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 6 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.
6 kg (18 m/s) → [3 kg] → Coupled: (9 kg) v = ? · m₁u₁ = (m₁ + m₂)v
2. 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
3. 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
4. A 4 kg cart moving at 40 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 (40 m/s) → [6 kg] → Coupled: (10 kg) v = ? · m₁u₁ = (m₁ + m₂)v
5. A 5 kg cart moving at 24 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 (24 m/s) → [3 kg] → Coupled: (8 kg) v = ? · m₁u₁ = (m₁ + m₂)v
6. A 7 kg cart moving at 70 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 (70 m/s) → [7 kg] → Coupled: (14 kg) v = ? · m₁u₁ = (m₁ + m₂)v
7. A 2 kg cart moving at 25 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 (25 m/s) → [3 kg] → Coupled: (5 kg) v = ? · m₁u₁ = (m₁ + m₂)v
8. A 10 kg cart moving at 48 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 (48 m/s) → [6 kg] → Coupled: (16 kg) v = ? · m₁u₁ = (m₁ + m₂)v
9. A 7 kg cart moving at 45 m/s collides with and couples to a stationary 8 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
7 kg (45 m/s) → [8 kg] → Coupled: (15 kg) v = ? · m₁u₁ = (m₁ + m₂)v
10. A 6 kg cart moving at 80 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 (80 m/s) → [4 kg] → Coupled: (10 kg) v = ? · m₁u₁ = (m₁ + m₂)v
11. A 5 kg cart moving at 10 m/s collides with and couples to a stationary 5 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
5 kg (10 m/s) → [5 kg] → Coupled: (10 kg) v = ? · m₁u₁ = (m₁ + m₂)v
12. A 9 kg cart moving at 136 m/s collides with and couples to a stationary 8 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
9 kg (136 m/s) → [8 kg] → Coupled: (17 kg) v = ? · m₁u₁ = (m₁ + m₂)v

12 questions · Seed 44 · 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 6 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.
12 m/s
Total momentum before collision p = 6 × 18 = 108 kg·m/s. Combined mass = 6 + 3 = 9 kg, so v = 108 ÷ 9 = 12 m/s.
2. 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.
3. 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.
4. A 4 kg cart moving at 40 m/s collides with and couples to a stationary 6 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
16 m/s
Total momentum before collision p = 4 × 40 = 160 kg·m/s. Combined mass = 4 + 6 = 10 kg, so v = 160 ÷ 10 = 16 m/s.
5. A 5 kg cart moving at 24 m/s collides with and couples to a stationary 3 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
15 m/s
Total momentum before collision p = 5 × 24 = 120 kg·m/s. Combined mass = 5 + 3 = 8 kg, so v = 120 ÷ 8 = 15 m/s.
6. A 7 kg cart moving at 70 m/s collides with and couples to a stationary 7 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
35 m/s
Total momentum before collision p = 7 × 70 = 490 kg·m/s. Combined mass = 7 + 7 = 14 kg, so v = 490 ÷ 14 = 35 m/s.
7. A 2 kg cart moving at 25 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 m/s
Total momentum before collision p = 2 × 25 = 50 kg·m/s. Combined mass = 2 + 3 = 5 kg, so v = 50 ÷ 5 = 10 m/s.
8. A 10 kg cart moving at 48 m/s collides with and couples to a stationary 6 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
30 m/s
Total momentum before collision p = 10 × 48 = 480 kg·m/s. Combined mass = 10 + 6 = 16 kg, so v = 480 ÷ 16 = 30 m/s.
9. A 7 kg cart moving at 45 m/s collides with and couples to a stationary 8 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
21 m/s
Total momentum before collision p = 7 × 45 = 315 kg·m/s. Combined mass = 7 + 8 = 15 kg, so v = 315 ÷ 15 = 21 m/s.
10. A 6 kg cart moving at 80 m/s collides with and couples to a stationary 4 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
48 m/s
Total momentum before collision p = 6 × 80 = 480 kg·m/s. Combined mass = 6 + 4 = 10 kg, so v = 480 ÷ 10 = 48 m/s.
11. A 5 kg cart moving at 10 m/s collides with and couples to a stationary 5 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
5 m/s
Total momentum before collision p = 5 × 10 = 50 kg·m/s. Combined mass = 5 + 5 = 10 kg, so v = 50 ÷ 10 = 5 m/s.
12. A 9 kg cart moving at 136 m/s collides with and couples to a stationary 8 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
72 m/s
Total momentum before collision p = 9 × 136 = 1224 kg·m/s. Combined mass = 9 + 8 = 17 kg, so v = 1224 ÷ 17 = 72 m/s.

12 questions · Seed 44 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 16-18

Conservation of momentum in collisions

Take your time. Show your thinking.

