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 34 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 (34 m/s) → [8 kg] → Coupled: (17 kg) v = ? · m₁u₁ = (m₁ + m₂)v
2. A 6 kg cart moving at 112 m/s collides with and couples to a stationary 8 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
6 kg (112 m/s) → [8 kg] → Coupled: (14 kg) v = ? · m₁u₁ = (m₁ + m₂)v
3. A 10 kg cart moving at 80 m/s collides with and couples to a stationary 10 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
10 kg (80 m/s) → [10 kg] → Coupled: (20 kg) v = ? · m₁u₁ = (m₁ + m₂)v
4. A 9 kg cart moving at 95 m/s collides with and couples to a stationary 10 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
9 kg (95 m/s) → [10 kg] → Coupled: (19 kg) v = ? · m₁u₁ = (m₁ + m₂)v
5. A 9 kg cart moving at 85 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 (85 m/s) → [8 kg] → Coupled: (17 kg) v = ? · m₁u₁ = (m₁ + m₂)v
6. 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
7. 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
8. 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
9. A 9 kg cart moving at 13 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 (13 m/s) → [4 kg] → Coupled: (13 kg) v = ? · m₁u₁ = (m₁ + m₂)v
10. A 5 kg cart moving at 72 m/s collides with and couples to a stationary 7 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
5 kg (72 m/s) → [7 kg] → Coupled: (12 kg) v = ? · m₁u₁ = (m₁ + m₂)v
11. A 9 kg cart moving at 105 m/s collides with and couples to a stationary 6 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
9 kg (105 m/s) → [6 kg] → Coupled: (15 kg) v = ? · m₁u₁ = (m₁ + m₂)v
12. A 6 kg cart moving at 64 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 (64 m/s) → [2 kg] → Coupled: (8 kg) v = ? · m₁u₁ = (m₁ + m₂)v

12 questions · Seed 104732 · 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 34 m/s collides with and couples to a stationary 8 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
18 m/s
Total momentum before collision p = 9 × 34 = 306 kg·m/s. Combined mass = 9 + 8 = 17 kg, so v = 306 ÷ 17 = 18 m/s.
2. A 6 kg cart moving at 112 m/s collides with and couples to a stationary 8 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
48 m/s
Total momentum before collision p = 6 × 112 = 672 kg·m/s. Combined mass = 6 + 8 = 14 kg, so v = 672 ÷ 14 = 48 m/s.
3. A 10 kg cart moving at 80 m/s collides with and couples to a stationary 10 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
40 m/s
Total momentum before collision p = 10 × 80 = 800 kg·m/s. Combined mass = 10 + 10 = 20 kg, so v = 800 ÷ 20 = 40 m/s.
4. A 9 kg cart moving at 95 m/s collides with and couples to a stationary 10 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
45 m/s
Total momentum before collision p = 9 × 95 = 855 kg·m/s. Combined mass = 9 + 10 = 19 kg, so v = 855 ÷ 19 = 45 m/s.
5. A 9 kg cart moving at 85 m/s collides with and couples to a stationary 8 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
45 m/s
Total momentum before collision p = 9 × 85 = 765 kg·m/s. Combined mass = 9 + 8 = 17 kg, so v = 765 ÷ 17 = 45 m/s.
6. 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.
7. 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.
8. 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.
9. A 9 kg cart moving at 13 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 m/s
Total momentum before collision p = 9 × 13 = 117 kg·m/s. Combined mass = 9 + 4 = 13 kg, so v = 117 ÷ 13 = 9 m/s.
10. A 5 kg cart moving at 72 m/s collides with and couples to a stationary 7 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
30 m/s
Total momentum before collision p = 5 × 72 = 360 kg·m/s. Combined mass = 5 + 7 = 12 kg, so v = 360 ÷ 12 = 30 m/s.
11. A 9 kg cart moving at 105 m/s collides with and couples to a stationary 6 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
63 m/s
Total momentum before collision p = 9 × 105 = 945 kg·m/s. Combined mass = 9 + 6 = 15 kg, so v = 945 ÷ 15 = 63 m/s.
12. A 6 kg cart moving at 64 m/s collides with and couples to a stationary 2 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
48 m/s
Total momentum before collision p = 6 × 64 = 384 kg·m/s. Combined mass = 6 + 2 = 8 kg, so v = 384 ÷ 8 = 48 m/s.

