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 4 kg cart moving at 14 m/s collides with and couples to a stationary 3 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
4 kg (14 m/s) → [3 kg] → Coupled: (7 kg) v = ? · m₁u₁ = (m₁ + m₂)v
2. A 4 kg cart moving at 56 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 kg (56 m/s) → [10 kg] → Coupled: (14 kg) v = ? · m₁u₁ = (m₁ + m₂)v
3. A 7 kg cart moving at 84 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 (84 m/s) → [7 kg] → Coupled: (14 kg) v = ? · m₁u₁ = (m₁ + m₂)v
4. A 7 kg cart moving at 39 m/s collides with and couples to a stationary 6 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
7 kg (39 m/s) → [6 kg] → Coupled: (13 kg) v = ? · m₁u₁ = (m₁ + m₂)v
5. A 4 kg cart moving at 72 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 (72 m/s) → [8 kg] → Coupled: (12 kg) v = ? · m₁u₁ = (m₁ + m₂)v
6. A 6 kg cart moving at 48 m/s collides with and couples to a stationary 10 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
6 kg (48 m/s) → [10 kg] → Coupled: (16 kg) v = ? · m₁u₁ = (m₁ + m₂)v
7. A 8 kg cart moving at 102 m/s collides with and couples to a stationary 9 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
8 kg (102 m/s) → [9 kg] → Coupled: (17 kg) v = ? · m₁u₁ = (m₁ + m₂)v
8. A 10 kg cart moving at 70 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 kg (70 m/s) → [4 kg] → Coupled: (14 kg) v = ? · m₁u₁ = (m₁ + m₂)v
9. A 7 kg cart moving at 10 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 (10 m/s) → [3 kg] → Coupled: (10 kg) v = ? · m₁u₁ = (m₁ + m₂)v
10. A 10 kg cart moving at 72 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 kg (72 m/s) → [2 kg] → Coupled: (12 kg) v = ? · m₁u₁ = (m₁ + m₂)v
11. A 7 kg cart moving at 30 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 (30 m/s) → [8 kg] → Coupled: (15 kg) v = ? · m₁u₁ = (m₁ + m₂)v
12. A 4 kg cart moving at 45 m/s collides with and couples to a stationary 5 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
4 kg (45 m/s) → [5 kg] → Coupled: (9 kg) v = ? · m₁u₁ = (m₁ + m₂)v

12 questions · Seed 104736 · 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 4 kg cart moving at 14 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 m/s
Total momentum before collision p = 4 × 14 = 56 kg·m/s. Combined mass = 4 + 3 = 7 kg, so v = 56 ÷ 7 = 8 m/s.
2. A 4 kg cart moving at 56 m/s collides with and couples to a stationary 10 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
16 m/s
Total momentum before collision p = 4 × 56 = 224 kg·m/s. Combined mass = 4 + 10 = 14 kg, so v = 224 ÷ 14 = 16 m/s.
3. A 7 kg cart moving at 84 m/s collides with and couples to a stationary 7 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
42 m/s
Total momentum before collision p = 7 × 84 = 588 kg·m/s. Combined mass = 7 + 7 = 14 kg, so v = 588 ÷ 14 = 42 m/s.
4. A 7 kg cart moving at 39 m/s collides with and couples to a stationary 6 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
21 m/s
Total momentum before collision p = 7 × 39 = 273 kg·m/s. Combined mass = 7 + 6 = 13 kg, so v = 273 ÷ 13 = 21 m/s.
5. A 4 kg cart moving at 72 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 = 4 × 72 = 288 kg·m/s. Combined mass = 4 + 8 = 12 kg, so v = 288 ÷ 12 = 24 m/s.
6. A 6 kg cart moving at 48 m/s collides with and couples to a stationary 10 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
18 m/s
Total momentum before collision p = 6 × 48 = 288 kg·m/s. Combined mass = 6 + 10 = 16 kg, so v = 288 ÷ 16 = 18 m/s.
7. A 8 kg cart moving at 102 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 = 8 × 102 = 816 kg·m/s. Combined mass = 8 + 9 = 17 kg, so v = 816 ÷ 17 = 48 m/s.
8. A 10 kg cart moving at 70 m/s collides with and couples to a stationary 4 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
50 m/s
Total momentum before collision p = 10 × 70 = 700 kg·m/s. Combined mass = 10 + 4 = 14 kg, so v = 700 ÷ 14 = 50 m/s.
9. A 7 kg cart moving at 10 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 m/s
Total momentum before collision p = 7 × 10 = 70 kg·m/s. Combined mass = 7 + 3 = 10 kg, so v = 70 ÷ 10 = 7 m/s.
10. A 10 kg cart moving at 72 m/s collides with and couples to a stationary 2 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
60 m/s
Total momentum before collision p = 10 × 72 = 720 kg·m/s. Combined mass = 10 + 2 = 12 kg, so v = 720 ÷ 12 = 60 m/s.
11. A 7 kg cart moving at 30 m/s collides with and couples to a stationary 8 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
14 m/s
Total momentum before collision p = 7 × 30 = 210 kg·m/s. Combined mass = 7 + 8 = 15 kg, so v = 210 ÷ 15 = 14 m/s.
12. A 4 kg cart moving at 45 m/s collides with and couples to a stationary 5 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
20 m/s
Total momentum before collision p = 4 × 45 = 180 kg·m/s. Combined mass = 4 + 5 = 9 kg, so v = 180 ÷ 9 = 20 m/s.

12 questions · Seed 104736 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 13-15

Conservation of momentum in collisions

Take your time. Show your thinking.

