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 10 kg cart moving at 84 m/s collides with and couples to a stationary 2 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
10 kg (84 m/s) → [2 kg] → Coupled: (12 kg) v = ? · m₁u₁ = (m₁ + m₂)v
2. 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
3. A 2 kg cart moving at 40 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 (40 m/s) → [3 kg] → Coupled: (5 kg) v = ? · m₁u₁ = (m₁ + m₂)v
4. A 7 kg cart moving at 27 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 (27 m/s) → [2 kg] → Coupled: (9 kg) v = ? · m₁u₁ = (m₁ + m₂)v
5. A 3 kg cart moving at 21 m/s collides with and couples to a stationary 4 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
3 kg (21 m/s) → [4 kg] → Coupled: (7 kg) v = ? · m₁u₁ = (m₁ + m₂)v
6. A 7 kg cart moving at 128 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 (128 m/s) → [9 kg] → Coupled: (16 kg) v = ? · m₁u₁ = (m₁ + m₂)v
7. A 3 kg cart moving at 6 m/s collides with and couples to a stationary 3 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
3 kg (6 m/s) → [3 kg] → Coupled: (6 kg) v = ? · m₁u₁ = (m₁ + m₂)v
8. A 2 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.
2 kg (30 m/s) → [4 kg] → Coupled: (6 kg) v = ? · m₁u₁ = (m₁ + m₂)v
9. A 9 kg cart moving at 18 m/s collides with and couples to a stationary 9 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
9 kg (18 m/s) → [9 kg] → Coupled: (18 kg) v = ? · m₁u₁ = (m₁ + m₂)v
10. A 4 kg cart moving at 63 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 (63 m/s) → [5 kg] → Coupled: (9 kg) v = ? · m₁u₁ = (m₁ + m₂)v
11. A 3 kg cart moving at 25 m/s collides with and couples to a stationary 2 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
3 kg (25 m/s) → [2 kg] → Coupled: (5 kg) v = ? · m₁u₁ = (m₁ + m₂)v
12. A 5 kg cart moving at 56 m/s collides with and couples to a stationary 3 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
5 kg (56 m/s) → [3 kg] → Coupled: (8 kg) v = ? · m₁u₁ = (m₁ + m₂)v

12 questions · Seed 42 · 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 10 kg cart moving at 84 m/s collides with and couples to a stationary 2 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
70 m/s
Total momentum before collision p = 10 × 84 = 840 kg·m/s. Combined mass = 10 + 2 = 12 kg, so v = 840 ÷ 12 = 70 m/s.
2. 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.
3. A 2 kg cart moving at 40 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 = 2 × 40 = 80 kg·m/s. Combined mass = 2 + 3 = 5 kg, so v = 80 ÷ 5 = 16 m/s.
4. A 7 kg cart moving at 27 m/s collides with and couples to a stationary 2 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
21 m/s
Total momentum before collision p = 7 × 27 = 189 kg·m/s. Combined mass = 7 + 2 = 9 kg, so v = 189 ÷ 9 = 21 m/s.
5. A 3 kg cart moving at 21 m/s collides with and couples to a stationary 4 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
9 m/s
Total momentum before collision p = 3 × 21 = 63 kg·m/s. Combined mass = 3 + 4 = 7 kg, so v = 63 ÷ 7 = 9 m/s.
6. A 7 kg cart moving at 128 m/s collides with and couples to a stationary 9 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
56 m/s
Total momentum before collision p = 7 × 128 = 896 kg·m/s. Combined mass = 7 + 9 = 16 kg, so v = 896 ÷ 16 = 56 m/s.
7. A 3 kg cart moving at 6 m/s collides with and couples to a stationary 3 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
3 m/s
Total momentum before collision p = 3 × 6 = 18 kg·m/s. Combined mass = 3 + 3 = 6 kg, so v = 18 ÷ 6 = 3 m/s.
8. A 2 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.
10 m/s
Total momentum before collision p = 2 × 30 = 60 kg·m/s. Combined mass = 2 + 4 = 6 kg, so v = 60 ÷ 6 = 10 m/s.
9. A 9 kg cart moving at 18 m/s collides with and couples to a stationary 9 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
9 m/s
Total momentum before collision p = 9 × 18 = 162 kg·m/s. Combined mass = 9 + 9 = 18 kg, so v = 162 ÷ 18 = 9 m/s.
10. A 4 kg cart moving at 63 m/s collides with and couples to a stationary 5 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
28 m/s
Total momentum before collision p = 4 × 63 = 252 kg·m/s. Combined mass = 4 + 5 = 9 kg, so v = 252 ÷ 9 = 28 m/s.
11. A 3 kg cart moving at 25 m/s collides with and couples to a stationary 2 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
15 m/s
Total momentum before collision p = 3 × 25 = 75 kg·m/s. Combined mass = 3 + 2 = 5 kg, so v = 75 ÷ 5 = 15 m/s.
12. A 5 kg cart moving at 56 m/s collides with and couples to a stationary 3 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
35 m/s
Total momentum before collision p = 5 × 56 = 280 kg·m/s. Combined mass = 5 + 3 = 8 kg, so v = 280 ÷ 8 = 35 m/s.

12 questions · Seed 42 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 13-15

Conservation of momentum in collisions

Take your time. Show your thinking.

