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 8 kg cart moving at 84 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 kg (84 m/s) → [6 kg] → Coupled: (14 kg) v = ? · m₁u₁ = (m₁ + m₂)v
2. A 8 kg cart moving at 22 m/s collides with and couples to a stationary 3 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
8 kg (22 m/s) → [3 kg] → Coupled: (11 kg) v = ? · m₁u₁ = (m₁ + m₂)v
3. A 5 kg cart moving at 42 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 (42 m/s) → [2 kg] → Coupled: (7 kg) v = ? · m₁u₁ = (m₁ + m₂)v
4. A 6 kg cart moving at 72 m/s collides with and couples to a stationary 6 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
6 kg (72 m/s) → [6 kg] → Coupled: (12 kg) v = ? · m₁u₁ = (m₁ + m₂)v
5. A 2 kg cart moving at 24 m/s collides with and couples to a stationary 10 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
2 kg (24 m/s) → [10 kg] → Coupled: (12 kg) v = ? · m₁u₁ = (m₁ + m₂)v
6. A 3 kg cart moving at 13 m/s collides with and couples to a stationary 10 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
3 kg (13 m/s) → [10 kg] → Coupled: (13 kg) v = ? · m₁u₁ = (m₁ + m₂)v
7. A 7 kg cart moving at 32 m/s collides with and couples to a stationary 9 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
7 kg (32 m/s) → [9 kg] → Coupled: (16 kg) v = ? · m₁u₁ = (m₁ + m₂)v
8. A 6 kg cart moving at 120 m/s collides with and couples to a stationary 9 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
6 kg (120 m/s) → [9 kg] → Coupled: (15 kg) v = ? · m₁u₁ = (m₁ + m₂)v
9. A 7 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.
7 kg (60 m/s) → [8 kg] → Coupled: (15 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 5 kg cart moving at 55 m/s collides with and couples to a stationary 6 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
5 kg (55 m/s) → [6 kg] → Coupled: (11 kg) v = ? · m₁u₁ = (m₁ + m₂)v
12. A 3 kg cart moving at 72 m/s collides with and couples to a stationary 6 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
3 kg (72 m/s) → [6 kg] → Coupled: (9 kg) v = ? · m₁u₁ = (m₁ + m₂)v

12 questions · Seed 104729 · 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 8 kg cart moving at 84 m/s collides with and couples to a stationary 6 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
48 m/s
Total momentum before collision p = 8 × 84 = 672 kg·m/s. Combined mass = 8 + 6 = 14 kg, so v = 672 ÷ 14 = 48 m/s.
2. A 8 kg cart moving at 22 m/s collides with and couples to a stationary 3 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
16 m/s
Total momentum before collision p = 8 × 22 = 176 kg·m/s. Combined mass = 8 + 3 = 11 kg, so v = 176 ÷ 11 = 16 m/s.
3. A 5 kg cart moving at 42 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 = 5 × 42 = 210 kg·m/s. Combined mass = 5 + 2 = 7 kg, so v = 210 ÷ 7 = 30 m/s.
4. A 6 kg cart moving at 72 m/s collides with and couples to a stationary 6 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
36 m/s
Total momentum before collision p = 6 × 72 = 432 kg·m/s. Combined mass = 6 + 6 = 12 kg, so v = 432 ÷ 12 = 36 m/s.
5. A 2 kg cart moving at 24 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 m/s
Total momentum before collision p = 2 × 24 = 48 kg·m/s. Combined mass = 2 + 10 = 12 kg, so v = 48 ÷ 12 = 4 m/s.
6. A 3 kg cart moving at 13 m/s collides with and couples to a stationary 10 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
3 m/s
Total momentum before collision p = 3 × 13 = 39 kg·m/s. Combined mass = 3 + 10 = 13 kg, so v = 39 ÷ 13 = 3 m/s.
7. A 7 kg cart moving at 32 m/s collides with and couples to a stationary 9 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
14 m/s
Total momentum before collision p = 7 × 32 = 224 kg·m/s. Combined mass = 7 + 9 = 16 kg, so v = 224 ÷ 16 = 14 m/s.
8. A 6 kg cart moving at 120 m/s collides with and couples to a stationary 9 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
48 m/s
Total momentum before collision p = 6 × 120 = 720 kg·m/s. Combined mass = 6 + 9 = 15 kg, so v = 720 ÷ 15 = 48 m/s.
9. A 7 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.
28 m/s
Total momentum before collision p = 7 × 60 = 420 kg·m/s. Combined mass = 7 + 8 = 15 kg, so v = 420 ÷ 15 = 28 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 5 kg cart moving at 55 m/s collides with and couples to a stationary 6 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
25 m/s
Total momentum before collision p = 5 × 55 = 275 kg·m/s. Combined mass = 5 + 6 = 11 kg, so v = 275 ÷ 11 = 25 m/s.
12. A 3 kg cart moving at 72 m/s collides with and couples to a stationary 6 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
24 m/s
Total momentum before collision p = 3 × 72 = 216 kg·m/s. Combined mass = 3 + 6 = 9 kg, so v = 216 ÷ 9 = 24 m/s.

12 questions · Seed 104729 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 13-15

Conservation of momentum in collisions

Take your time. Show your thinking.

