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 10 kg cart moving at 16 m/s collides with and couples to a stationary 6 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
10 kg (16 m/s) → [6 kg] → Coupled: (16 kg) v = ? · m₁u₁ = (m₁ + m₂)v
2. A 4 kg cart moving at 24 m/s collides with and couples to a stationary 8 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
4 kg (24 m/s) → [8 kg] → Coupled: (12 kg) v = ? · m₁u₁ = (m₁ + m₂)v
3. A 3 kg cart moving at 18 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 (18 m/s) → [3 kg] → Coupled: (6 kg) v = ? · m₁u₁ = (m₁ + m₂)v
4. A 3 kg cart moving at 88 m/s collides with and couples to a stationary 8 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
3 kg (88 m/s) → [8 kg] → Coupled: (11 kg) v = ? · m₁u₁ = (m₁ + m₂)v
5. A 5 kg cart moving at 14 m/s collides with and couples to a stationary 9 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
5 kg (14 m/s) → [9 kg] → Coupled: (14 kg) v = ? · m₁u₁ = (m₁ + m₂)v
6. A 5 kg cart moving at 65 m/s collides with and couples to a stationary 8 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
5 kg (65 m/s) → [8 kg] → Coupled: (13 kg) v = ? · m₁u₁ = (m₁ + m₂)v
7. A 10 kg cart moving at 39 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 (39 m/s) → [3 kg] → Coupled: (13 kg) v = ? · m₁u₁ = (m₁ + m₂)v
8. A 7 kg cart moving at 12 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 (12 m/s) → [5 kg] → Coupled: (12 kg) v = ? · m₁u₁ = (m₁ + m₂)v
9. A 2 kg cart moving at 32 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 (32 m/s) → [2 kg] → Coupled: (4 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 9 kg cart moving at 112 m/s collides with and couples to a stationary 5 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
9 kg (112 m/s) → [5 kg] → Coupled: (14 kg) v = ? · m₁u₁ = (m₁ + m₂)v
12. A 6 kg cart moving at 10 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 (10 m/s) → [4 kg] → Coupled: (10 kg) v = ? · m₁u₁ = (m₁ + m₂)v

12 questions · Seed 104735 · 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 10 kg cart moving at 16 m/s collides with and couples to a stationary 6 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
10 m/s
Total momentum before collision p = 10 × 16 = 160 kg·m/s. Combined mass = 10 + 6 = 16 kg, so v = 160 ÷ 16 = 10 m/s.
2. A 4 kg cart moving at 24 m/s collides with and couples to a stationary 8 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
8 m/s
Total momentum before collision p = 4 × 24 = 96 kg·m/s. Combined mass = 4 + 8 = 12 kg, so v = 96 ÷ 12 = 8 m/s.
3. A 3 kg cart moving at 18 m/s collides with and couples to a stationary 3 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
9 m/s
Total momentum before collision p = 3 × 18 = 54 kg·m/s. Combined mass = 3 + 3 = 6 kg, so v = 54 ÷ 6 = 9 m/s.
4. A 3 kg cart moving at 88 m/s collides with and couples to a stationary 8 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
24 m/s
Total momentum before collision p = 3 × 88 = 264 kg·m/s. Combined mass = 3 + 8 = 11 kg, so v = 264 ÷ 11 = 24 m/s.
5. A 5 kg cart moving at 14 m/s collides with and couples to a stationary 9 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
5 m/s
Total momentum before collision p = 5 × 14 = 70 kg·m/s. Combined mass = 5 + 9 = 14 kg, so v = 70 ÷ 14 = 5 m/s.
6. A 5 kg cart moving at 65 m/s collides with and couples to a stationary 8 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
25 m/s
Total momentum before collision p = 5 × 65 = 325 kg·m/s. Combined mass = 5 + 8 = 13 kg, so v = 325 ÷ 13 = 25 m/s.
7. A 10 kg cart moving at 39 m/s collides with and couples to a stationary 3 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
30 m/s
Total momentum before collision p = 10 × 39 = 390 kg·m/s. Combined mass = 10 + 3 = 13 kg, so v = 390 ÷ 13 = 30 m/s.
8. A 7 kg cart moving at 12 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 m/s
Total momentum before collision p = 7 × 12 = 84 kg·m/s. Combined mass = 7 + 5 = 12 kg, so v = 84 ÷ 12 = 7 m/s.
9. A 2 kg cart moving at 32 m/s collides with and couples to a stationary 2 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
16 m/s
Total momentum before collision p = 2 × 32 = 64 kg·m/s. Combined mass = 2 + 2 = 4 kg, so v = 64 ÷ 4 = 16 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 9 kg cart moving at 112 m/s collides with and couples to a stationary 5 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
72 m/s
Total momentum before collision p = 9 × 112 = 1008 kg·m/s. Combined mass = 9 + 5 = 14 kg, so v = 1008 ÷ 14 = 72 m/s.
12. A 6 kg cart moving at 10 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 m/s
Total momentum before collision p = 6 × 10 = 60 kg·m/s. Combined mass = 6 + 4 = 10 kg, so v = 60 ÷ 10 = 6 m/s.

12 questions · Seed 104735 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 16-18

Conservation of momentum in collisions

Take your time. Show your thinking.

