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 15 m/s collides with and couples to a stationary 5 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
10 kg (15 m/s) → [5 kg] → Coupled: (15 kg) v = ? · m₁u₁ = (m₁ + m₂)v
2. A 7 kg cart moving at 80 m/s collides with and couples to a stationary 3 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
7 kg (80 m/s) → [3 kg] → Coupled: (10 kg) v = ? · m₁u₁ = (m₁ + m₂)v
3. A 3 kg cart moving at 60 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 (60 m/s) → [9 kg] → Coupled: (12 kg) v = ? · m₁u₁ = (m₁ + m₂)v
4. A 6 kg cart moving at 8 m/s collides with and couples to a stationary 2 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
6 kg (8 m/s) → [2 kg] → Coupled: (8 kg) v = ? · m₁u₁ = (m₁ + m₂)v
5. A 7 kg cart moving at 85 m/s collides with and couples to a stationary 10 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
7 kg (85 m/s) → [10 kg] → Coupled: (17 kg) v = ? · m₁u₁ = (m₁ + m₂)v
6. A 9 kg cart moving at 16 m/s collides with and couples to a stationary 7 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
9 kg (16 m/s) → [7 kg] → Coupled: (16 kg) v = ? · m₁u₁ = (m₁ + m₂)v
7. A 5 kg cart moving at 80 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 (80 m/s) → [5 kg] → Coupled: (10 kg) v = ? · m₁u₁ = (m₁ + m₂)v
8. A 6 kg cart moving at 16 m/s collides with and couples to a stationary 2 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
6 kg (16 m/s) → [2 kg] → Coupled: (8 kg) v = ? · m₁u₁ = (m₁ + m₂)v
9. A 7 kg cart moving at 51 m/s collides with and couples to a stationary 10 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
7 kg (51 m/s) → [10 kg] → Coupled: (17 kg) v = ? · m₁u₁ = (m₁ + m₂)v
10. A 2 kg cart moving at 60 m/s collides with and couples to a stationary 8 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
2 kg (60 m/s) → [8 kg] → Coupled: (10 kg) v = ? · m₁u₁ = (m₁ + m₂)v
11. A 8 kg cart moving at 45 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 kg (45 m/s) → [7 kg] → Coupled: (15 kg) v = ? · m₁u₁ = (m₁ + m₂)v
12. 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

12 questions · Seed 104730 · 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 15 m/s collides with and couples to a stationary 5 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
10 m/s
Total momentum before collision p = 10 × 15 = 150 kg·m/s. Combined mass = 10 + 5 = 15 kg, so v = 150 ÷ 15 = 10 m/s.
2. A 7 kg cart moving at 80 m/s collides with and couples to a stationary 3 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
56 m/s
Total momentum before collision p = 7 × 80 = 560 kg·m/s. Combined mass = 7 + 3 = 10 kg, so v = 560 ÷ 10 = 56 m/s.
3. A 3 kg cart moving at 60 m/s collides with and couples to a stationary 9 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
15 m/s
Total momentum before collision p = 3 × 60 = 180 kg·m/s. Combined mass = 3 + 9 = 12 kg, so v = 180 ÷ 12 = 15 m/s.
4. A 6 kg cart moving at 8 m/s collides with and couples to a stationary 2 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
6 m/s
Total momentum before collision p = 6 × 8 = 48 kg·m/s. Combined mass = 6 + 2 = 8 kg, so v = 48 ÷ 8 = 6 m/s.
5. A 7 kg cart moving at 85 m/s collides with and couples to a stationary 10 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
35 m/s
Total momentum before collision p = 7 × 85 = 595 kg·m/s. Combined mass = 7 + 10 = 17 kg, so v = 595 ÷ 17 = 35 m/s.
6. A 9 kg cart moving at 16 m/s collides with and couples to a stationary 7 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
9 m/s
Total momentum before collision p = 9 × 16 = 144 kg·m/s. Combined mass = 9 + 7 = 16 kg, so v = 144 ÷ 16 = 9 m/s.
7. A 5 kg cart moving at 80 m/s collides with and couples to a stationary 5 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
40 m/s
Total momentum before collision p = 5 × 80 = 400 kg·m/s. Combined mass = 5 + 5 = 10 kg, so v = 400 ÷ 10 = 40 m/s.
8. A 6 kg cart moving at 16 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 = 6 × 16 = 96 kg·m/s. Combined mass = 6 + 2 = 8 kg, so v = 96 ÷ 8 = 12 m/s.
9. A 7 kg cart moving at 51 m/s collides with and couples to a stationary 10 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
21 m/s
Total momentum before collision p = 7 × 51 = 357 kg·m/s. Combined mass = 7 + 10 = 17 kg, so v = 357 ÷ 17 = 21 m/s.
10. A 2 kg cart moving at 60 m/s collides with and couples to a stationary 8 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
12 m/s
Total momentum before collision p = 2 × 60 = 120 kg·m/s. Combined mass = 2 + 8 = 10 kg, so v = 120 ÷ 10 = 12 m/s.
11. A 8 kg cart moving at 45 m/s collides with and couples to a stationary 7 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
24 m/s
Total momentum before collision p = 8 × 45 = 360 kg·m/s. Combined mass = 8 + 7 = 15 kg, so v = 360 ÷ 15 = 24 m/s.
12. 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.