1. A 8 kg cart moving at 84 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 kg (84 m/s) → [6 kg] → Coupled: (14 kg) v = ? · m₁u₁ = (m₁ + m₂)v
2. A 8 kg cart moving at 22 m/s collides with and couples to a stationary 3 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
8 kg (22 m/s) → [3 kg] → Coupled: (11 kg) v = ? · m₁u₁ = (m₁ + m₂)v
3. A 5 kg cart moving at 42 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 (42 m/s) → [2 kg] → Coupled: (7 kg) v = ? · m₁u₁ = (m₁ + m₂)v
4. A 6 kg cart moving at 72 m/s collides with and couples to a stationary 6 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
6 kg (72 m/s) → [6 kg] → Coupled: (12 kg) v = ? · m₁u₁ = (m₁ + m₂)v
5. A 2 kg cart moving at 24 m/s collides with and couples to a stationary 10 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
2 kg (24 m/s) → [10 kg] → Coupled: (12 kg) v = ? · m₁u₁ = (m₁ + m₂)v
6. A 3 kg cart moving at 13 m/s collides with and couples to a stationary 10 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
3 kg (13 m/s) → [10 kg] → Coupled: (13 kg) v = ? · m₁u₁ = (m₁ + m₂)v
7. A 7 kg cart moving at 32 m/s collides with and couples to a stationary 9 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
7 kg (32 m/s) → [9 kg] → Coupled: (16 kg) v = ? · m₁u₁ = (m₁ + m₂)v
8. A 6 kg cart moving at 120 m/s collides with and couples to a stationary 9 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
6 kg (120 m/s) → [9 kg] → Coupled: (15 kg) v = ? · m₁u₁ = (m₁ + m₂)v
9. A 7 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.
7 kg (60 m/s) → [8 kg] → Coupled: (15 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 5 kg cart moving at 55 m/s collides with and couples to a stationary 6 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
5 kg (55 m/s) → [6 kg] → Coupled: (11 kg) v = ? · m₁u₁ = (m₁ + m₂)v
12. A 3 kg cart moving at 72 m/s collides with and couples to a stationary 6 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
3 kg (72 m/s) → [6 kg] → Coupled: (9 kg) v = ? · m₁u₁ = (m₁ + m₂)v

12 questions · Seed 104729 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 13-15

Conservation of momentum in collisions

Answers and reasoning. Review before teaching.

1. A 8 kg cart moving at 84 m/s collides with and couples to a stationary 6 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
48 m/s
Total momentum before collision p = 8 × 84 = 672 kg·m/s. Combined mass = 8 + 6 = 14 kg, so v = 672 ÷ 14 = 48 m/s.
2. A 8 kg cart moving at 22 m/s collides with and couples to a stationary 3 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
16 m/s
Total momentum before collision p = 8 × 22 = 176 kg·m/s. Combined mass = 8 + 3 = 11 kg, so v = 176 ÷ 11 = 16 m/s.
3. A 5 kg cart moving at 42 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 = 5 × 42 = 210 kg·m/s. Combined mass = 5 + 2 = 7 kg, so v = 210 ÷ 7 = 30 m/s.
4. A 6 kg cart moving at 72 m/s collides with and couples to a stationary 6 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
36 m/s
Total momentum before collision p = 6 × 72 = 432 kg·m/s. Combined mass = 6 + 6 = 12 kg, so v = 432 ÷ 12 = 36 m/s.
5. A 2 kg cart moving at 24 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 m/s
Total momentum before collision p = 2 × 24 = 48 kg·m/s. Combined mass = 2 + 10 = 12 kg, so v = 48 ÷ 12 = 4 m/s.
6. A 3 kg cart moving at 13 m/s collides with and couples to a stationary 10 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
3 m/s
Total momentum before collision p = 3 × 13 = 39 kg·m/s. Combined mass = 3 + 10 = 13 kg, so v = 39 ÷ 13 = 3 m/s.
7. A 7 kg cart moving at 32 m/s collides with and couples to a stationary 9 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
14 m/s
Total momentum before collision p = 7 × 32 = 224 kg·m/s. Combined mass = 7 + 9 = 16 kg, so v = 224 ÷ 16 = 14 m/s.
8. A 6 kg cart moving at 120 m/s collides with and couples to a stationary 9 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
48 m/s
Total momentum before collision p = 6 × 120 = 720 kg·m/s. Combined mass = 6 + 9 = 15 kg, so v = 720 ÷ 15 = 48 m/s.
9. A 7 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.
28 m/s
Total momentum before collision p = 7 × 60 = 420 kg·m/s. Combined mass = 7 + 8 = 15 kg, so v = 420 ÷ 15 = 28 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 5 kg cart moving at 55 m/s collides with and couples to a stationary 6 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
25 m/s
Total momentum before collision p = 5 × 55 = 275 kg·m/s. Combined mass = 5 + 6 = 11 kg, so v = 275 ÷ 11 = 25 m/s.
12. A 3 kg cart moving at 72 m/s collides with and couples to a stationary 6 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
24 m/s
Total momentum before collision p = 3 × 72 = 216 kg·m/s. Combined mass = 3 + 6 = 9 kg, so v = 216 ÷ 9 = 24 m/s.

12 questions · Seed 104729 · Age guidance, not curriculum certification