ScienceAges 16-18

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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Age band:Ages 13-15 Ages 16-18

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Worksheet StudioPractice pack · Ages 16-18

Conservation of momentum in collisions

Take your time. Show your thinking.

1. A 5 kg cart moving at 15 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 (15 m/s) → [10 kg] → Coupled: (15 kg) v = ? · m₁u₁ = (m₁ + m₂)v
2. A 10 kg cart moving at 108 m/s collides with and couples to a stationary 8 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
10 kg (108 m/s) → [8 kg] → Coupled: (18 kg) v = ? · m₁u₁ = (m₁ + m₂)v
3. A 4 kg cart moving at 30 m/s collides with and couples to a stationary 6 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
4 kg (30 m/s) → [6 kg] → Coupled: (10 kg) v = ? · m₁u₁ = (m₁ + m₂)v
4. A 10 kg cart moving at 60 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 kg (60 m/s) → [10 kg] → Coupled: (20 kg) v = ? · m₁u₁ = (m₁ + m₂)v
5. A 4 kg cart moving at 20 m/s collides with and couples to a stationary 6 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
4 kg (20 m/s) → [6 kg] → Coupled: (10 kg) v = ? · m₁u₁ = (m₁ + m₂)v
6. A 8 kg cart moving at 78 m/s collides with and couples to a stationary 5 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
8 kg (78 m/s) → [5 kg] → Coupled: (13 kg) v = ? · m₁u₁ = (m₁ + m₂)v
7. A 10 kg cart moving at 36 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 (36 m/s) → [2 kg] → Coupled: (12 kg) v = ? · m₁u₁ = (m₁ + m₂)v
8. A 7 kg cart moving at 77 m/s collides with and couples to a stationary 4 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
7 kg (77 m/s) → [4 kg] → Coupled: (11 kg) v = ? · m₁u₁ = (m₁ + m₂)v
9. A 3 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.
3 kg (20 m/s) → [2 kg] → Coupled: (5 kg) v = ? · m₁u₁ = (m₁ + m₂)v
10. A 10 kg cart moving at 91 m/s collides with and couples to a stationary 3 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
10 kg (91 m/s) → [3 kg] → Coupled: (13 kg) v = ? · m₁u₁ = (m₁ + m₂)v
11. A 10 kg cart moving at 160 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 kg (160 m/s) → [10 kg] → Coupled: (20 kg) v = ? · m₁u₁ = (m₁ + m₂)v
12. A 7 kg cart moving at 84 m/s collides with and couples to a stationary 5 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
7 kg (84 m/s) → [5 kg] → Coupled: (12 kg) v = ? · m₁u₁ = (m₁ + m₂)v

12 questions · Seed 46 · Age guidance, not curriculum certification

View the answer key

Worksheet StudioAnswer key · Ages 16-18

Conservation of momentum in collisions

Answers and reasoning. Review before teaching.

