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.

New variation Try interactive challenge Browse templates

Age band:Ages 13-15 Ages 16-18

Choose “Save as PDF” to keep a copy. Use your browser’s paper setting for A4 or Letter.

Worksheet StudioPractice pack · Ages 13-15

Conservation of momentum in collisions

Take your time. Show your thinking.

1. 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
2. A 7 kg cart moving at 72 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 (72 m/s) → [5 kg] → Coupled: (12 kg) v = ? · m₁u₁ = (m₁ + m₂)v
3. A 7 kg cart moving at 15 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 (15 m/s) → [8 kg] → Coupled: (15 kg) v = ? · m₁u₁ = (m₁ + m₂)v
4. A 10 kg cart moving at 112 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 (112 m/s) → [4 kg] → Coupled: (14 kg) v = ? · m₁u₁ = (m₁ + m₂)v
5. A 2 kg cart moving at 36 m/s collides with and couples to a stationary 7 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
2 kg (36 m/s) → [7 kg] → Coupled: (9 kg) v = ? · m₁u₁ = (m₁ + m₂)v
6. A 3 kg cart moving at 14 m/s collides with and couples to a stationary 4 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
3 kg (14 m/s) → [4 kg] → Coupled: (7 kg) v = ? · m₁u₁ = (m₁ + m₂)v
7. A 5 kg cart moving at 27 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 (27 m/s) → [4 kg] → Coupled: (9 kg) v = ? · m₁u₁ = (m₁ + m₂)v
8. A 4 kg cart moving at 64 m/s collides with and couples to a stationary 4 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
4 kg (64 m/s) → [4 kg] → Coupled: (8 kg) v = ? · m₁u₁ = (m₁ + m₂)v
9. A 7 kg cart moving at 16 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 (16 m/s) → [9 kg] → Coupled: (16 kg) v = ? · m₁u₁ = (m₁ + m₂)v
10. A 10 kg cart moving at 90 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 (90 m/s) → [5 kg] → Coupled: (15 kg) v = ? · m₁u₁ = (m₁ + m₂)v
11. A 3 kg cart moving at 12 m/s collides with and couples to a stationary 9 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
3 kg (12 m/s) → [9 kg] → Coupled: (12 kg) v = ? · m₁u₁ = (m₁ + m₂)v
12. A 4 kg cart moving at 88 m/s collides with and couples to a stationary 7 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
4 kg (88 m/s) → [7 kg] → Coupled: (11 kg) v = ? · m₁u₁ = (m₁ + m₂)v

12 questions · Seed 48 · 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 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.
2. A 7 kg cart moving at 72 m/s collides with and couples to a stationary 5 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
42 m/s
Total momentum before collision p = 7 × 72 = 504 kg·m/s. Combined mass = 7 + 5 = 12 kg, so v = 504 ÷ 12 = 42 m/s.
3. A 7 kg cart moving at 15 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 m/s
Total momentum before collision p = 7 × 15 = 105 kg·m/s. Combined mass = 7 + 8 = 15 kg, so v = 105 ÷ 15 = 7 m/s.
4. A 10 kg cart moving at 112 m/s collides with and couples to a stationary 4 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
80 m/s
Total momentum before collision p = 10 × 112 = 1120 kg·m/s. Combined mass = 10 + 4 = 14 kg, so v = 1120 ÷ 14 = 80 m/s.
5. A 2 kg cart moving at 36 m/s collides with and couples to a stationary 7 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
8 m/s
Total momentum before collision p = 2 × 36 = 72 kg·m/s. Combined mass = 2 + 7 = 9 kg, so v = 72 ÷ 9 = 8 m/s.
6. A 3 kg cart moving at 14 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 m/s
Total momentum before collision p = 3 × 14 = 42 kg·m/s. Combined mass = 3 + 4 = 7 kg, so v = 42 ÷ 7 = 6 m/s.
7. A 5 kg cart moving at 27 m/s collides with and couples to a stationary 4 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
15 m/s
Total momentum before collision p = 5 × 27 = 135 kg·m/s. Combined mass = 5 + 4 = 9 kg, so v = 135 ÷ 9 = 15 m/s.
8. A 4 kg cart moving at 64 m/s collides with and couples to a stationary 4 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
32 m/s
Total momentum before collision p = 4 × 64 = 256 kg·m/s. Combined mass = 4 + 4 = 8 kg, so v = 256 ÷ 8 = 32 m/s.
9. A 7 kg cart moving at 16 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 m/s
Total momentum before collision p = 7 × 16 = 112 kg·m/s. Combined mass = 7 + 9 = 16 kg, so v = 112 ÷ 16 = 7 m/s.
10. A 10 kg cart moving at 90 m/s collides with and couples to a stationary 5 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
60 m/s
Total momentum before collision p = 10 × 90 = 900 kg·m/s. Combined mass = 10 + 5 = 15 kg, so v = 900 ÷ 15 = 60 m/s.
11. A 3 kg cart moving at 12 m/s collides with and couples to a stationary 9 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
3 m/s
Total momentum before collision p = 3 × 12 = 36 kg·m/s. Combined mass = 3 + 9 = 12 kg, so v = 36 ÷ 12 = 3 m/s.
12. A 4 kg cart moving at 88 m/s collides with and couples to a stationary 7 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
32 m/s
Total momentum before collision p = 4 × 88 = 352 kg·m/s. Combined mass = 4 + 7 = 11 kg, so v = 352 ÷ 11 = 32 m/s.