1. A 4 kg cart moving at 14 m/s collides with and couples to a stationary 3 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
4 kg (14 m/s) → [3 kg] → Coupled: (7 kg) v = ? · m₁u₁ = (m₁ + m₂)v
2. A 4 kg cart moving at 56 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 kg (56 m/s) → [10 kg] → Coupled: (14 kg) v = ? · m₁u₁ = (m₁ + m₂)v
3. A 7 kg cart moving at 84 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 (84 m/s) → [7 kg] → Coupled: (14 kg) v = ? · m₁u₁ = (m₁ + m₂)v
4. A 7 kg cart moving at 39 m/s collides with and couples to a stationary 6 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
7 kg (39 m/s) → [6 kg] → Coupled: (13 kg) v = ? · m₁u₁ = (m₁ + m₂)v
5. A 4 kg cart moving at 72 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 (72 m/s) → [8 kg] → Coupled: (12 kg) v = ? · m₁u₁ = (m₁ + m₂)v
6. A 6 kg cart moving at 48 m/s collides with and couples to a stationary 10 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
6 kg (48 m/s) → [10 kg] → Coupled: (16 kg) v = ? · m₁u₁ = (m₁ + m₂)v
7. A 8 kg cart moving at 102 m/s collides with and couples to a stationary 9 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
8 kg (102 m/s) → [9 kg] → Coupled: (17 kg) v = ? · m₁u₁ = (m₁ + m₂)v
8. A 10 kg cart moving at 70 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 kg (70 m/s) → [4 kg] → Coupled: (14 kg) v = ? · m₁u₁ = (m₁ + m₂)v
9. A 7 kg cart moving at 10 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 (10 m/s) → [3 kg] → Coupled: (10 kg) v = ? · m₁u₁ = (m₁ + m₂)v
10. A 10 kg cart moving at 72 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 kg (72 m/s) → [2 kg] → Coupled: (12 kg) v = ? · m₁u₁ = (m₁ + m₂)v
11. A 7 kg cart moving at 30 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 (30 m/s) → [8 kg] → Coupled: (15 kg) v = ? · m₁u₁ = (m₁ + m₂)v
12. A 4 kg cart moving at 45 m/s collides with and couples to a stationary 5 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
4 kg (45 m/s) → [5 kg] → Coupled: (9 kg) v = ? · m₁u₁ = (m₁ + m₂)v

12 questions · Seed 104736 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 13-15

Conservation of momentum in collisions

Answers and reasoning. Review before teaching.

1. A 4 kg cart moving at 14 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 m/s
Total momentum before collision p = 4 × 14 = 56 kg·m/s. Combined mass = 4 + 3 = 7 kg, so v = 56 ÷ 7 = 8 m/s.
2. A 4 kg cart moving at 56 m/s collides with and couples to a stationary 10 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
16 m/s
Total momentum before collision p = 4 × 56 = 224 kg·m/s. Combined mass = 4 + 10 = 14 kg, so v = 224 ÷ 14 = 16 m/s.
3. A 7 kg cart moving at 84 m/s collides with and couples to a stationary 7 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
42 m/s
Total momentum before collision p = 7 × 84 = 588 kg·m/s. Combined mass = 7 + 7 = 14 kg, so v = 588 ÷ 14 = 42 m/s.
4. A 7 kg cart moving at 39 m/s collides with and couples to a stationary 6 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
21 m/s
Total momentum before collision p = 7 × 39 = 273 kg·m/s. Combined mass = 7 + 6 = 13 kg, so v = 273 ÷ 13 = 21 m/s.
5. A 4 kg cart moving at 72 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 = 4 × 72 = 288 kg·m/s. Combined mass = 4 + 8 = 12 kg, so v = 288 ÷ 12 = 24 m/s.
6. A 6 kg cart moving at 48 m/s collides with and couples to a stationary 10 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
18 m/s
Total momentum before collision p = 6 × 48 = 288 kg·m/s. Combined mass = 6 + 10 = 16 kg, so v = 288 ÷ 16 = 18 m/s.
7. A 8 kg cart moving at 102 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 = 8 × 102 = 816 kg·m/s. Combined mass = 8 + 9 = 17 kg, so v = 816 ÷ 17 = 48 m/s.
8. A 10 kg cart moving at 70 m/s collides with and couples to a stationary 4 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
50 m/s
Total momentum before collision p = 10 × 70 = 700 kg·m/s. Combined mass = 10 + 4 = 14 kg, so v = 700 ÷ 14 = 50 m/s.
9. A 7 kg cart moving at 10 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 m/s
Total momentum before collision p = 7 × 10 = 70 kg·m/s. Combined mass = 7 + 3 = 10 kg, so v = 70 ÷ 10 = 7 m/s.
10. A 10 kg cart moving at 72 m/s collides with and couples to a stationary 2 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
60 m/s
Total momentum before collision p = 10 × 72 = 720 kg·m/s. Combined mass = 10 + 2 = 12 kg, so v = 720 ÷ 12 = 60 m/s.
11. A 7 kg cart moving at 30 m/s collides with and couples to a stationary 8 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
14 m/s
Total momentum before collision p = 7 × 30 = 210 kg·m/s. Combined mass = 7 + 8 = 15 kg, so v = 210 ÷ 15 = 14 m/s.
12. A 4 kg cart moving at 45 m/s collides with and couples to a stationary 5 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
20 m/s
Total momentum before collision p = 4 × 45 = 180 kg·m/s. Combined mass = 4 + 5 = 9 kg, so v = 180 ÷ 9 = 20 m/s.

12 questions · Seed 104736 · Age guidance, not curriculum certification