1. A 5 kg cart moving at 15 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 m/s
Total momentum before collision p = 5 × 15 = 75 kg·m/s. Combined mass = 5 + 10 = 15 kg, so v = 75 ÷ 15 = 5 m/s.
2. A 10 kg cart moving at 108 m/s collides with and couples to a stationary 8 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
60 m/s
Total momentum before collision p = 10 × 108 = 1080 kg·m/s. Combined mass = 10 + 8 = 18 kg, so v = 1080 ÷ 18 = 60 m/s.
3. A 4 kg cart moving at 30 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 = 4 × 30 = 120 kg·m/s. Combined mass = 4 + 6 = 10 kg, so v = 120 ÷ 10 = 12 m/s.
4. A 10 kg cart moving at 60 m/s collides with and couples to a stationary 10 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
30 m/s
Total momentum before collision p = 10 × 60 = 600 kg·m/s. Combined mass = 10 + 10 = 20 kg, so v = 600 ÷ 20 = 30 m/s.
5. A 4 kg cart moving at 20 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 = 4 × 20 = 80 kg·m/s. Combined mass = 4 + 6 = 10 kg, so v = 80 ÷ 10 = 8 m/s.
6. A 8 kg cart moving at 78 m/s collides with and couples to a stationary 5 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
48 m/s
Total momentum before collision p = 8 × 78 = 624 kg·m/s. Combined mass = 8 + 5 = 13 kg, so v = 624 ÷ 13 = 48 m/s.
7. A 10 kg cart moving at 36 m/s collides with and couples to a stationary 2 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
30 m/s
Total momentum before collision p = 10 × 36 = 360 kg·m/s. Combined mass = 10 + 2 = 12 kg, so v = 360 ÷ 12 = 30 m/s.
8. A 7 kg cart moving at 77 m/s collides with and couples to a stationary 4 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
49 m/s
Total momentum before collision p = 7 × 77 = 539 kg·m/s. Combined mass = 7 + 4 = 11 kg, so v = 539 ÷ 11 = 49 m/s.
9. A 3 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.
12 m/s
Total momentum before collision p = 3 × 20 = 60 kg·m/s. Combined mass = 3 + 2 = 5 kg, so v = 60 ÷ 5 = 12 m/s.
10. A 10 kg cart moving at 91 m/s collides with and couples to a stationary 3 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
70 m/s
Total momentum before collision p = 10 × 91 = 910 kg·m/s. Combined mass = 10 + 3 = 13 kg, so v = 910 ÷ 13 = 70 m/s.
11. A 10 kg cart moving at 160 m/s collides with and couples to a stationary 10 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
80 m/s
Total momentum before collision p = 10 × 160 = 1600 kg·m/s. Combined mass = 10 + 10 = 20 kg, so v = 1600 ÷ 20 = 80 m/s.
12. A 7 kg cart moving at 84 m/s collides with and couples to a stationary 5 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
49 m/s
Total momentum before collision p = 7 × 84 = 588 kg·m/s. Combined mass = 7 + 5 = 12 kg, so v = 588 ÷ 12 = 49 m/s.

12 questions · Seed 46 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 16-18

Conservation of momentum in collisions

Take your time. Show your thinking.

1. A 5 kg cart moving at 15 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 (15 m/s) → [10 kg] → Coupled: (15 kg) v = ? · m₁u₁ = (m₁ + m₂)v
2. A 10 kg cart moving at 108 m/s collides with and couples to a stationary 8 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
10 kg (108 m/s) → [8 kg] → Coupled: (18 kg) v = ? · m₁u₁ = (m₁ + m₂)v
3. A 4 kg cart moving at 30 m/s collides with and couples to a stationary 6 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
4 kg (30 m/s) → [6 kg] → Coupled: (10 kg) v = ? · m₁u₁ = (m₁ + m₂)v
4. A 10 kg cart moving at 60 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 kg (60 m/s) → [10 kg] → Coupled: (20 kg) v = ? · m₁u₁ = (m₁ + m₂)v
5. A 4 kg cart moving at 20 m/s collides with and couples to a stationary 6 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
4 kg (20 m/s) → [6 kg] → Coupled: (10 kg) v = ? · m₁u₁ = (m₁ + m₂)v
6. A 8 kg cart moving at 78 m/s collides with and couples to a stationary 5 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
8 kg (78 m/s) → [5 kg] → Coupled: (13 kg) v = ? · m₁u₁ = (m₁ + m₂)v
7. A 10 kg cart moving at 36 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 (36 m/s) → [2 kg] → Coupled: (12 kg) v = ? · m₁u₁ = (m₁ + m₂)v
8. A 7 kg cart moving at 77 m/s collides with and couples to a stationary 4 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
7 kg (77 m/s) → [4 kg] → Coupled: (11 kg) v = ? · m₁u₁ = (m₁ + m₂)v
9. A 3 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.
3 kg (20 m/s) → [2 kg] → Coupled: (5 kg) v = ? · m₁u₁ = (m₁ + m₂)v
10. A 10 kg cart moving at 91 m/s collides with and couples to a stationary 3 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
10 kg (91 m/s) → [3 kg] → Coupled: (13 kg) v = ? · m₁u₁ = (m₁ + m₂)v
11. A 10 kg cart moving at 160 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 kg (160 m/s) → [10 kg] → Coupled: (20 kg) v = ? · m₁u₁ = (m₁ + m₂)v
12. A 7 kg cart moving at 84 m/s collides with and couples to a stationary 5 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
7 kg (84 m/s) → [5 kg] → Coupled: (12 kg) v = ? · m₁u₁ = (m₁ + m₂)v

