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 6 kg cart moving at 78 m/s collides with and couples to a stationary 7 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
6 kg (78 m/s) → [7 kg] → Coupled: (13 kg) v = ? · m₁u₁ = (m₁ + m₂)v
2. A 2 kg cart moving at 20 m/s collides with and couples to a stationary 3 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
2 kg (20 m/s) → [3 kg] → Coupled: (5 kg) v = ? · m₁u₁ = (m₁ + m₂)v
3. 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
4. A 9 kg cart moving at 24 m/s collides with and couples to a stationary 3 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
9 kg (24 m/s) → [3 kg] → Coupled: (12 kg) v = ? · m₁u₁ = (m₁ + m₂)v
5. A 7 kg cart moving at 32 m/s collides with and couples to a stationary 9 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
7 kg (32 m/s) → [9 kg] → Coupled: (16 kg) v = ? · m₁u₁ = (m₁ + m₂)v
6. A 4 kg cart moving at 12 m/s collides with and couples to a stationary 2 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
4 kg (12 m/s) → [2 kg] → Coupled: (6 kg) v = ? · m₁u₁ = (m₁ + m₂)v
7. A 10 kg cart moving at 128 m/s collides with and couples to a stationary 6 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
10 kg (128 m/s) → [6 kg] → Coupled: (16 kg) v = ? · m₁u₁ = (m₁ + m₂)v
8. 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
9. A 5 kg cart moving at 30 m/s collides with and couples to a stationary 10 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
5 kg (30 m/s) → [10 kg] → Coupled: (15 kg) v = ? · m₁u₁ = (m₁ + m₂)v
10. A 2 kg cart moving at 4 m/s collides with and couples to a stationary 2 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
2 kg (4 m/s) → [2 kg] → Coupled: (4 kg) v = ? · m₁u₁ = (m₁ + m₂)v
11. A 6 kg cart moving at 128 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 (128 m/s) → [10 kg] → Coupled: (16 kg) v = ? · m₁u₁ = (m₁ + m₂)v
12. 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

12 questions · Seed 47 · 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 6 kg cart moving at 78 m/s collides with and couples to a stationary 7 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
36 m/s
Total momentum before collision p = 6 × 78 = 468 kg·m/s. Combined mass = 6 + 7 = 13 kg, so v = 468 ÷ 13 = 36 m/s.
2. A 2 kg cart moving at 20 m/s collides with and couples to a stationary 3 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
8 m/s
Total momentum before collision p = 2 × 20 = 40 kg·m/s. Combined mass = 2 + 3 = 5 kg, so v = 40 ÷ 5 = 8 m/s.
3. 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.
4. A 9 kg cart moving at 24 m/s collides with and couples to a stationary 3 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
18 m/s
Total momentum before collision p = 9 × 24 = 216 kg·m/s. Combined mass = 9 + 3 = 12 kg, so v = 216 ÷ 12 = 18 m/s.
5. A 7 kg cart moving at 32 m/s collides with and couples to a stationary 9 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
14 m/s
Total momentum before collision p = 7 × 32 = 224 kg·m/s. Combined mass = 7 + 9 = 16 kg, so v = 224 ÷ 16 = 14 m/s.
6. A 4 kg cart moving at 12 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 m/s
Total momentum before collision p = 4 × 12 = 48 kg·m/s. Combined mass = 4 + 2 = 6 kg, so v = 48 ÷ 6 = 8 m/s.
7. A 10 kg cart moving at 128 m/s collides with and couples to a stationary 6 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
80 m/s
Total momentum before collision p = 10 × 128 = 1280 kg·m/s. Combined mass = 10 + 6 = 16 kg, so v = 1280 ÷ 16 = 80 m/s.
8. 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.
9. A 5 kg cart moving at 30 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 m/s
Total momentum before collision p = 5 × 30 = 150 kg·m/s. Combined mass = 5 + 10 = 15 kg, so v = 150 ÷ 15 = 10 m/s.
10. A 2 kg cart moving at 4 m/s collides with and couples to a stationary 2 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
2 m/s
Total momentum before collision p = 2 × 4 = 8 kg·m/s. Combined mass = 2 + 2 = 4 kg, so v = 8 ÷ 4 = 2 m/s.
11. A 6 kg cart moving at 128 m/s collides with and couples to a stationary 10 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
48 m/s
Total momentum before collision p = 6 × 128 = 768 kg·m/s. Combined mass = 6 + 10 = 16 kg, so v = 768 ÷ 16 = 48 m/s.
12. 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.

12 questions · Seed 47 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 13-15

Conservation of momentum in collisions

Take your time. Show your thinking.

