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.
4 n ← 2.0 kg → 8 n; 8 n ← 0.25 kg → 6 n
6 n ← 4.0 kg; 2 n ←; 10.0 kg → 8 n; → 2 n
2.0 kg → 4 n; → 2 n; 16.0 kg → 6 n; → 2 n
4 n ← 0.50 kg; 2 n ←; 4 n ← 0.25 kg → 4 n

Explanation:

Step1: Define Net Force Calculation

Net force ($F_{net}$) is the vector sum of forces. Let right be positive (+) and left be negative (-). For each object, sum the forces:

Object 1 (2.0 kg):

Forces: $-4\,\text{N}$ (left), $+8\,\text{N}$ (right)
$F_{net1} = -4 + 8 = +4\,\text{N}$

Object 2 (0.25 kg):

Forces: $-8\,\text{N}$ (left), $+6\,\text{N}$ (right)
$F_{net2} = -8 + 6 = -2\,\text{N}$

Object 3 (4.0 kg):

Forces: $-6\,\text{N}$ (left), $-2\,\text{N}$ (left)
$F_{net3} = -6 - 2 = -8\,\text{N}$

Object 4 (10.0 kg):

Forces: $+8\,\text{N}$ (right), $+2\,\text{N}$ (right)
$F_{net4} = 8 + 2 = +10\,\text{N}$

Object 5 (2.0 kg):

Forces: $+4\,\text{N}$ (right), $+2\,\text{N}$ (right)
$F_{net5} = 4 + 2 = +6\,\text{N}$

Object 6 (16.0 kg):

Forces: $+6\,\text{N}$ (right), $+2\,\text{N}$ (right)
$F_{net6} = 6 + 2 = +8\,\text{N}$

Object 7 (0.50 kg):

Forces: $-4\,\text{N}$ (left), $-2\,\text{N}$ (left)
$F_{net7} = -4 - 2 = -6\,\text{N}$

Object 8 (0.25 kg):

Forces: $-4\,\text{N}$ (left), $+4\,\text{N}$ (right)
$F_{net8} = -4 + 4 = 0\,\text{N}$

Step2: Rank by Net Force (1=most negative, 8=most positive)

Sort $F_{net}$ from most negative to most positive:
$F_{net3} = -8\,\text{N}$ (most negative, rank 1)
$F_{net7} = -6\,\text{N}$ (rank 2)
$F_{net2} = -2\,\text{N}$ (rank 3)
$F_{net8} = 0\,\text{N}$ (rank 4)
$F_{net1} = +4\,\text{N}$ (rank 5)
$F_{net5} = +6\,\text{N}$ (rank 6)
$F_{net6} = +8\,\text{N}$ (rank 7)
$F_{net4} = +10\,\text{N}$ (most positive, rank 8)

Answer:

1. 4.0 kg (6N ←, 2N ←)
2. 0.50 kg (4N ←, 2N ←)
3. 0.25 kg (8N ←, 6N →)
4. 0.25 kg (4N ←, 4N →)
5. 2.0 kg (4N ←, 8N →)
6. 2.0 kg (4N →, 2N →)
7. 16.0 kg (6N →, 2N →)
8. 10.0 kg (8N →, 2N →)

(Note: Rankings correspond to the objects’ net forces in ascending order: -8, -6, -2, 0, +4, +6, +8, +10.)