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 4 kg cart moving at 28 m/s collides with and couples to a stationary 3 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
4 kg (28 m/s) → [3 kg] → Coupled: (7 kg) v = ? · m₁u₁ = (m₁ + m₂)v
2. A 6 kg cart moving at 24 m/s collides with and couples to a stationary 6 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
6 kg (24 m/s) → [6 kg] → Coupled: (12 kg) v = ? · m₁u₁ = (m₁ + m₂)v
3. A 2 kg cart moving at 36 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 (36 m/s) → [7 kg] → Coupled: (9 kg) v = ? · m₁u₁ = (m₁ + m₂)v
4. A 8 kg cart moving at 77 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 kg (77 m/s) → [3 kg] → Coupled: (11 kg) v = ? · m₁u₁ = (m₁ + m₂)v
5. A 6 kg cart moving at 30 m/s collides with and couples to a stationary 4 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
6 kg (30 m/s) → [4 kg] → Coupled: (10 kg) v = ? · m₁u₁ = (m₁ + m₂)v
6. A 2 kg cart moving at 32 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 (32 m/s) → [6 kg] → Coupled: (8 kg) v = ? · m₁u₁ = (m₁ + m₂)v
7. A 10 kg cart moving at 119 m/s collides with and couples to a stationary 7 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
10 kg (119 m/s) → [7 kg] → Coupled: (17 kg) v = ? · m₁u₁ = (m₁ + m₂)v
8. A 6 kg cart moving at 27 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 (27 m/s) → [3 kg] → Coupled: (9 kg) v = ? · m₁u₁ = (m₁ + m₂)v
9. A 4 kg cart moving at 84 m/s collides with and couples to a stationary 10 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
4 kg (84 m/s) → [10 kg] → Coupled: (14 kg) v = ? · m₁u₁ = (m₁ + m₂)v
10. A 2 kg cart moving at 96 m/s collides with and couples to a stationary 10 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
2 kg (96 m/s) → [10 kg] → Coupled: (12 kg) v = ? · m₁u₁ = (m₁ + m₂)v
11. A 7 kg cart moving at 54 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 (54 m/s) → [2 kg] → Coupled: (9 kg) v = ? · m₁u₁ = (m₁ + m₂)v
12. A 6 kg cart moving at 22 m/s collides with and couples to a stationary 5 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
6 kg (22 m/s) → [5 kg] → Coupled: (11 kg) v = ? · m₁u₁ = (m₁ + m₂)v

12 questions · Seed 104733 · 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 4 kg cart moving at 28 m/s collides with and couples to a stationary 3 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
16 m/s
Total momentum before collision p = 4 × 28 = 112 kg·m/s. Combined mass = 4 + 3 = 7 kg, so v = 112 ÷ 7 = 16 m/s.
2. A 6 kg cart moving at 24 m/s collides with and couples to a stationary 6 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
12 m/s
Total momentum before collision p = 6 × 24 = 144 kg·m/s. Combined mass = 6 + 6 = 12 kg, so v = 144 ÷ 12 = 12 m/s.
3. A 2 kg cart moving at 36 m/s collides with and couples to a stationary 7 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
8 m/s
Total momentum before collision p = 2 × 36 = 72 kg·m/s. Combined mass = 2 + 7 = 9 kg, so v = 72 ÷ 9 = 8 m/s.
4. A 8 kg cart moving at 77 m/s collides with and couples to a stationary 3 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
56 m/s
Total momentum before collision p = 8 × 77 = 616 kg·m/s. Combined mass = 8 + 3 = 11 kg, so v = 616 ÷ 11 = 56 m/s.
5. A 6 kg cart moving at 30 m/s collides with and couples to a stationary 4 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
18 m/s
Total momentum before collision p = 6 × 30 = 180 kg·m/s. Combined mass = 6 + 4 = 10 kg, so v = 180 ÷ 10 = 18 m/s.
6. A 2 kg cart moving at 32 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 m/s
Total momentum before collision p = 2 × 32 = 64 kg·m/s. Combined mass = 2 + 6 = 8 kg, so v = 64 ÷ 8 = 8 m/s.
7. A 10 kg cart moving at 119 m/s collides with and couples to a stationary 7 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
70 m/s
Total momentum before collision p = 10 × 119 = 1190 kg·m/s. Combined mass = 10 + 7 = 17 kg, so v = 1190 ÷ 17 = 70 m/s.
8. A 6 kg cart moving at 27 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 = 6 × 27 = 162 kg·m/s. Combined mass = 6 + 3 = 9 kg, so v = 162 ÷ 9 = 18 m/s.
9. A 4 kg cart moving at 84 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 = 4 × 84 = 336 kg·m/s. Combined mass = 4 + 10 = 14 kg, so v = 336 ÷ 14 = 24 m/s.
10. A 2 kg cart moving at 96 m/s collides with and couples to a stationary 10 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
16 m/s
Total momentum before collision p = 2 × 96 = 192 kg·m/s. Combined mass = 2 + 10 = 12 kg, so v = 192 ÷ 12 = 16 m/s.
11. A 7 kg cart moving at 54 m/s collides with and couples to a stationary 2 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
42 m/s
Total momentum before collision p = 7 × 54 = 378 kg·m/s. Combined mass = 7 + 2 = 9 kg, so v = 378 ÷ 9 = 42 m/s.
12. A 6 kg cart moving at 22 m/s collides with and couples to a stationary 5 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
12 m/s
Total momentum before collision p = 6 × 22 = 132 kg·m/s. Combined mass = 6 + 5 = 11 kg, so v = 132 ÷ 11 = 12 m/s.

12 questions · Seed 104733 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 13-15

Conservation of momentum in collisions

Take your time. Show your thinking.

