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 9 kg cart moving at 78 m/s collides with and couples to a stationary 4 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
9 kg (78 m/s) → [4 kg] → Coupled: (13 kg) v = ? · m₁u₁ = (m₁ + m₂)v
2. A 8 kg cart moving at 72 m/s collides with and couples to a stationary 10 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
8 kg (72 m/s) → [10 kg] → Coupled: (18 kg) v = ? · m₁u₁ = (m₁ + m₂)v
3. A 8 kg cart moving at 84 m/s collides with and couples to a stationary 4 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
8 kg (84 m/s) → [4 kg] → Coupled: (12 kg) v = ? · m₁u₁ = (m₁ + m₂)v
4. A 7 kg cart moving at 64 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 (64 m/s) → [9 kg] → Coupled: (16 kg) v = ? · m₁u₁ = (m₁ + m₂)v
5. A 2 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.
2 kg (8 m/s) → [2 kg] → Coupled: (4 kg) v = ? · m₁u₁ = (m₁ + m₂)v
6. A 2 kg cart moving at 80 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 (80 m/s) → [8 kg] → Coupled: (10 kg) v = ? · m₁u₁ = (m₁ + m₂)v
7. A 7 kg cart moving at 36 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 (36 m/s) → [5 kg] → Coupled: (12 kg) v = ? · m₁u₁ = (m₁ + m₂)v
8. A 2 kg cart moving at 24 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 (24 m/s) → [2 kg] → Coupled: (4 kg) v = ? · m₁u₁ = (m₁ + m₂)v
9. 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
10. A 10 kg cart moving at 76 m/s collides with and couples to a stationary 9 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
10 kg (76 m/s) → [9 kg] → Coupled: (19 kg) v = ? · m₁u₁ = (m₁ + m₂)v
11. A 5 kg cart moving at 18 m/s collides with and couples to a stationary 4 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
5 kg (18 m/s) → [4 kg] → Coupled: (9 kg) v = ? · m₁u₁ = (m₁ + m₂)v
12. A 9 kg cart moving at 42 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 (42 m/s) → [5 kg] → Coupled: (14 kg) v = ? · m₁u₁ = (m₁ + m₂)v

12 questions · Seed 104740 · 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 9 kg cart moving at 78 m/s collides with and couples to a stationary 4 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
54 m/s
Total momentum before collision p = 9 × 78 = 702 kg·m/s. Combined mass = 9 + 4 = 13 kg, so v = 702 ÷ 13 = 54 m/s.
2. A 8 kg cart moving at 72 m/s collides with and couples to a stationary 10 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
32 m/s
Total momentum before collision p = 8 × 72 = 576 kg·m/s. Combined mass = 8 + 10 = 18 kg, so v = 576 ÷ 18 = 32 m/s.
3. A 8 kg cart moving at 84 m/s collides with and couples to a stationary 4 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
56 m/s
Total momentum before collision p = 8 × 84 = 672 kg·m/s. Combined mass = 8 + 4 = 12 kg, so v = 672 ÷ 12 = 56 m/s.
4. A 7 kg cart moving at 64 m/s collides with and couples to a stationary 9 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
28 m/s
Total momentum before collision p = 7 × 64 = 448 kg·m/s. Combined mass = 7 + 9 = 16 kg, so v = 448 ÷ 16 = 28 m/s.
5. A 2 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.
4 m/s
Total momentum before collision p = 2 × 8 = 16 kg·m/s. Combined mass = 2 + 2 = 4 kg, so v = 16 ÷ 4 = 4 m/s.
6. A 2 kg cart moving at 80 m/s collides with and couples to a stationary 8 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
16 m/s
Total momentum before collision p = 2 × 80 = 160 kg·m/s. Combined mass = 2 + 8 = 10 kg, so v = 160 ÷ 10 = 16 m/s.
7. A 7 kg cart moving at 36 m/s collides with and couples to a stationary 5 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
21 m/s
Total momentum before collision p = 7 × 36 = 252 kg·m/s. Combined mass = 7 + 5 = 12 kg, so v = 252 ÷ 12 = 21 m/s.
8. A 2 kg cart moving at 24 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 = 2 × 24 = 48 kg·m/s. Combined mass = 2 + 2 = 4 kg, so v = 48 ÷ 4 = 12 m/s.
9. 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.
10. A 10 kg cart moving at 76 m/s collides with and couples to a stationary 9 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
40 m/s
Total momentum before collision p = 10 × 76 = 760 kg·m/s. Combined mass = 10 + 9 = 19 kg, so v = 760 ÷ 19 = 40 m/s.
11. A 5 kg cart moving at 18 m/s collides with and couples to a stationary 4 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
10 m/s
Total momentum before collision p = 5 × 18 = 90 kg·m/s. Combined mass = 5 + 4 = 9 kg, so v = 90 ÷ 9 = 10 m/s.
12. A 9 kg cart moving at 42 m/s collides with and couples to a stationary 5 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
27 m/s
Total momentum before collision p = 9 × 42 = 378 kg·m/s. Combined mass = 9 + 5 = 14 kg, so v = 378 ÷ 14 = 27 m/s.

12 questions · Seed 104740 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 13-15

Conservation of momentum in collisions

Take your time. Show your thinking.

