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 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
2. A 7 kg cart moving at 42 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 (42 m/s) → [7 kg] → Coupled: (14 kg) v = ? · m₁u₁ = (m₁ + m₂)v
3. A 5 kg cart moving at 14 m/s collides with and couples to a stationary 2 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
5 kg (14 m/s) → [2 kg] → Coupled: (7 kg) v = ? · m₁u₁ = (m₁ + m₂)v
4. A 4 kg cart moving at 112 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 (112 m/s) → [10 kg] → Coupled: (14 kg) v = ? · m₁u₁ = (m₁ + m₂)v
5. A 4 kg cart moving at 21 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 (21 m/s) → [3 kg] → Coupled: (7 kg) v = ? · m₁u₁ = (m₁ + m₂)v
6. A 8 kg cart moving at 36 m/s collides with and couples to a stationary 4 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
8 kg (36 m/s) → [4 kg] → Coupled: (12 kg) v = ? · m₁u₁ = (m₁ + m₂)v
7. A 3 kg cart moving at 48 m/s collides with and couples to a stationary 9 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
3 kg (48 m/s) → [9 kg] → Coupled: (12 kg) v = ? · m₁u₁ = (m₁ + m₂)v
8. A 4 kg cart moving at 77 m/s collides with and couples to a stationary 7 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
4 kg (77 m/s) → [7 kg] → Coupled: (11 kg) v = ? · m₁u₁ = (m₁ + m₂)v
9. A 4 kg cart moving at 16 m/s collides with and couples to a stationary 4 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
4 kg (16 m/s) → [4 kg] → Coupled: (8 kg) v = ? · m₁u₁ = (m₁ + m₂)v
10. A 2 kg cart moving at 20 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 (20 m/s) → [2 kg] → Coupled: (4 kg) v = ? · m₁u₁ = (m₁ + m₂)v
11. A 8 kg cart moving at 136 m/s collides with and couples to a stationary 9 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
8 kg (136 m/s) → [9 kg] → Coupled: (17 kg) v = ? · m₁u₁ = (m₁ + m₂)v
12. A 9 kg cart moving at 90 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 (90 m/s) → [9 kg] → Coupled: (18 kg) v = ? · m₁u₁ = (m₁ + m₂)v

12 questions · Seed 104739 · 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 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.
2. A 7 kg cart moving at 42 m/s collides with and couples to a stationary 7 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
21 m/s
Total momentum before collision p = 7 × 42 = 294 kg·m/s. Combined mass = 7 + 7 = 14 kg, so v = 294 ÷ 14 = 21 m/s.
3. A 5 kg cart moving at 14 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 m/s
Total momentum before collision p = 5 × 14 = 70 kg·m/s. Combined mass = 5 + 2 = 7 kg, so v = 70 ÷ 7 = 10 m/s.
4. A 4 kg cart moving at 112 m/s collides with and couples to a stationary 10 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
32 m/s
Total momentum before collision p = 4 × 112 = 448 kg·m/s. Combined mass = 4 + 10 = 14 kg, so v = 448 ÷ 14 = 32 m/s.
5. A 4 kg cart moving at 21 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 = 4 × 21 = 84 kg·m/s. Combined mass = 4 + 3 = 7 kg, so v = 84 ÷ 7 = 12 m/s.
6. A 8 kg cart moving at 36 m/s collides with and couples to a stationary 4 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
24 m/s
Total momentum before collision p = 8 × 36 = 288 kg·m/s. Combined mass = 8 + 4 = 12 kg, so v = 288 ÷ 12 = 24 m/s.
7. A 3 kg cart moving at 48 m/s collides with and couples to a stationary 9 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
12 m/s
Total momentum before collision p = 3 × 48 = 144 kg·m/s. Combined mass = 3 + 9 = 12 kg, so v = 144 ÷ 12 = 12 m/s.
8. A 4 kg cart moving at 77 m/s collides with and couples to a stationary 7 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
28 m/s
Total momentum before collision p = 4 × 77 = 308 kg·m/s. Combined mass = 4 + 7 = 11 kg, so v = 308 ÷ 11 = 28 m/s.
9. A 4 kg cart moving at 16 m/s collides with and couples to a stationary 4 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
8 m/s
Total momentum before collision p = 4 × 16 = 64 kg·m/s. Combined mass = 4 + 4 = 8 kg, so v = 64 ÷ 8 = 8 m/s.
10. A 2 kg cart moving at 20 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 m/s
Total momentum before collision p = 2 × 20 = 40 kg·m/s. Combined mass = 2 + 2 = 4 kg, so v = 40 ÷ 4 = 10 m/s.
11. A 8 kg cart moving at 136 m/s collides with and couples to a stationary 9 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
64 m/s
Total momentum before collision p = 8 × 136 = 1088 kg·m/s. Combined mass = 8 + 9 = 17 kg, so v = 1088 ÷ 17 = 64 m/s.
12. A 9 kg cart moving at 90 m/s collides with and couples to a stationary 9 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
45 m/s
Total momentum before collision p = 9 × 90 = 810 kg·m/s. Combined mass = 9 + 9 = 18 kg, so v = 810 ÷ 18 = 45 m/s.

12 questions · Seed 104739 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 13-15

Conservation of momentum in collisions

Take your time. Show your thinking.