1. A 6 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.
6 kg (18 m/s) → [3 kg] → Coupled: (9 kg) v = ? · m₁u₁ = (m₁ + m₂)v
2. 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
3. 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
4. A 4 kg cart moving at 40 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 (40 m/s) → [6 kg] → Coupled: (10 kg) v = ? · m₁u₁ = (m₁ + m₂)v
5. A 5 kg cart moving at 24 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 (24 m/s) → [3 kg] → Coupled: (8 kg) v = ? · m₁u₁ = (m₁ + m₂)v
6. A 7 kg cart moving at 70 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 (70 m/s) → [7 kg] → Coupled: (14 kg) v = ? · m₁u₁ = (m₁ + m₂)v
7. A 2 kg cart moving at 25 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 (25 m/s) → [3 kg] → Coupled: (5 kg) v = ? · m₁u₁ = (m₁ + m₂)v
8. A 10 kg cart moving at 48 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 (48 m/s) → [6 kg] → Coupled: (16 kg) v = ? · m₁u₁ = (m₁ + m₂)v
9. A 7 kg cart moving at 45 m/s collides with and couples to a stationary 8 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
7 kg (45 m/s) → [8 kg] → Coupled: (15 kg) v = ? · m₁u₁ = (m₁ + m₂)v
10. A 6 kg cart moving at 80 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 (80 m/s) → [4 kg] → Coupled: (10 kg) v = ? · m₁u₁ = (m₁ + m₂)v
11. A 5 kg cart moving at 10 m/s collides with and couples to a stationary 5 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
5 kg (10 m/s) → [5 kg] → Coupled: (10 kg) v = ? · m₁u₁ = (m₁ + m₂)v
12. A 9 kg cart moving at 136 m/s collides with and couples to a stationary 8 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
9 kg (136 m/s) → [8 kg] → Coupled: (17 kg) v = ? · m₁u₁ = (m₁ + m₂)v

12 questions · Seed 44 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 16-18

Conservation of momentum in collisions

Answers and reasoning. Review before teaching.

1. A 6 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.
12 m/s
Total momentum before collision p = 6 × 18 = 108 kg·m/s. Combined mass = 6 + 3 = 9 kg, so v = 108 ÷ 9 = 12 m/s.
2. 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.
3. 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.
4. A 4 kg cart moving at 40 m/s collides with and couples to a stationary 6 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
16 m/s
Total momentum before collision p = 4 × 40 = 160 kg·m/s. Combined mass = 4 + 6 = 10 kg, so v = 160 ÷ 10 = 16 m/s.
5. A 5 kg cart moving at 24 m/s collides with and couples to a stationary 3 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
15 m/s
Total momentum before collision p = 5 × 24 = 120 kg·m/s. Combined mass = 5 + 3 = 8 kg, so v = 120 ÷ 8 = 15 m/s.
6. A 7 kg cart moving at 70 m/s collides with and couples to a stationary 7 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
35 m/s
Total momentum before collision p = 7 × 70 = 490 kg·m/s. Combined mass = 7 + 7 = 14 kg, so v = 490 ÷ 14 = 35 m/s.
7. A 2 kg cart moving at 25 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 m/s
Total momentum before collision p = 2 × 25 = 50 kg·m/s. Combined mass = 2 + 3 = 5 kg, so v = 50 ÷ 5 = 10 m/s.
8. A 10 kg cart moving at 48 m/s collides with and couples to a stationary 6 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
30 m/s
Total momentum before collision p = 10 × 48 = 480 kg·m/s. Combined mass = 10 + 6 = 16 kg, so v = 480 ÷ 16 = 30 m/s.
9. A 7 kg cart moving at 45 m/s collides with and couples to a stationary 8 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
21 m/s
Total momentum before collision p = 7 × 45 = 315 kg·m/s. Combined mass = 7 + 8 = 15 kg, so v = 315 ÷ 15 = 21 m/s.
10. A 6 kg cart moving at 80 m/s collides with and couples to a stationary 4 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
48 m/s
Total momentum before collision p = 6 × 80 = 480 kg·m/s. Combined mass = 6 + 4 = 10 kg, so v = 480 ÷ 10 = 48 m/s.
11. A 5 kg cart moving at 10 m/s collides with and couples to a stationary 5 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
5 m/s
Total momentum before collision p = 5 × 10 = 50 kg·m/s. Combined mass = 5 + 5 = 10 kg, so v = 50 ÷ 10 = 5 m/s.
12. A 9 kg cart moving at 136 m/s collides with and couples to a stationary 8 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
72 m/s
Total momentum before collision p = 9 × 136 = 1224 kg·m/s. Combined mass = 9 + 8 = 17 kg, so v = 1224 ÷ 17 = 72 m/s.

12 questions · Seed 44 · Age guidance, not curriculum certification