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 6 kg cart moving at 27 m/s collides with and couples to a stationary 3 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
6 kg (27 m/s) → [3 kg] → Coupled: (9 kg) v = ? · m₁u₁ = (m₁ + m₂)v
2. 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
3. A 3 kg cart moving at 55 m/s collides with and couples to a stationary 8 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
3 kg (55 m/s) → [8 kg] → Coupled: (11 kg) v = ? · m₁u₁ = (m₁ + m₂)v
4. A 6 kg cart moving at 40 m/s collides with and couples to a stationary 4 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
6 kg (40 m/s) → [4 kg] → Coupled: (10 kg) v = ? · m₁u₁ = (m₁ + m₂)v
5. A 7 kg cart moving at 44 m/s collides with and couples to a stationary 4 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
7 kg (44 m/s) → [4 kg] → Coupled: (11 kg) v = ? · m₁u₁ = (m₁ + m₂)v
6. A 2 kg cart moving at 40 m/s collides with and couples to a stationary 3 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
2 kg (40 m/s) → [3 kg] → Coupled: (5 kg) v = ? · m₁u₁ = (m₁ + m₂)v
7. A 5 kg cart moving at 60 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 (60 m/s) → [5 kg] → Coupled: (10 kg) v = ? · m₁u₁ = (m₁ + m₂)v
8. A 5 kg cart moving at 72 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 (72 m/s) → [4 kg] → Coupled: (9 kg) v = ? · m₁u₁ = (m₁ + m₂)v
9. A 10 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.
10 kg (45 m/s) → [5 kg] → Coupled: (15 kg) v = ? · m₁u₁ = (m₁ + m₂)v
10. A 9 kg cart moving at 57 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 (57 m/s) → [10 kg] → Coupled: (19 kg) v = ? · m₁u₁ = (m₁ + m₂)v
11. A 9 kg cart moving at 45 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 (45 m/s) → [6 kg] → Coupled: (15 kg) v = ? · m₁u₁ = (m₁ + m₂)v
12. A 9 kg cart moving at 108 m/s collides with and couples to a stationary 9 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
9 kg (108 m/s) → [9 kg] → Coupled: (18 kg) v = ? · m₁u₁ = (m₁ + m₂)v

12 questions · Seed 104734 · 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 6 kg cart moving at 27 m/s collides with and couples to a stationary 3 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
18 m/s
Total momentum before collision p = 6 × 27 = 162 kg·m/s. Combined mass = 6 + 3 = 9 kg, so v = 162 ÷ 9 = 18 m/s.
2. 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.
3. A 3 kg cart moving at 55 m/s collides with and couples to a stationary 8 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
15 m/s
Total momentum before collision p = 3 × 55 = 165 kg·m/s. Combined mass = 3 + 8 = 11 kg, so v = 165 ÷ 11 = 15 m/s.
4. A 6 kg cart moving at 40 m/s collides with and couples to a stationary 4 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
24 m/s
Total momentum before collision p = 6 × 40 = 240 kg·m/s. Combined mass = 6 + 4 = 10 kg, so v = 240 ÷ 10 = 24 m/s.
5. A 7 kg cart moving at 44 m/s collides with and couples to a stationary 4 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
28 m/s
Total momentum before collision p = 7 × 44 = 308 kg·m/s. Combined mass = 7 + 4 = 11 kg, so v = 308 ÷ 11 = 28 m/s.
6. A 2 kg cart moving at 40 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 = 2 × 40 = 80 kg·m/s. Combined mass = 2 + 3 = 5 kg, so v = 80 ÷ 5 = 16 m/s.
7. A 5 kg cart moving at 60 m/s collides with and couples to a stationary 5 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
30 m/s
Total momentum before collision p = 5 × 60 = 300 kg·m/s. Combined mass = 5 + 5 = 10 kg, so v = 300 ÷ 10 = 30 m/s.
8. A 5 kg cart moving at 72 m/s collides with and couples to a stationary 4 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
40 m/s
Total momentum before collision p = 5 × 72 = 360 kg·m/s. Combined mass = 5 + 4 = 9 kg, so v = 360 ÷ 9 = 40 m/s.
9. A 10 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.
30 m/s
Total momentum before collision p = 10 × 45 = 450 kg·m/s. Combined mass = 10 + 5 = 15 kg, so v = 450 ÷ 15 = 30 m/s.
10. A 9 kg cart moving at 57 m/s collides with and couples to a stationary 10 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
27 m/s
Total momentum before collision p = 9 × 57 = 513 kg·m/s. Combined mass = 9 + 10 = 19 kg, so v = 513 ÷ 19 = 27 m/s.
11. A 9 kg cart moving at 45 m/s collides with and couples to a stationary 6 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
27 m/s
Total momentum before collision p = 9 × 45 = 405 kg·m/s. Combined mass = 9 + 6 = 15 kg, so v = 405 ÷ 15 = 27 m/s.
12. A 9 kg cart moving at 108 m/s collides with and couples to a stationary 9 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
54 m/s
Total momentum before collision p = 9 × 108 = 972 kg·m/s. Combined mass = 9 + 9 = 18 kg, so v = 972 ÷ 18 = 54 m/s.

12 questions · Seed 104734 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 13-15

Conservation of momentum in collisions

Take your time. Show your thinking.

