ScienceAges 13-15

Conservation of momentum in collisions

Apply conservation of linear momentum m₁u₁ = (m₁ + m₂)v to find the shared velocity after an inelastic collision. Review suitability for your learners before teaching.

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Worksheet StudioPractice pack · Ages 13-15

Conservation of momentum in collisions

Take your time. Show your thinking.

1. A 7 kg cart moving at 84 m/s collides with and couples to a stationary 7 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
7 kg (84 m/s) → [7 kg] → Coupled: (14 kg) v = ? · m₁u₁ = (m₁ + m₂)v
2. A 10 kg cart moving at 100 m/s collides with and couples to a stationary 10 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
10 kg (100 m/s) → [10 kg] → Coupled: (20 kg) v = ? · m₁u₁ = (m₁ + m₂)v
3. A 9 kg cart moving at 133 m/s collides with and couples to a stationary 10 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
9 kg (133 m/s) → [10 kg] → Coupled: (19 kg) v = ? · m₁u₁ = (m₁ + m₂)v
4. A 2 kg cart moving at 56 m/s collides with and couples to a stationary 6 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
2 kg (56 m/s) → [6 kg] → Coupled: (8 kg) v = ? · m₁u₁ = (m₁ + m₂)v
5. A 5 kg cart moving at 104 m/s collides with and couples to a stationary 8 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
5 kg (104 m/s) → [8 kg] → Coupled: (13 kg) v = ? · m₁u₁ = (m₁ + m₂)v
6. A 4 kg cart moving at 54 m/s collides with and couples to a stationary 5 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
4 kg (54 m/s) → [5 kg] → Coupled: (9 kg) v = ? · m₁u₁ = (m₁ + m₂)v
7. A 8 kg cart moving at 26 m/s collides with and couples to a stationary 5 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
8 kg (26 m/s) → [5 kg] → Coupled: (13 kg) v = ? · m₁u₁ = (m₁ + m₂)v
8. A 3 kg cart moving at 64 m/s collides with and couples to a stationary 5 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
3 kg (64 m/s) → [5 kg] → Coupled: (8 kg) v = ? · m₁u₁ = (m₁ + m₂)v
9. A 6 kg cart moving at 18 m/s collides with and couples to a stationary 3 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
6 kg (18 m/s) → [3 kg] → Coupled: (9 kg) v = ? · m₁u₁ = (m₁ + m₂)v
10. A 6 kg cart moving at 64 m/s collides with and couples to a stationary 10 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
6 kg (64 m/s) → [10 kg] → Coupled: (16 kg) v = ? · m₁u₁ = (m₁ + m₂)v
11. A 8 kg cart moving at 70 m/s collides with and couples to a stationary 2 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
8 kg (70 m/s) → [2 kg] → Coupled: (10 kg) v = ? · m₁u₁ = (m₁ + m₂)v
12. A 8 kg cart moving at 52 m/s collides with and couples to a stationary 5 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
8 kg (52 m/s) → [5 kg] → Coupled: (13 kg) v = ? · m₁u₁ = (m₁ + m₂)v

12 questions · Seed 104738 · Age guidance, not curriculum certification

View the answer key

Worksheet StudioAnswer key · Ages 13-15

Conservation of momentum in collisions

Answers and reasoning. Review before teaching.