1. A 10 kg cart moving at 16 m/s collides with and couples to a stationary 6 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
10 kg (16 m/s) → [6 kg] → Coupled: (16 kg) v = ? · m₁u₁ = (m₁ + m₂)v
2. A 4 kg cart moving at 24 m/s collides with and couples to a stationary 8 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
4 kg (24 m/s) → [8 kg] → Coupled: (12 kg) v = ? · m₁u₁ = (m₁ + m₂)v
3. A 3 kg cart moving at 18 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 (18 m/s) → [3 kg] → Coupled: (6 kg) v = ? · m₁u₁ = (m₁ + m₂)v
4. A 3 kg cart moving at 88 m/s collides with and couples to a stationary 8 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
3 kg (88 m/s) → [8 kg] → Coupled: (11 kg) v = ? · m₁u₁ = (m₁ + m₂)v
5. A 5 kg cart moving at 14 m/s collides with and couples to a stationary 9 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
5 kg (14 m/s) → [9 kg] → Coupled: (14 kg) v = ? · m₁u₁ = (m₁ + m₂)v
6. A 5 kg cart moving at 65 m/s collides with and couples to a stationary 8 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
5 kg (65 m/s) → [8 kg] → Coupled: (13 kg) v = ? · m₁u₁ = (m₁ + m₂)v
7. A 10 kg cart moving at 39 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 (39 m/s) → [3 kg] → Coupled: (13 kg) v = ? · m₁u₁ = (m₁ + m₂)v
8. A 7 kg cart moving at 12 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 (12 m/s) → [5 kg] → Coupled: (12 kg) v = ? · m₁u₁ = (m₁ + m₂)v
9. A 2 kg cart moving at 32 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 (32 m/s) → [2 kg] → Coupled: (4 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 9 kg cart moving at 112 m/s collides with and couples to a stationary 5 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
9 kg (112 m/s) → [5 kg] → Coupled: (14 kg) v = ? · m₁u₁ = (m₁ + m₂)v
12. A 6 kg cart moving at 10 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 (10 m/s) → [4 kg] → Coupled: (10 kg) v = ? · m₁u₁ = (m₁ + m₂)v

12 questions · Seed 104735 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 16-18

Conservation of momentum in collisions

Answers and reasoning. Review before teaching.

1. A 10 kg cart moving at 16 m/s collides with and couples to a stationary 6 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
10 m/s
Total momentum before collision p = 10 × 16 = 160 kg·m/s. Combined mass = 10 + 6 = 16 kg, so v = 160 ÷ 16 = 10 m/s.
2. A 4 kg cart moving at 24 m/s collides with and couples to a stationary 8 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
8 m/s
Total momentum before collision p = 4 × 24 = 96 kg·m/s. Combined mass = 4 + 8 = 12 kg, so v = 96 ÷ 12 = 8 m/s.
3. A 3 kg cart moving at 18 m/s collides with and couples to a stationary 3 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
9 m/s
Total momentum before collision p = 3 × 18 = 54 kg·m/s. Combined mass = 3 + 3 = 6 kg, so v = 54 ÷ 6 = 9 m/s.
4. A 3 kg cart moving at 88 m/s collides with and couples to a stationary 8 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
24 m/s
Total momentum before collision p = 3 × 88 = 264 kg·m/s. Combined mass = 3 + 8 = 11 kg, so v = 264 ÷ 11 = 24 m/s.
5. A 5 kg cart moving at 14 m/s collides with and couples to a stationary 9 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
5 m/s
Total momentum before collision p = 5 × 14 = 70 kg·m/s. Combined mass = 5 + 9 = 14 kg, so v = 70 ÷ 14 = 5 m/s.
6. A 5 kg cart moving at 65 m/s collides with and couples to a stationary 8 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
25 m/s
Total momentum before collision p = 5 × 65 = 325 kg·m/s. Combined mass = 5 + 8 = 13 kg, so v = 325 ÷ 13 = 25 m/s.
7. A 10 kg cart moving at 39 m/s collides with and couples to a stationary 3 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
30 m/s
Total momentum before collision p = 10 × 39 = 390 kg·m/s. Combined mass = 10 + 3 = 13 kg, so v = 390 ÷ 13 = 30 m/s.
8. A 7 kg cart moving at 12 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 m/s
Total momentum before collision p = 7 × 12 = 84 kg·m/s. Combined mass = 7 + 5 = 12 kg, so v = 84 ÷ 12 = 7 m/s.
9. A 2 kg cart moving at 32 m/s collides with and couples to a stationary 2 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
16 m/s
Total momentum before collision p = 2 × 32 = 64 kg·m/s. Combined mass = 2 + 2 = 4 kg, so v = 64 ÷ 4 = 16 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 9 kg cart moving at 112 m/s collides with and couples to a stationary 5 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
72 m/s
Total momentum before collision p = 9 × 112 = 1008 kg·m/s. Combined mass = 9 + 5 = 14 kg, so v = 1008 ÷ 14 = 72 m/s.
12. A 6 kg cart moving at 10 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 m/s
Total momentum before collision p = 6 × 10 = 60 kg·m/s. Combined mass = 6 + 4 = 10 kg, so v = 60 ÷ 10 = 6 m/s.

12 questions · Seed 104735 · Age guidance, not curriculum certification