1. A 6 kg cart moving at 27 m/s collides with and couples to a stationary 3 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
6 kg (27 m/s) → [3 kg] → Coupled: (9 kg) v = ? · m₁u₁ = (m₁ + m₂)v
2. 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
3. A 3 kg cart moving at 55 m/s collides with and couples to a stationary 8 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
3 kg (55 m/s) → [8 kg] → Coupled: (11 kg) v = ? · m₁u₁ = (m₁ + m₂)v
4. A 6 kg cart moving at 40 m/s collides with and couples to a stationary 4 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
6 kg (40 m/s) → [4 kg] → Coupled: (10 kg) v = ? · m₁u₁ = (m₁ + m₂)v
5. A 7 kg cart moving at 44 m/s collides with and couples to a stationary 4 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
7 kg (44 m/s) → [4 kg] → Coupled: (11 kg) v = ? · m₁u₁ = (m₁ + m₂)v
6. A 2 kg cart moving at 40 m/s collides with and couples to a stationary 3 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
2 kg (40 m/s) → [3 kg] → Coupled: (5 kg) v = ? · m₁u₁ = (m₁ + m₂)v
7. A 5 kg cart moving at 60 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 (60 m/s) → [5 kg] → Coupled: (10 kg) v = ? · m₁u₁ = (m₁ + m₂)v
8. A 5 kg cart moving at 72 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 (72 m/s) → [4 kg] → Coupled: (9 kg) v = ? · m₁u₁ = (m₁ + m₂)v
9. A 10 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.
10 kg (45 m/s) → [5 kg] → Coupled: (15 kg) v = ? · m₁u₁ = (m₁ + m₂)v
10. A 9 kg cart moving at 57 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 (57 m/s) → [10 kg] → Coupled: (19 kg) v = ? · m₁u₁ = (m₁ + m₂)v
11. A 9 kg cart moving at 45 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 (45 m/s) → [6 kg] → Coupled: (15 kg) v = ? · m₁u₁ = (m₁ + m₂)v
12. A 9 kg cart moving at 108 m/s collides with and couples to a stationary 9 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
9 kg (108 m/s) → [9 kg] → Coupled: (18 kg) v = ? · m₁u₁ = (m₁ + m₂)v

12 questions · Seed 104734 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 13-15

Conservation of momentum in collisions

Answers and reasoning. Review before teaching.

1. A 6 kg cart moving at 27 m/s collides with and couples to a stationary 3 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
18 m/s
Total momentum before collision p = 6 × 27 = 162 kg·m/s. Combined mass = 6 + 3 = 9 kg, so v = 162 ÷ 9 = 18 m/s.
2. 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.
3. A 3 kg cart moving at 55 m/s collides with and couples to a stationary 8 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
15 m/s
Total momentum before collision p = 3 × 55 = 165 kg·m/s. Combined mass = 3 + 8 = 11 kg, so v = 165 ÷ 11 = 15 m/s.
4. A 6 kg cart moving at 40 m/s collides with and couples to a stationary 4 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
24 m/s
Total momentum before collision p = 6 × 40 = 240 kg·m/s. Combined mass = 6 + 4 = 10 kg, so v = 240 ÷ 10 = 24 m/s.
5. A 7 kg cart moving at 44 m/s collides with and couples to a stationary 4 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
28 m/s
Total momentum before collision p = 7 × 44 = 308 kg·m/s. Combined mass = 7 + 4 = 11 kg, so v = 308 ÷ 11 = 28 m/s.
6. A 2 kg cart moving at 40 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 = 2 × 40 = 80 kg·m/s. Combined mass = 2 + 3 = 5 kg, so v = 80 ÷ 5 = 16 m/s.
7. A 5 kg cart moving at 60 m/s collides with and couples to a stationary 5 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
30 m/s
Total momentum before collision p = 5 × 60 = 300 kg·m/s. Combined mass = 5 + 5 = 10 kg, so v = 300 ÷ 10 = 30 m/s.
8. A 5 kg cart moving at 72 m/s collides with and couples to a stationary 4 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
40 m/s
Total momentum before collision p = 5 × 72 = 360 kg·m/s. Combined mass = 5 + 4 = 9 kg, so v = 360 ÷ 9 = 40 m/s.
9. A 10 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.
30 m/s
Total momentum before collision p = 10 × 45 = 450 kg·m/s. Combined mass = 10 + 5 = 15 kg, so v = 450 ÷ 15 = 30 m/s.
10. A 9 kg cart moving at 57 m/s collides with and couples to a stationary 10 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
27 m/s
Total momentum before collision p = 9 × 57 = 513 kg·m/s. Combined mass = 9 + 10 = 19 kg, so v = 513 ÷ 19 = 27 m/s.
11. A 9 kg cart moving at 45 m/s collides with and couples to a stationary 6 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
27 m/s
Total momentum before collision p = 9 × 45 = 405 kg·m/s. Combined mass = 9 + 6 = 15 kg, so v = 405 ÷ 15 = 27 m/s.
12. A 9 kg cart moving at 108 m/s collides with and couples to a stationary 9 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
54 m/s
Total momentum before collision p = 9 × 108 = 972 kg·m/s. Combined mass = 9 + 9 = 18 kg, so v = 972 ÷ 18 = 54 m/s.

12 questions · Seed 104734 · Age guidance, not curriculum certification