1. A 7 kg cart moving at 84 m/s collides with and couples to a stationary 7 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
42 m/s
Total momentum before collision p = 7 × 84 = 588 kg·m/s. Combined mass = 7 + 7 = 14 kg, so v = 588 ÷ 14 = 42 m/s.
2. A 10 kg cart moving at 100 m/s collides with and couples to a stationary 10 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
50 m/s
Total momentum before collision p = 10 × 100 = 1000 kg·m/s. Combined mass = 10 + 10 = 20 kg, so v = 1000 ÷ 20 = 50 m/s.
3. A 9 kg cart moving at 133 m/s collides with and couples to a stationary 10 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
63 m/s
Total momentum before collision p = 9 × 133 = 1197 kg·m/s. Combined mass = 9 + 10 = 19 kg, so v = 1197 ÷ 19 = 63 m/s.
4. A 2 kg cart moving at 56 m/s collides with and couples to a stationary 6 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
14 m/s
Total momentum before collision p = 2 × 56 = 112 kg·m/s. Combined mass = 2 + 6 = 8 kg, so v = 112 ÷ 8 = 14 m/s.
5. A 5 kg cart moving at 104 m/s collides with and couples to a stationary 8 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
40 m/s
Total momentum before collision p = 5 × 104 = 520 kg·m/s. Combined mass = 5 + 8 = 13 kg, so v = 520 ÷ 13 = 40 m/s.
6. A 4 kg cart moving at 54 m/s collides with and couples to a stationary 5 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
24 m/s
Total momentum before collision p = 4 × 54 = 216 kg·m/s. Combined mass = 4 + 5 = 9 kg, so v = 216 ÷ 9 = 24 m/s.
7. A 8 kg cart moving at 26 m/s collides with and couples to a stationary 5 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
16 m/s
Total momentum before collision p = 8 × 26 = 208 kg·m/s. Combined mass = 8 + 5 = 13 kg, so v = 208 ÷ 13 = 16 m/s.
8. A 3 kg cart moving at 64 m/s collides with and couples to a stationary 5 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
24 m/s
Total momentum before collision p = 3 × 64 = 192 kg·m/s. Combined mass = 3 + 5 = 8 kg, so v = 192 ÷ 8 = 24 m/s.
9. A 6 kg cart moving at 18 m/s collides with and couples to a stationary 3 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
12 m/s
Total momentum before collision p = 6 × 18 = 108 kg·m/s. Combined mass = 6 + 3 = 9 kg, so v = 108 ÷ 9 = 12 m/s.
10. A 6 kg cart moving at 64 m/s collides with and couples to a stationary 10 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
24 m/s
Total momentum before collision p = 6 × 64 = 384 kg·m/s. Combined mass = 6 + 10 = 16 kg, so v = 384 ÷ 16 = 24 m/s.
11. A 8 kg cart moving at 70 m/s collides with and couples to a stationary 2 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
56 m/s
Total momentum before collision p = 8 × 70 = 560 kg·m/s. Combined mass = 8 + 2 = 10 kg, so v = 560 ÷ 10 = 56 m/s.
12. A 8 kg cart moving at 52 m/s collides with and couples to a stationary 5 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
32 m/s
Total momentum before collision p = 8 × 52 = 416 kg·m/s. Combined mass = 8 + 5 = 13 kg, so v = 416 ÷ 13 = 32 m/s.

12 questions · Seed 104738 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 13-15

Conservation of momentum in collisions

Take your time. Show your thinking.

1. A 7 kg cart moving at 84 m/s collides with and couples to a stationary 7 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
7 kg (84 m/s) → [7 kg] → Coupled: (14 kg) v = ? · m₁u₁ = (m₁ + m₂)v
2. A 10 kg cart moving at 100 m/s collides with and couples to a stationary 10 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
10 kg (100 m/s) → [10 kg] → Coupled: (20 kg) v = ? · m₁u₁ = (m₁ + m₂)v
3. A 9 kg cart moving at 133 m/s collides with and couples to a stationary 10 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
9 kg (133 m/s) → [10 kg] → Coupled: (19 kg) v = ? · m₁u₁ = (m₁ + m₂)v
4. A 2 kg cart moving at 56 m/s collides with and couples to a stationary 6 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
2 kg (56 m/s) → [6 kg] → Coupled: (8 kg) v = ? · m₁u₁ = (m₁ + m₂)v
5. A 5 kg cart moving at 104 m/s collides with and couples to a stationary 8 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
5 kg (104 m/s) → [8 kg] → Coupled: (13 kg) v = ? · m₁u₁ = (m₁ + m₂)v
6. A 4 kg cart moving at 54 m/s collides with and couples to a stationary 5 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
4 kg (54 m/s) → [5 kg] → Coupled: (9 kg) v = ? · m₁u₁ = (m₁ + m₂)v
7. A 8 kg cart moving at 26 m/s collides with and couples to a stationary 5 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
8 kg (26 m/s) → [5 kg] → Coupled: (13 kg) v = ? · m₁u₁ = (m₁ + m₂)v
8. A 3 kg cart moving at 64 m/s collides with and couples to a stationary 5 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
3 kg (64 m/s) → [5 kg] → Coupled: (8 kg) v = ? · m₁u₁ = (m₁ + m₂)v
9. A 6 kg cart moving at 18 m/s collides with and couples to a stationary 3 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
6 kg (18 m/s) → [3 kg] → Coupled: (9 kg) v = ? · m₁u₁ = (m₁ + m₂)v
10. A 6 kg cart moving at 64 m/s collides with and couples to a stationary 10 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
6 kg (64 m/s) → [10 kg] → Coupled: (16 kg) v = ? · m₁u₁ = (m₁ + m₂)v
11. A 8 kg cart moving at 70 m/s collides with and couples to a stationary 2 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
8 kg (70 m/s) → [2 kg] → Coupled: (10 kg) v = ? · m₁u₁ = (m₁ + m₂)v
12. A 8 kg cart moving at 52 m/s collides with and couples to a stationary 5 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
8 kg (52 m/s) → [5 kg] → Coupled: (13 kg) v = ? · m₁u₁ = (m₁ + m₂)v