1. A 4 kg cart moving at 28 m/s collides with and couples to a stationary 3 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
4 kg (28 m/s) → [3 kg] → Coupled: (7 kg) v = ? · m₁u₁ = (m₁ + m₂)v
2. A 6 kg cart moving at 24 m/s collides with and couples to a stationary 6 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
6 kg (24 m/s) → [6 kg] → Coupled: (12 kg) v = ? · m₁u₁ = (m₁ + m₂)v
3. A 2 kg cart moving at 36 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 (36 m/s) → [7 kg] → Coupled: (9 kg) v = ? · m₁u₁ = (m₁ + m₂)v
4. A 8 kg cart moving at 77 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 kg (77 m/s) → [3 kg] → Coupled: (11 kg) v = ? · m₁u₁ = (m₁ + m₂)v
5. A 6 kg cart moving at 30 m/s collides with and couples to a stationary 4 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
6 kg (30 m/s) → [4 kg] → Coupled: (10 kg) v = ? · m₁u₁ = (m₁ + m₂)v
6. A 2 kg cart moving at 32 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 (32 m/s) → [6 kg] → Coupled: (8 kg) v = ? · m₁u₁ = (m₁ + m₂)v
7. A 10 kg cart moving at 119 m/s collides with and couples to a stationary 7 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
10 kg (119 m/s) → [7 kg] → Coupled: (17 kg) v = ? · m₁u₁ = (m₁ + m₂)v
8. A 6 kg cart moving at 27 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 (27 m/s) → [3 kg] → Coupled: (9 kg) v = ? · m₁u₁ = (m₁ + m₂)v
9. A 4 kg cart moving at 84 m/s collides with and couples to a stationary 10 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
4 kg (84 m/s) → [10 kg] → Coupled: (14 kg) v = ? · m₁u₁ = (m₁ + m₂)v
10. A 2 kg cart moving at 96 m/s collides with and couples to a stationary 10 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
2 kg (96 m/s) → [10 kg] → Coupled: (12 kg) v = ? · m₁u₁ = (m₁ + m₂)v
11. A 7 kg cart moving at 54 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 (54 m/s) → [2 kg] → Coupled: (9 kg) v = ? · m₁u₁ = (m₁ + m₂)v
12. A 6 kg cart moving at 22 m/s collides with and couples to a stationary 5 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
6 kg (22 m/s) → [5 kg] → Coupled: (11 kg) v = ? · m₁u₁ = (m₁ + m₂)v

12 questions · Seed 104733 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 13-15

Conservation of momentum in collisions

Answers and reasoning. Review before teaching.

1. A 4 kg cart moving at 28 m/s collides with and couples to a stationary 3 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
16 m/s
Total momentum before collision p = 4 × 28 = 112 kg·m/s. Combined mass = 4 + 3 = 7 kg, so v = 112 ÷ 7 = 16 m/s.
2. A 6 kg cart moving at 24 m/s collides with and couples to a stationary 6 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
12 m/s
Total momentum before collision p = 6 × 24 = 144 kg·m/s. Combined mass = 6 + 6 = 12 kg, so v = 144 ÷ 12 = 12 m/s.
3. A 2 kg cart moving at 36 m/s collides with and couples to a stationary 7 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
8 m/s
Total momentum before collision p = 2 × 36 = 72 kg·m/s. Combined mass = 2 + 7 = 9 kg, so v = 72 ÷ 9 = 8 m/s.
4. A 8 kg cart moving at 77 m/s collides with and couples to a stationary 3 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
56 m/s
Total momentum before collision p = 8 × 77 = 616 kg·m/s. Combined mass = 8 + 3 = 11 kg, so v = 616 ÷ 11 = 56 m/s.
5. A 6 kg cart moving at 30 m/s collides with and couples to a stationary 4 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
18 m/s
Total momentum before collision p = 6 × 30 = 180 kg·m/s. Combined mass = 6 + 4 = 10 kg, so v = 180 ÷ 10 = 18 m/s.
6. A 2 kg cart moving at 32 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 m/s
Total momentum before collision p = 2 × 32 = 64 kg·m/s. Combined mass = 2 + 6 = 8 kg, so v = 64 ÷ 8 = 8 m/s.
7. A 10 kg cart moving at 119 m/s collides with and couples to a stationary 7 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
70 m/s
Total momentum before collision p = 10 × 119 = 1190 kg·m/s. Combined mass = 10 + 7 = 17 kg, so v = 1190 ÷ 17 = 70 m/s.
8. A 6 kg cart moving at 27 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 = 6 × 27 = 162 kg·m/s. Combined mass = 6 + 3 = 9 kg, so v = 162 ÷ 9 = 18 m/s.
9. A 4 kg cart moving at 84 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 = 4 × 84 = 336 kg·m/s. Combined mass = 4 + 10 = 14 kg, so v = 336 ÷ 14 = 24 m/s.
10. A 2 kg cart moving at 96 m/s collides with and couples to a stationary 10 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
16 m/s
Total momentum before collision p = 2 × 96 = 192 kg·m/s. Combined mass = 2 + 10 = 12 kg, so v = 192 ÷ 12 = 16 m/s.
11. A 7 kg cart moving at 54 m/s collides with and couples to a stationary 2 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
42 m/s
Total momentum before collision p = 7 × 54 = 378 kg·m/s. Combined mass = 7 + 2 = 9 kg, so v = 378 ÷ 9 = 42 m/s.
12. A 6 kg cart moving at 22 m/s collides with and couples to a stationary 5 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
12 m/s
Total momentum before collision p = 6 × 22 = 132 kg·m/s. Combined mass = 6 + 5 = 11 kg, so v = 132 ÷ 11 = 12 m/s.

12 questions · Seed 104733 · Age guidance, not curriculum certification