1. A 9 kg cart moving at 78 m/s collides with and couples to a stationary 4 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
9 kg (78 m/s) → [4 kg] → Coupled: (13 kg) v = ? · m₁u₁ = (m₁ + m₂)v
2. A 8 kg cart moving at 72 m/s collides with and couples to a stationary 10 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
8 kg (72 m/s) → [10 kg] → Coupled: (18 kg) v = ? · m₁u₁ = (m₁ + m₂)v
3. A 8 kg cart moving at 84 m/s collides with and couples to a stationary 4 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
8 kg (84 m/s) → [4 kg] → Coupled: (12 kg) v = ? · m₁u₁ = (m₁ + m₂)v
4. A 7 kg cart moving at 64 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 (64 m/s) → [9 kg] → Coupled: (16 kg) v = ? · m₁u₁ = (m₁ + m₂)v
5. A 2 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.
2 kg (8 m/s) → [2 kg] → Coupled: (4 kg) v = ? · m₁u₁ = (m₁ + m₂)v
6. A 2 kg cart moving at 80 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 (80 m/s) → [8 kg] → Coupled: (10 kg) v = ? · m₁u₁ = (m₁ + m₂)v
7. A 7 kg cart moving at 36 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 (36 m/s) → [5 kg] → Coupled: (12 kg) v = ? · m₁u₁ = (m₁ + m₂)v
8. A 2 kg cart moving at 24 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 (24 m/s) → [2 kg] → Coupled: (4 kg) v = ? · m₁u₁ = (m₁ + m₂)v
9. 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
10. A 10 kg cart moving at 76 m/s collides with and couples to a stationary 9 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
10 kg (76 m/s) → [9 kg] → Coupled: (19 kg) v = ? · m₁u₁ = (m₁ + m₂)v
11. A 5 kg cart moving at 18 m/s collides with and couples to a stationary 4 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
5 kg (18 m/s) → [4 kg] → Coupled: (9 kg) v = ? · m₁u₁ = (m₁ + m₂)v
12. A 9 kg cart moving at 42 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 (42 m/s) → [5 kg] → Coupled: (14 kg) v = ? · m₁u₁ = (m₁ + m₂)v

12 questions · Seed 104740 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 13-15

Conservation of momentum in collisions

Answers and reasoning. Review before teaching.

1. A 9 kg cart moving at 78 m/s collides with and couples to a stationary 4 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
54 m/s
Total momentum before collision p = 9 × 78 = 702 kg·m/s. Combined mass = 9 + 4 = 13 kg, so v = 702 ÷ 13 = 54 m/s.
2. A 8 kg cart moving at 72 m/s collides with and couples to a stationary 10 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
32 m/s
Total momentum before collision p = 8 × 72 = 576 kg·m/s. Combined mass = 8 + 10 = 18 kg, so v = 576 ÷ 18 = 32 m/s.
3. A 8 kg cart moving at 84 m/s collides with and couples to a stationary 4 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
56 m/s
Total momentum before collision p = 8 × 84 = 672 kg·m/s. Combined mass = 8 + 4 = 12 kg, so v = 672 ÷ 12 = 56 m/s.
4. A 7 kg cart moving at 64 m/s collides with and couples to a stationary 9 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
28 m/s
Total momentum before collision p = 7 × 64 = 448 kg·m/s. Combined mass = 7 + 9 = 16 kg, so v = 448 ÷ 16 = 28 m/s.
5. A 2 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.
4 m/s
Total momentum before collision p = 2 × 8 = 16 kg·m/s. Combined mass = 2 + 2 = 4 kg, so v = 16 ÷ 4 = 4 m/s.
6. A 2 kg cart moving at 80 m/s collides with and couples to a stationary 8 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
16 m/s
Total momentum before collision p = 2 × 80 = 160 kg·m/s. Combined mass = 2 + 8 = 10 kg, so v = 160 ÷ 10 = 16 m/s.
7. A 7 kg cart moving at 36 m/s collides with and couples to a stationary 5 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
21 m/s
Total momentum before collision p = 7 × 36 = 252 kg·m/s. Combined mass = 7 + 5 = 12 kg, so v = 252 ÷ 12 = 21 m/s.
8. A 2 kg cart moving at 24 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 = 2 × 24 = 48 kg·m/s. Combined mass = 2 + 2 = 4 kg, so v = 48 ÷ 4 = 12 m/s.
9. 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.
10. A 10 kg cart moving at 76 m/s collides with and couples to a stationary 9 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
40 m/s
Total momentum before collision p = 10 × 76 = 760 kg·m/s. Combined mass = 10 + 9 = 19 kg, so v = 760 ÷ 19 = 40 m/s.
11. A 5 kg cart moving at 18 m/s collides with and couples to a stationary 4 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
10 m/s
Total momentum before collision p = 5 × 18 = 90 kg·m/s. Combined mass = 5 + 4 = 9 kg, so v = 90 ÷ 9 = 10 m/s.
12. A 9 kg cart moving at 42 m/s collides with and couples to a stationary 5 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
27 m/s
Total momentum before collision p = 9 × 42 = 378 kg·m/s. Combined mass = 9 + 5 = 14 kg, so v = 378 ÷ 14 = 27 m/s.

12 questions · Seed 104740 · Age guidance, not curriculum certification