Question

rank the objects according to acceleration; use 1 for the most negative and 6 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.
6 n ← 0.50 kg → 4 n
0.25 kg → 6 n → 2 n
2.0 kg → 4 n → 2 n
6 n ← 2.0 kg ← 4 n
2 n ← 0.25 kg → 4 n
6 n ← 4.0 kg ← 2 n

Explanation:

Step1: Recall Newton's Second Law

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

Step2: Object 1 (0.50 kg, 6N left, 4N right)

Net force \( F_{net}= -6 + 4 = -2 \, N \). Acceleration \( a_1=\frac{-2}{0.50} = -4 \, m/s^2 \).

Step3: Object 2 (0.25 kg, 6N right, 2N right)

Net force \( F_{net}=6 + 2 = 8 \, N \). Acceleration \( a_2=\frac{8}{0.25} = 32 \, m/s^2 \).

Step4: Object 3 (2.0 kg, 4N right, 2N right)

Net force \( F_{net}=4 + 2 = 6 \, N \). Acceleration \( a_3=\frac{6}{2.0} = 3 \, m/s^2 \).

Step5: Object 4 (2.0 kg, 6N left, 4N left)

Net force \( F_{net}= -6 - 4 = -10 \, N \). Acceleration \( a_4=\frac{-10}{2.0} = -5 \, m/s^2 \).

Step6: Object 5 (0.25 kg, 2N left, 4N right)

Net force \( F_{net}= -2 + 4 = 2 \, N \). Acceleration \( a_5=\frac{2}{0.25} = 8 \, m/s^2 \).

Step7: Object 6 (4.0 kg, 6N left, 2N left)

Net force \( F_{net}= -6 - 2 = -8 \, N \). Acceleration \( a_6=\frac{-8}{4.0} = -2 \, m/s^2 \).

Step8: Rank by Acceleration (1 most negative, 6 most positive)

Accelerations: \( a_4=-5 \), \( a_1=-4 \), \( a_6=-2 \), \( a_3=3 \), \( a_5=8 \), \( a_2=32 \).
Ranking (1 to 6, 1 most negative, 6 most positive):
1: Object 4 (a=-5)
2: Object 1 (a=-4)
3: Object 6 (a=-2)
4: Object 3 (a=3)
5: Object 5 (a=8)
6: Object 2 (a=32)

Answer:

1: Object with 2.0 kg, 6N left, 4N left (fourth diagram)
2: Object with 0.50 kg, 6N left, 4N right (first diagram)
3: Object with 4.0 kg, 6N left, 2N left (sixth diagram)
4: Object with 2.0 kg, 4N right, 2N right (third diagram)
5: Object with 0.25 kg, 2N left, 4N right (fifth diagram)
6: Object with 0.25 kg, 6N right, 2N right (second diagram)