12 questions · Seed 104732 · 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 34 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 (34 m/s) → [8 kg] → Coupled: (17 kg) v = ? · m₁u₁ = (m₁ + m₂)v
2. A 6 kg cart moving at 112 m/s collides with and couples to a stationary 8 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
6 kg (112 m/s) → [8 kg] → Coupled: (14 kg) v = ? · m₁u₁ = (m₁ + m₂)v
3. A 10 kg cart moving at 80 m/s collides with and couples to a stationary 10 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
10 kg (80 m/s) → [10 kg] → Coupled: (20 kg) v = ? · m₁u₁ = (m₁ + m₂)v
4. A 9 kg cart moving at 95 m/s collides with and couples to a stationary 10 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
9 kg (95 m/s) → [10 kg] → Coupled: (19 kg) v = ? · m₁u₁ = (m₁ + m₂)v
5. A 9 kg cart moving at 85 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 (85 m/s) → [8 kg] → Coupled: (17 kg) v = ? · m₁u₁ = (m₁ + m₂)v
6. 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
7. 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
8. 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
9. A 9 kg cart moving at 13 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 (13 m/s) → [4 kg] → Coupled: (13 kg) v = ? · m₁u₁ = (m₁ + m₂)v
10. A 5 kg cart moving at 72 m/s collides with and couples to a stationary 7 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
5 kg (72 m/s) → [7 kg] → Coupled: (12 kg) v = ? · m₁u₁ = (m₁ + m₂)v
11. A 9 kg cart moving at 105 m/s collides with and couples to a stationary 6 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
9 kg (105 m/s) → [6 kg] → Coupled: (15 kg) v = ? · m₁u₁ = (m₁ + m₂)v
12. A 6 kg cart moving at 64 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 (64 m/s) → [2 kg] → Coupled: (8 kg) v = ? · m₁u₁ = (m₁ + m₂)v

12 questions · Seed 104732 · 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 34 m/s collides with and couples to a stationary 8 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
18 m/s
Total momentum before collision p = 9 × 34 = 306 kg·m/s. Combined mass = 9 + 8 = 17 kg, so v = 306 ÷ 17 = 18 m/s.
2. A 6 kg cart moving at 112 m/s collides with and couples to a stationary 8 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
48 m/s
Total momentum before collision p = 6 × 112 = 672 kg·m/s. Combined mass = 6 + 8 = 14 kg, so v = 672 ÷ 14 = 48 m/s.
3. A 10 kg cart moving at 80 m/s collides with and couples to a stationary 10 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
40 m/s
Total momentum before collision p = 10 × 80 = 800 kg·m/s. Combined mass = 10 + 10 = 20 kg, so v = 800 ÷ 20 = 40 m/s.
4. A 9 kg cart moving at 95 m/s collides with and couples to a stationary 10 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
45 m/s
Total momentum before collision p = 9 × 95 = 855 kg·m/s. Combined mass = 9 + 10 = 19 kg, so v = 855 ÷ 19 = 45 m/s.
5. A 9 kg cart moving at 85 m/s collides with and couples to a stationary 8 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
45 m/s
Total momentum before collision p = 9 × 85 = 765 kg·m/s. Combined mass = 9 + 8 = 17 kg, so v = 765 ÷ 17 = 45 m/s.
6. 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.
7. 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.
8. 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.
9. A 9 kg cart moving at 13 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 m/s
Total momentum before collision p = 9 × 13 = 117 kg·m/s. Combined mass = 9 + 4 = 13 kg, so v = 117 ÷ 13 = 9 m/s.
10. A 5 kg cart moving at 72 m/s collides with and couples to a stationary 7 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
30 m/s
Total momentum before collision p = 5 × 72 = 360 kg·m/s. Combined mass = 5 + 7 = 12 kg, so v = 360 ÷ 12 = 30 m/s.
11. A 9 kg cart moving at 105 m/s collides with and couples to a stationary 6 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
63 m/s
Total momentum before collision p = 9 × 105 = 945 kg·m/s. Combined mass = 9 + 6 = 15 kg, so v = 945 ÷ 15 = 63 m/s.
12. A 6 kg cart moving at 64 m/s collides with and couples to a stationary 2 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
48 m/s
Total momentum before collision p = 6 × 64 = 384 kg·m/s. Combined mass = 6 + 2 = 8 kg, so v = 384 ÷ 8 = 48 m/s.

12 questions · Seed 104732 · Age guidance, not curriculum certification