1. A 6 kg cart moving at 78 m/s collides with and couples to a stationary 7 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
6 kg (78 m/s) → [7 kg] → Coupled: (13 kg) v = ? · m₁u₁ = (m₁ + m₂)v
2. A 2 kg cart moving at 20 m/s collides with and couples to a stationary 3 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
2 kg (20 m/s) → [3 kg] → Coupled: (5 kg) v = ? · m₁u₁ = (m₁ + m₂)v
3. 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
4. A 9 kg cart moving at 24 m/s collides with and couples to a stationary 3 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
9 kg (24 m/s) → [3 kg] → Coupled: (12 kg) v = ? · m₁u₁ = (m₁ + m₂)v
5. A 7 kg cart moving at 32 m/s collides with and couples to a stationary 9 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
7 kg (32 m/s) → [9 kg] → Coupled: (16 kg) v = ? · m₁u₁ = (m₁ + m₂)v
6. A 4 kg cart moving at 12 m/s collides with and couples to a stationary 2 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
4 kg (12 m/s) → [2 kg] → Coupled: (6 kg) v = ? · m₁u₁ = (m₁ + m₂)v
7. A 10 kg cart moving at 128 m/s collides with and couples to a stationary 6 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
10 kg (128 m/s) → [6 kg] → Coupled: (16 kg) v = ? · m₁u₁ = (m₁ + m₂)v
8. 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
9. A 5 kg cart moving at 30 m/s collides with and couples to a stationary 10 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
5 kg (30 m/s) → [10 kg] → Coupled: (15 kg) v = ? · m₁u₁ = (m₁ + m₂)v
10. A 2 kg cart moving at 4 m/s collides with and couples to a stationary 2 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
2 kg (4 m/s) → [2 kg] → Coupled: (4 kg) v = ? · m₁u₁ = (m₁ + m₂)v
11. A 6 kg cart moving at 128 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 (128 m/s) → [10 kg] → Coupled: (16 kg) v = ? · m₁u₁ = (m₁ + m₂)v
12. 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

12 questions · Seed 47 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 13-15

Conservation of momentum in collisions

Answers and reasoning. Review before teaching.

1. A 6 kg cart moving at 78 m/s collides with and couples to a stationary 7 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
36 m/s
Total momentum before collision p = 6 × 78 = 468 kg·m/s. Combined mass = 6 + 7 = 13 kg, so v = 468 ÷ 13 = 36 m/s.
2. A 2 kg cart moving at 20 m/s collides with and couples to a stationary 3 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
8 m/s
Total momentum before collision p = 2 × 20 = 40 kg·m/s. Combined mass = 2 + 3 = 5 kg, so v = 40 ÷ 5 = 8 m/s.
3. 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.
4. A 9 kg cart moving at 24 m/s collides with and couples to a stationary 3 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
18 m/s
Total momentum before collision p = 9 × 24 = 216 kg·m/s. Combined mass = 9 + 3 = 12 kg, so v = 216 ÷ 12 = 18 m/s.
5. A 7 kg cart moving at 32 m/s collides with and couples to a stationary 9 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
14 m/s
Total momentum before collision p = 7 × 32 = 224 kg·m/s. Combined mass = 7 + 9 = 16 kg, so v = 224 ÷ 16 = 14 m/s.
6. A 4 kg cart moving at 12 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 m/s
Total momentum before collision p = 4 × 12 = 48 kg·m/s. Combined mass = 4 + 2 = 6 kg, so v = 48 ÷ 6 = 8 m/s.
7. A 10 kg cart moving at 128 m/s collides with and couples to a stationary 6 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
80 m/s
Total momentum before collision p = 10 × 128 = 1280 kg·m/s. Combined mass = 10 + 6 = 16 kg, so v = 1280 ÷ 16 = 80 m/s.
8. 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.
9. A 5 kg cart moving at 30 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 m/s
Total momentum before collision p = 5 × 30 = 150 kg·m/s. Combined mass = 5 + 10 = 15 kg, so v = 150 ÷ 15 = 10 m/s.
10. A 2 kg cart moving at 4 m/s collides with and couples to a stationary 2 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
2 m/s
Total momentum before collision p = 2 × 4 = 8 kg·m/s. Combined mass = 2 + 2 = 4 kg, so v = 8 ÷ 4 = 2 m/s.
11. A 6 kg cart moving at 128 m/s collides with and couples to a stationary 10 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
48 m/s
Total momentum before collision p = 6 × 128 = 768 kg·m/s. Combined mass = 6 + 10 = 16 kg, so v = 768 ÷ 16 = 48 m/s.
12. 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.

12 questions · Seed 47 · Age guidance, not curriculum certification