 0.25 kg → 6 n; 8 n ← 0.50 kg 2 n ←; 16.0 kg → 6 n →2 n; 4 n ← 0.25 kg 4 n ←

Explanation:

Step1: Recall Newton's Second Law

Newton's second law is \( F_{net} = ma \), so \( a = \frac{F_{net}}{m} \). We'll calculate the net force and then acceleration for each object, considering direction (left as negative, right as positive).

Step2: Calculate for First Object (0.25 kg, 2N left, 6N right)

Net force \( F_{net1} = 6 - 2 = 4 \, \text{N (right)} \).
Acceleration \( a_1 = \frac{4}{0.25} = 16 \, \text{m/s}^2 \) (positive, right).

Step3: Calculate for Second Object (0.50 kg, 8N left, 2N left)

Net force \( F_{net2} = -8 - 2 = -10 \, \text{N (left)} \).
Acceleration \( a_2 = \frac{-10}{0.50} = -20 \, \text{m/s}^2 \) (negative, left).

Step4: Calculate for Third Object (16.0 kg, 6N right, 2N right)

Net force \( F_{net3} = 6 + 2 = 8 \, \text{N (right)} \).
Acceleration \( a_3 = \frac{8}{16.0} = 0.5 \, \text{m/s}^2 \) (positive, right).

Step5: Calculate for Fourth Object (0.25 kg, 4N left, 4N left)

Net force \( F_{net4} = -4 - 4 = -8 \, \text{N (left)} \).
Acceleration \( a_4 = \frac{-8}{0.25} = -32 \, \text{m/s}^2 \) (negative, left).

Step6: Rank by Acceleration (1: most negative, 4: most positive)

• \( a_4 = -32 \) (most negative, rank 1)
• \( a_2 = -20 \) (next negative, rank 2)
• \( a_3 = 0.5 \) (next positive, rank 3)
• \( a_1 = 16 \) (most positive, rank 4)

Answer:

Rank order (from most negative to most positive):

1. Fourth Object (0.25 kg, 4N left, 4N left)
2. Second Object (0.50 kg, 8N left, 2N left)
3. Third Object (16.0 kg, 6N right, 2N right)
4. First Object (0.25 kg, 2N left, 6N right)

(If ranking the diagrams as per their positions: Top-Left (1st) → rank 4, Top-Right (2nd) → rank 2, Bottom-Left (3rd) → rank 3, Bottom-Right (4th) → rank 1)