12 questions · Seed 104730 · 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 15 m/s collides with and couples to a stationary 5 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
10 kg (15 m/s) → [5 kg] → Coupled: (15 kg) v = ? · m₁u₁ = (m₁ + m₂)v
2. A 7 kg cart moving at 80 m/s collides with and couples to a stationary 3 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
7 kg (80 m/s) → [3 kg] → Coupled: (10 kg) v = ? · m₁u₁ = (m₁ + m₂)v
3. A 3 kg cart moving at 60 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 (60 m/s) → [9 kg] → Coupled: (12 kg) v = ? · m₁u₁ = (m₁ + m₂)v
4. A 6 kg cart moving at 8 m/s collides with and couples to a stationary 2 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
6 kg (8 m/s) → [2 kg] → Coupled: (8 kg) v = ? · m₁u₁ = (m₁ + m₂)v
5. A 7 kg cart moving at 85 m/s collides with and couples to a stationary 10 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
7 kg (85 m/s) → [10 kg] → Coupled: (17 kg) v = ? · m₁u₁ = (m₁ + m₂)v
6. A 9 kg cart moving at 16 m/s collides with and couples to a stationary 7 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
9 kg (16 m/s) → [7 kg] → Coupled: (16 kg) v = ? · m₁u₁ = (m₁ + m₂)v
7. A 5 kg cart moving at 80 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 (80 m/s) → [5 kg] → Coupled: (10 kg) v = ? · m₁u₁ = (m₁ + m₂)v
8. A 6 kg cart moving at 16 m/s collides with and couples to a stationary 2 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
6 kg (16 m/s) → [2 kg] → Coupled: (8 kg) v = ? · m₁u₁ = (m₁ + m₂)v
9. A 7 kg cart moving at 51 m/s collides with and couples to a stationary 10 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
7 kg (51 m/s) → [10 kg] → Coupled: (17 kg) v = ? · m₁u₁ = (m₁ + m₂)v
10. A 2 kg cart moving at 60 m/s collides with and couples to a stationary 8 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
2 kg (60 m/s) → [8 kg] → Coupled: (10 kg) v = ? · m₁u₁ = (m₁ + m₂)v
11. A 8 kg cart moving at 45 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 kg (45 m/s) → [7 kg] → Coupled: (15 kg) v = ? · m₁u₁ = (m₁ + m₂)v
12. 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

12 questions · Seed 104730 · 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 15 m/s collides with and couples to a stationary 5 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
10 m/s
Total momentum before collision p = 10 × 15 = 150 kg·m/s. Combined mass = 10 + 5 = 15 kg, so v = 150 ÷ 15 = 10 m/s.
2. A 7 kg cart moving at 80 m/s collides with and couples to a stationary 3 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
56 m/s
Total momentum before collision p = 7 × 80 = 560 kg·m/s. Combined mass = 7 + 3 = 10 kg, so v = 560 ÷ 10 = 56 m/s.
3. A 3 kg cart moving at 60 m/s collides with and couples to a stationary 9 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
15 m/s
Total momentum before collision p = 3 × 60 = 180 kg·m/s. Combined mass = 3 + 9 = 12 kg, so v = 180 ÷ 12 = 15 m/s.
4. A 6 kg cart moving at 8 m/s collides with and couples to a stationary 2 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
6 m/s
Total momentum before collision p = 6 × 8 = 48 kg·m/s. Combined mass = 6 + 2 = 8 kg, so v = 48 ÷ 8 = 6 m/s.
5. A 7 kg cart moving at 85 m/s collides with and couples to a stationary 10 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
35 m/s
Total momentum before collision p = 7 × 85 = 595 kg·m/s. Combined mass = 7 + 10 = 17 kg, so v = 595 ÷ 17 = 35 m/s.
6. A 9 kg cart moving at 16 m/s collides with and couples to a stationary 7 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
9 m/s
Total momentum before collision p = 9 × 16 = 144 kg·m/s. Combined mass = 9 + 7 = 16 kg, so v = 144 ÷ 16 = 9 m/s.
7. A 5 kg cart moving at 80 m/s collides with and couples to a stationary 5 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
40 m/s
Total momentum before collision p = 5 × 80 = 400 kg·m/s. Combined mass = 5 + 5 = 10 kg, so v = 400 ÷ 10 = 40 m/s.
8. A 6 kg cart moving at 16 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 = 6 × 16 = 96 kg·m/s. Combined mass = 6 + 2 = 8 kg, so v = 96 ÷ 8 = 12 m/s.
9. A 7 kg cart moving at 51 m/s collides with and couples to a stationary 10 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
21 m/s
Total momentum before collision p = 7 × 51 = 357 kg·m/s. Combined mass = 7 + 10 = 17 kg, so v = 357 ÷ 17 = 21 m/s.
10. A 2 kg cart moving at 60 m/s collides with and couples to a stationary 8 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
12 m/s
Total momentum before collision p = 2 × 60 = 120 kg·m/s. Combined mass = 2 + 8 = 10 kg, so v = 120 ÷ 10 = 12 m/s.
11. A 8 kg cart moving at 45 m/s collides with and couples to a stationary 7 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
24 m/s
Total momentum before collision p = 8 × 45 = 360 kg·m/s. Combined mass = 8 + 7 = 15 kg, so v = 360 ÷ 15 = 24 m/s.
12. 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.

12 questions · Seed 104730 · Age guidance, not curriculum certification