1. 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
2. A 7 kg cart moving at 42 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 (42 m/s) → [7 kg] → Coupled: (14 kg) v = ? · m₁u₁ = (m₁ + m₂)v
3. A 5 kg cart moving at 14 m/s collides with and couples to a stationary 2 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
5 kg (14 m/s) → [2 kg] → Coupled: (7 kg) v = ? · m₁u₁ = (m₁ + m₂)v
4. A 4 kg cart moving at 112 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 (112 m/s) → [10 kg] → Coupled: (14 kg) v = ? · m₁u₁ = (m₁ + m₂)v
5. A 4 kg cart moving at 21 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 (21 m/s) → [3 kg] → Coupled: (7 kg) v = ? · m₁u₁ = (m₁ + m₂)v
6. A 8 kg cart moving at 36 m/s collides with and couples to a stationary 4 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
8 kg (36 m/s) → [4 kg] → Coupled: (12 kg) v = ? · m₁u₁ = (m₁ + m₂)v
7. A 3 kg cart moving at 48 m/s collides with and couples to a stationary 9 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
3 kg (48 m/s) → [9 kg] → Coupled: (12 kg) v = ? · m₁u₁ = (m₁ + m₂)v
8. A 4 kg cart moving at 77 m/s collides with and couples to a stationary 7 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
4 kg (77 m/s) → [7 kg] → Coupled: (11 kg) v = ? · m₁u₁ = (m₁ + m₂)v
9. A 4 kg cart moving at 16 m/s collides with and couples to a stationary 4 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
4 kg (16 m/s) → [4 kg] → Coupled: (8 kg) v = ? · m₁u₁ = (m₁ + m₂)v
10. A 2 kg cart moving at 20 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 (20 m/s) → [2 kg] → Coupled: (4 kg) v = ? · m₁u₁ = (m₁ + m₂)v
11. A 8 kg cart moving at 136 m/s collides with and couples to a stationary 9 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
8 kg (136 m/s) → [9 kg] → Coupled: (17 kg) v = ? · m₁u₁ = (m₁ + m₂)v
12. A 9 kg cart moving at 90 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 (90 m/s) → [9 kg] → Coupled: (18 kg) v = ? · m₁u₁ = (m₁ + m₂)v

12 questions · Seed 104739 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 13-15

Conservation of momentum in collisions

Answers and reasoning. Review before teaching.

1. 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.
2. A 7 kg cart moving at 42 m/s collides with and couples to a stationary 7 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
21 m/s
Total momentum before collision p = 7 × 42 = 294 kg·m/s. Combined mass = 7 + 7 = 14 kg, so v = 294 ÷ 14 = 21 m/s.
3. A 5 kg cart moving at 14 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 m/s
Total momentum before collision p = 5 × 14 = 70 kg·m/s. Combined mass = 5 + 2 = 7 kg, so v = 70 ÷ 7 = 10 m/s.
4. A 4 kg cart moving at 112 m/s collides with and couples to a stationary 10 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
32 m/s
Total momentum before collision p = 4 × 112 = 448 kg·m/s. Combined mass = 4 + 10 = 14 kg, so v = 448 ÷ 14 = 32 m/s.
5. A 4 kg cart moving at 21 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 = 4 × 21 = 84 kg·m/s. Combined mass = 4 + 3 = 7 kg, so v = 84 ÷ 7 = 12 m/s.
6. A 8 kg cart moving at 36 m/s collides with and couples to a stationary 4 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
24 m/s
Total momentum before collision p = 8 × 36 = 288 kg·m/s. Combined mass = 8 + 4 = 12 kg, so v = 288 ÷ 12 = 24 m/s.
7. A 3 kg cart moving at 48 m/s collides with and couples to a stationary 9 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
12 m/s
Total momentum before collision p = 3 × 48 = 144 kg·m/s. Combined mass = 3 + 9 = 12 kg, so v = 144 ÷ 12 = 12 m/s.
8. A 4 kg cart moving at 77 m/s collides with and couples to a stationary 7 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
28 m/s
Total momentum before collision p = 4 × 77 = 308 kg·m/s. Combined mass = 4 + 7 = 11 kg, so v = 308 ÷ 11 = 28 m/s.
9. A 4 kg cart moving at 16 m/s collides with and couples to a stationary 4 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
8 m/s
Total momentum before collision p = 4 × 16 = 64 kg·m/s. Combined mass = 4 + 4 = 8 kg, so v = 64 ÷ 8 = 8 m/s.
10. A 2 kg cart moving at 20 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 m/s
Total momentum before collision p = 2 × 20 = 40 kg·m/s. Combined mass = 2 + 2 = 4 kg, so v = 40 ÷ 4 = 10 m/s.
11. A 8 kg cart moving at 136 m/s collides with and couples to a stationary 9 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
64 m/s
Total momentum before collision p = 8 × 136 = 1088 kg·m/s. Combined mass = 8 + 9 = 17 kg, so v = 1088 ÷ 17 = 64 m/s.
12. A 9 kg cart moving at 90 m/s collides with and couples to a stationary 9 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
45 m/s
Total momentum before collision p = 9 × 90 = 810 kg·m/s. Combined mass = 9 + 9 = 18 kg, so v = 810 ÷ 18 = 45 m/s.

12 questions · Seed 104739 · Age guidance, not curriculum certification