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 98 m/s collides with and couples to a stationary 8 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
6 kg (98 m/s) → [8 kg] → Coupled: (14 kg) v = ? · m₁u₁ = (m₁ + m₂)v
2. A 9 kg cart moving at 96 m/s collides with and couples to a stationary 7 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
9 kg (96 m/s) → [7 kg] → Coupled: (16 kg) v = ? · m₁u₁ = (m₁ + m₂)v
3. 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
4. A 7 kg cart moving at 28 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 (28 m/s) → [7 kg] → Coupled: (14 kg) v = ? · m₁u₁ = (m₁ + m₂)v
5. A 8 kg cart moving at 28 m/s collides with and couples to a stationary 6 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
8 kg (28 m/s) → [6 kg] → Coupled: (14 kg) v = ? · m₁u₁ = (m₁ + m₂)v
6. A 2 kg cart moving at 77 m/s collides with and couples to a stationary 9 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
2 kg (77 m/s) → [9 kg] → Coupled: (11 kg) v = ? · m₁u₁ = (m₁ + m₂)v
7. A 5 kg cart moving at 20 m/s collides with and couples to a stationary 5 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
5 kg (20 m/s) → [5 kg] → Coupled: (10 kg) v = ? · m₁u₁ = (m₁ + m₂)v
8. A 2 kg cart moving at 60 m/s collides with and couples to a stationary 8 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
2 kg (60 m/s) → [8 kg] → Coupled: (10 kg) v = ? · m₁u₁ = (m₁ + m₂)v
9. A 3 kg cart moving at 8 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 (8 m/s) → [5 kg] → Coupled: (8 kg) v = ? · m₁u₁ = (m₁ + m₂)v
10. A 2 kg cart moving at 54 m/s collides with and couples to a stationary 7 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
2 kg (54 m/s) → [7 kg] → Coupled: (9 kg) v = ? · m₁u₁ = (m₁ + m₂)v
11. A 9 kg cart moving at 85 m/s collides with and couples to a stationary 8 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
9 kg (85 m/s) → [8 kg] → Coupled: (17 kg) v = ? · m₁u₁ = (m₁ + m₂)v
12. A 7 kg cart moving at 72 m/s collides with and couples to a stationary 2 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
7 kg (72 m/s) → [2 kg] → Coupled: (9 kg) v = ? · m₁u₁ = (m₁ + m₂)v

12 questions · Seed 104731 · 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 98 m/s collides with and couples to a stationary 8 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
42 m/s
Total momentum before collision p = 6 × 98 = 588 kg·m/s. Combined mass = 6 + 8 = 14 kg, so v = 588 ÷ 14 = 42 m/s.
2. A 9 kg cart moving at 96 m/s collides with and couples to a stationary 7 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
54 m/s
Total momentum before collision p = 9 × 96 = 864 kg·m/s. Combined mass = 9 + 7 = 16 kg, so v = 864 ÷ 16 = 54 m/s.
3. 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.
4. A 7 kg cart moving at 28 m/s collides with and couples to a stationary 7 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
14 m/s
Total momentum before collision p = 7 × 28 = 196 kg·m/s. Combined mass = 7 + 7 = 14 kg, so v = 196 ÷ 14 = 14 m/s.
5. A 8 kg cart moving at 28 m/s collides with and couples to a stationary 6 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
16 m/s
Total momentum before collision p = 8 × 28 = 224 kg·m/s. Combined mass = 8 + 6 = 14 kg, so v = 224 ÷ 14 = 16 m/s.
6. A 2 kg cart moving at 77 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 = 2 × 77 = 154 kg·m/s. Combined mass = 2 + 9 = 11 kg, so v = 154 ÷ 11 = 14 m/s.
7. A 5 kg cart moving at 20 m/s collides with and couples to a stationary 5 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
10 m/s
Total momentum before collision p = 5 × 20 = 100 kg·m/s. Combined mass = 5 + 5 = 10 kg, so v = 100 ÷ 10 = 10 m/s.
8. A 2 kg cart moving at 60 m/s collides with and couples to a stationary 8 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
12 m/s
Total momentum before collision p = 2 × 60 = 120 kg·m/s. Combined mass = 2 + 8 = 10 kg, so v = 120 ÷ 10 = 12 m/s.
9. A 3 kg cart moving at 8 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 m/s
Total momentum before collision p = 3 × 8 = 24 kg·m/s. Combined mass = 3 + 5 = 8 kg, so v = 24 ÷ 8 = 3 m/s.
10. A 2 kg cart moving at 54 m/s collides with and couples to a stationary 7 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
12 m/s
Total momentum before collision p = 2 × 54 = 108 kg·m/s. Combined mass = 2 + 7 = 9 kg, so v = 108 ÷ 9 = 12 m/s.
11. A 9 kg cart moving at 85 m/s collides with and couples to a stationary 8 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
45 m/s
Total momentum before collision p = 9 × 85 = 765 kg·m/s. Combined mass = 9 + 8 = 17 kg, so v = 765 ÷ 17 = 45 m/s.
12. A 7 kg cart moving at 72 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 = 7 × 72 = 504 kg·m/s. Combined mass = 7 + 2 = 9 kg, so v = 504 ÷ 9 = 56 m/s.