12 questions · Seed 104738 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 13-15

Conservation of momentum in collisions

Answers and reasoning. Review before teaching.

1. A 7 kg cart moving at 84 m/s collides with and couples to a stationary 7 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
42 m/s
Total momentum before collision p = 7 × 84 = 588 kg·m/s. Combined mass = 7 + 7 = 14 kg, so v = 588 ÷ 14 = 42 m/s.
2. A 10 kg cart moving at 100 m/s collides with and couples to a stationary 10 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
50 m/s
Total momentum before collision p = 10 × 100 = 1000 kg·m/s. Combined mass = 10 + 10 = 20 kg, so v = 1000 ÷ 20 = 50 m/s.
3. A 9 kg cart moving at 133 m/s collides with and couples to a stationary 10 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
63 m/s
Total momentum before collision p = 9 × 133 = 1197 kg·m/s. Combined mass = 9 + 10 = 19 kg, so v = 1197 ÷ 19 = 63 m/s.
4. A 2 kg cart moving at 56 m/s collides with and couples to a stationary 6 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
14 m/s
Total momentum before collision p = 2 × 56 = 112 kg·m/s. Combined mass = 2 + 6 = 8 kg, so v = 112 ÷ 8 = 14 m/s.
5. A 5 kg cart moving at 104 m/s collides with and couples to a stationary 8 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
40 m/s
Total momentum before collision p = 5 × 104 = 520 kg·m/s. Combined mass = 5 + 8 = 13 kg, so v = 520 ÷ 13 = 40 m/s.
6. A 4 kg cart moving at 54 m/s collides with and couples to a stationary 5 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
24 m/s
Total momentum before collision p = 4 × 54 = 216 kg·m/s. Combined mass = 4 + 5 = 9 kg, so v = 216 ÷ 9 = 24 m/s.
7. A 8 kg cart moving at 26 m/s collides with and couples to a stationary 5 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
16 m/s
Total momentum before collision p = 8 × 26 = 208 kg·m/s. Combined mass = 8 + 5 = 13 kg, so v = 208 ÷ 13 = 16 m/s.
8. A 3 kg cart moving at 64 m/s collides with and couples to a stationary 5 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
24 m/s
Total momentum before collision p = 3 × 64 = 192 kg·m/s. Combined mass = 3 + 5 = 8 kg, so v = 192 ÷ 8 = 24 m/s.
9. A 6 kg cart moving at 18 m/s collides with and couples to a stationary 3 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
12 m/s
Total momentum before collision p = 6 × 18 = 108 kg·m/s. Combined mass = 6 + 3 = 9 kg, so v = 108 ÷ 9 = 12 m/s.
10. A 6 kg cart moving at 64 m/s collides with and couples to a stationary 10 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
24 m/s
Total momentum before collision p = 6 × 64 = 384 kg·m/s. Combined mass = 6 + 10 = 16 kg, so v = 384 ÷ 16 = 24 m/s.
11. A 8 kg cart moving at 70 m/s collides with and couples to a stationary 2 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
56 m/s
Total momentum before collision p = 8 × 70 = 560 kg·m/s. Combined mass = 8 + 2 = 10 kg, so v = 560 ÷ 10 = 56 m/s.
12. A 8 kg cart moving at 52 m/s collides with and couples to a stationary 5 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
32 m/s
Total momentum before collision p = 8 × 52 = 416 kg·m/s. Combined mass = 8 + 5 = 13 kg, so v = 416 ÷ 13 = 32 m/s.

12 questions · Seed 104738 · Age guidance, not curriculum certification