1. A 10 kg cart moving at 84 m/s collides with and couples to a stationary 2 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
10 kg (84 m/s) → [2 kg] → Coupled: (12 kg) v = ? · m₁u₁ = (m₁ + m₂)v
2. 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
3. A 2 kg cart moving at 40 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 (40 m/s) → [3 kg] → Coupled: (5 kg) v = ? · m₁u₁ = (m₁ + m₂)v
4. A 7 kg cart moving at 27 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 (27 m/s) → [2 kg] → Coupled: (9 kg) v = ? · m₁u₁ = (m₁ + m₂)v
5. A 3 kg cart moving at 21 m/s collides with and couples to a stationary 4 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
3 kg (21 m/s) → [4 kg] → Coupled: (7 kg) v = ? · m₁u₁ = (m₁ + m₂)v
6. A 7 kg cart moving at 128 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 (128 m/s) → [9 kg] → Coupled: (16 kg) v = ? · m₁u₁ = (m₁ + m₂)v
7. A 3 kg cart moving at 6 m/s collides with and couples to a stationary 3 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
3 kg (6 m/s) → [3 kg] → Coupled: (6 kg) v = ? · m₁u₁ = (m₁ + m₂)v
8. A 2 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.
2 kg (30 m/s) → [4 kg] → Coupled: (6 kg) v = ? · m₁u₁ = (m₁ + m₂)v
9. A 9 kg cart moving at 18 m/s collides with and couples to a stationary 9 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
9 kg (18 m/s) → [9 kg] → Coupled: (18 kg) v = ? · m₁u₁ = (m₁ + m₂)v
10. A 4 kg cart moving at 63 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 (63 m/s) → [5 kg] → Coupled: (9 kg) v = ? · m₁u₁ = (m₁ + m₂)v
11. A 3 kg cart moving at 25 m/s collides with and couples to a stationary 2 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
3 kg (25 m/s) → [2 kg] → Coupled: (5 kg) v = ? · m₁u₁ = (m₁ + m₂)v
12. A 5 kg cart moving at 56 m/s collides with and couples to a stationary 3 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
5 kg (56 m/s) → [3 kg] → Coupled: (8 kg) v = ? · m₁u₁ = (m₁ + m₂)v

12 questions · Seed 42 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 13-15

Conservation of momentum in collisions

Answers and reasoning. Review before teaching.

1. A 10 kg cart moving at 84 m/s collides with and couples to a stationary 2 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
70 m/s
Total momentum before collision p = 10 × 84 = 840 kg·m/s. Combined mass = 10 + 2 = 12 kg, so v = 840 ÷ 12 = 70 m/s.
2. 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.
3. A 2 kg cart moving at 40 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 = 2 × 40 = 80 kg·m/s. Combined mass = 2 + 3 = 5 kg, so v = 80 ÷ 5 = 16 m/s.
4. A 7 kg cart moving at 27 m/s collides with and couples to a stationary 2 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
21 m/s
Total momentum before collision p = 7 × 27 = 189 kg·m/s. Combined mass = 7 + 2 = 9 kg, so v = 189 ÷ 9 = 21 m/s.
5. A 3 kg cart moving at 21 m/s collides with and couples to a stationary 4 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
9 m/s
Total momentum before collision p = 3 × 21 = 63 kg·m/s. Combined mass = 3 + 4 = 7 kg, so v = 63 ÷ 7 = 9 m/s.
6. A 7 kg cart moving at 128 m/s collides with and couples to a stationary 9 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
56 m/s
Total momentum before collision p = 7 × 128 = 896 kg·m/s. Combined mass = 7 + 9 = 16 kg, so v = 896 ÷ 16 = 56 m/s.
7. A 3 kg cart moving at 6 m/s collides with and couples to a stationary 3 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
3 m/s
Total momentum before collision p = 3 × 6 = 18 kg·m/s. Combined mass = 3 + 3 = 6 kg, so v = 18 ÷ 6 = 3 m/s.
8. A 2 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.
10 m/s
Total momentum before collision p = 2 × 30 = 60 kg·m/s. Combined mass = 2 + 4 = 6 kg, so v = 60 ÷ 6 = 10 m/s.
9. A 9 kg cart moving at 18 m/s collides with and couples to a stationary 9 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
9 m/s
Total momentum before collision p = 9 × 18 = 162 kg·m/s. Combined mass = 9 + 9 = 18 kg, so v = 162 ÷ 18 = 9 m/s.
10. A 4 kg cart moving at 63 m/s collides with and couples to a stationary 5 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
28 m/s
Total momentum before collision p = 4 × 63 = 252 kg·m/s. Combined mass = 4 + 5 = 9 kg, so v = 252 ÷ 9 = 28 m/s.
11. A 3 kg cart moving at 25 m/s collides with and couples to a stationary 2 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
15 m/s
Total momentum before collision p = 3 × 25 = 75 kg·m/s. Combined mass = 3 + 2 = 5 kg, so v = 75 ÷ 5 = 15 m/s.
12. A 5 kg cart moving at 56 m/s collides with and couples to a stationary 3 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
35 m/s
Total momentum before collision p = 5 × 56 = 280 kg·m/s. Combined mass = 5 + 3 = 8 kg, so v = 280 ÷ 8 = 35 m/s.

12 questions · Seed 42 · Age guidance, not curriculum certification