12 questions · Seed 46 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 16-18

Conservation of momentum in collisions

Answers and reasoning. Review before teaching.

1. A 5 kg cart moving at 15 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 m/s
Total momentum before collision p = 5 × 15 = 75 kg·m/s. Combined mass = 5 + 10 = 15 kg, so v = 75 ÷ 15 = 5 m/s.
2. A 10 kg cart moving at 108 m/s collides with and couples to a stationary 8 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
60 m/s
Total momentum before collision p = 10 × 108 = 1080 kg·m/s. Combined mass = 10 + 8 = 18 kg, so v = 1080 ÷ 18 = 60 m/s.
3. A 4 kg cart moving at 30 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 = 4 × 30 = 120 kg·m/s. Combined mass = 4 + 6 = 10 kg, so v = 120 ÷ 10 = 12 m/s.
4. A 10 kg cart moving at 60 m/s collides with and couples to a stationary 10 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
30 m/s
Total momentum before collision p = 10 × 60 = 600 kg·m/s. Combined mass = 10 + 10 = 20 kg, so v = 600 ÷ 20 = 30 m/s.
5. A 4 kg cart moving at 20 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 = 4 × 20 = 80 kg·m/s. Combined mass = 4 + 6 = 10 kg, so v = 80 ÷ 10 = 8 m/s.
6. A 8 kg cart moving at 78 m/s collides with and couples to a stationary 5 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
48 m/s
Total momentum before collision p = 8 × 78 = 624 kg·m/s. Combined mass = 8 + 5 = 13 kg, so v = 624 ÷ 13 = 48 m/s.
7. A 10 kg cart moving at 36 m/s collides with and couples to a stationary 2 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
30 m/s
Total momentum before collision p = 10 × 36 = 360 kg·m/s. Combined mass = 10 + 2 = 12 kg, so v = 360 ÷ 12 = 30 m/s.
8. A 7 kg cart moving at 77 m/s collides with and couples to a stationary 4 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
49 m/s
Total momentum before collision p = 7 × 77 = 539 kg·m/s. Combined mass = 7 + 4 = 11 kg, so v = 539 ÷ 11 = 49 m/s.
9. A 3 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.
12 m/s
Total momentum before collision p = 3 × 20 = 60 kg·m/s. Combined mass = 3 + 2 = 5 kg, so v = 60 ÷ 5 = 12 m/s.
10. A 10 kg cart moving at 91 m/s collides with and couples to a stationary 3 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
70 m/s
Total momentum before collision p = 10 × 91 = 910 kg·m/s. Combined mass = 10 + 3 = 13 kg, so v = 910 ÷ 13 = 70 m/s.
11. A 10 kg cart moving at 160 m/s collides with and couples to a stationary 10 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
80 m/s
Total momentum before collision p = 10 × 160 = 1600 kg·m/s. Combined mass = 10 + 10 = 20 kg, so v = 1600 ÷ 20 = 80 m/s.
12. A 7 kg cart moving at 84 m/s collides with and couples to a stationary 5 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
49 m/s
Total momentum before collision p = 7 × 84 = 588 kg·m/s. Combined mass = 7 + 5 = 12 kg, so v = 588 ÷ 12 = 49 m/s.

12 questions · Seed 46 · Age guidance, not curriculum certification