12 questions · Seed 104731 · 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 98 m/s collides with and couples to a stationary 8 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
6 kg (98 m/s) → [8 kg] → Coupled: (14 kg) v = ? · m₁u₁ = (m₁ + m₂)v
2. A 9 kg cart moving at 96 m/s collides with and couples to a stationary 7 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
9 kg (96 m/s) → [7 kg] → Coupled: (16 kg) v = ? · m₁u₁ = (m₁ + m₂)v
3. 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
4. A 7 kg cart moving at 28 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 (28 m/s) → [7 kg] → Coupled: (14 kg) v = ? · m₁u₁ = (m₁ + m₂)v
5. A 8 kg cart moving at 28 m/s collides with and couples to a stationary 6 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
8 kg (28 m/s) → [6 kg] → Coupled: (14 kg) v = ? · m₁u₁ = (m₁ + m₂)v
6. A 2 kg cart moving at 77 m/s collides with and couples to a stationary 9 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
2 kg (77 m/s) → [9 kg] → Coupled: (11 kg) v = ? · m₁u₁ = (m₁ + m₂)v
7. A 5 kg cart moving at 20 m/s collides with and couples to a stationary 5 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
5 kg (20 m/s) → [5 kg] → Coupled: (10 kg) v = ? · m₁u₁ = (m₁ + m₂)v
8. A 2 kg cart moving at 60 m/s collides with and couples to a stationary 8 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
2 kg (60 m/s) → [8 kg] → Coupled: (10 kg) v = ? · m₁u₁ = (m₁ + m₂)v
9. A 3 kg cart moving at 8 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 (8 m/s) → [5 kg] → Coupled: (8 kg) v = ? · m₁u₁ = (m₁ + m₂)v
10. A 2 kg cart moving at 54 m/s collides with and couples to a stationary 7 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
2 kg (54 m/s) → [7 kg] → Coupled: (9 kg) v = ? · m₁u₁ = (m₁ + m₂)v
11. A 9 kg cart moving at 85 m/s collides with and couples to a stationary 8 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
9 kg (85 m/s) → [8 kg] → Coupled: (17 kg) v = ? · m₁u₁ = (m₁ + m₂)v
12. A 7 kg cart moving at 72 m/s collides with and couples to a stationary 2 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
7 kg (72 m/s) → [2 kg] → Coupled: (9 kg) v = ? · m₁u₁ = (m₁ + m₂)v

12 questions · Seed 104731 · 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 98 m/s collides with and couples to a stationary 8 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
42 m/s
Total momentum before collision p = 6 × 98 = 588 kg·m/s. Combined mass = 6 + 8 = 14 kg, so v = 588 ÷ 14 = 42 m/s.
2. A 9 kg cart moving at 96 m/s collides with and couples to a stationary 7 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
54 m/s
Total momentum before collision p = 9 × 96 = 864 kg·m/s. Combined mass = 9 + 7 = 16 kg, so v = 864 ÷ 16 = 54 m/s.
3. 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.
4. A 7 kg cart moving at 28 m/s collides with and couples to a stationary 7 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
14 m/s
Total momentum before collision p = 7 × 28 = 196 kg·m/s. Combined mass = 7 + 7 = 14 kg, so v = 196 ÷ 14 = 14 m/s.
5. A 8 kg cart moving at 28 m/s collides with and couples to a stationary 6 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
16 m/s
Total momentum before collision p = 8 × 28 = 224 kg·m/s. Combined mass = 8 + 6 = 14 kg, so v = 224 ÷ 14 = 16 m/s.
6. A 2 kg cart moving at 77 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 = 2 × 77 = 154 kg·m/s. Combined mass = 2 + 9 = 11 kg, so v = 154 ÷ 11 = 14 m/s.
7. A 5 kg cart moving at 20 m/s collides with and couples to a stationary 5 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
10 m/s
Total momentum before collision p = 5 × 20 = 100 kg·m/s. Combined mass = 5 + 5 = 10 kg, so v = 100 ÷ 10 = 10 m/s.
8. A 2 kg cart moving at 60 m/s collides with and couples to a stationary 8 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
12 m/s
Total momentum before collision p = 2 × 60 = 120 kg·m/s. Combined mass = 2 + 8 = 10 kg, so v = 120 ÷ 10 = 12 m/s.
9. A 3 kg cart moving at 8 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 m/s
Total momentum before collision p = 3 × 8 = 24 kg·m/s. Combined mass = 3 + 5 = 8 kg, so v = 24 ÷ 8 = 3 m/s.
10. A 2 kg cart moving at 54 m/s collides with and couples to a stationary 7 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
12 m/s
Total momentum before collision p = 2 × 54 = 108 kg·m/s. Combined mass = 2 + 7 = 9 kg, so v = 108 ÷ 9 = 12 m/s.
11. A 9 kg cart moving at 85 m/s collides with and couples to a stationary 8 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
45 m/s
Total momentum before collision p = 9 × 85 = 765 kg·m/s. Combined mass = 9 + 8 = 17 kg, so v = 765 ÷ 17 = 45 m/s.
12. A 7 kg cart moving at 72 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 = 7 × 72 = 504 kg·m/s. Combined mass = 7 + 2 = 9 kg, so v = 504 ÷ 9 = 56 m/s.

12 questions · Seed 104731 · Age guidance, not curriculum certification