12 questions · Seed 48 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 13-15

Conservation of momentum in collisions

Take your time. Show your thinking.

1. 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
2. A 7 kg cart moving at 72 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 (72 m/s) → [5 kg] → Coupled: (12 kg) v = ? · m₁u₁ = (m₁ + m₂)v
3. A 7 kg cart moving at 15 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 (15 m/s) → [8 kg] → Coupled: (15 kg) v = ? · m₁u₁ = (m₁ + m₂)v
4. A 10 kg cart moving at 112 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 (112 m/s) → [4 kg] → Coupled: (14 kg) v = ? · m₁u₁ = (m₁ + m₂)v
5. A 2 kg cart moving at 36 m/s collides with and couples to a stationary 7 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
2 kg (36 m/s) → [7 kg] → Coupled: (9 kg) v = ? · m₁u₁ = (m₁ + m₂)v
6. A 3 kg cart moving at 14 m/s collides with and couples to a stationary 4 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
3 kg (14 m/s) → [4 kg] → Coupled: (7 kg) v = ? · m₁u₁ = (m₁ + m₂)v
7. A 5 kg cart moving at 27 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 (27 m/s) → [4 kg] → Coupled: (9 kg) v = ? · m₁u₁ = (m₁ + m₂)v
8. A 4 kg cart moving at 64 m/s collides with and couples to a stationary 4 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
4 kg (64 m/s) → [4 kg] → Coupled: (8 kg) v = ? · m₁u₁ = (m₁ + m₂)v
9. A 7 kg cart moving at 16 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 (16 m/s) → [9 kg] → Coupled: (16 kg) v = ? · m₁u₁ = (m₁ + m₂)v
10. A 10 kg cart moving at 90 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 (90 m/s) → [5 kg] → Coupled: (15 kg) v = ? · m₁u₁ = (m₁ + m₂)v
11. A 3 kg cart moving at 12 m/s collides with and couples to a stationary 9 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
3 kg (12 m/s) → [9 kg] → Coupled: (12 kg) v = ? · m₁u₁ = (m₁ + m₂)v
12. A 4 kg cart moving at 88 m/s collides with and couples to a stationary 7 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
4 kg (88 m/s) → [7 kg] → Coupled: (11 kg) v = ? · m₁u₁ = (m₁ + m₂)v

12 questions · Seed 48 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 13-15

Conservation of momentum in collisions

Answers and reasoning. Review before teaching.

1. 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.
2. A 7 kg cart moving at 72 m/s collides with and couples to a stationary 5 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
42 m/s
Total momentum before collision p = 7 × 72 = 504 kg·m/s. Combined mass = 7 + 5 = 12 kg, so v = 504 ÷ 12 = 42 m/s.
3. A 7 kg cart moving at 15 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 m/s
Total momentum before collision p = 7 × 15 = 105 kg·m/s. Combined mass = 7 + 8 = 15 kg, so v = 105 ÷ 15 = 7 m/s.
4. A 10 kg cart moving at 112 m/s collides with and couples to a stationary 4 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
80 m/s
Total momentum before collision p = 10 × 112 = 1120 kg·m/s. Combined mass = 10 + 4 = 14 kg, so v = 1120 ÷ 14 = 80 m/s.
5. A 2 kg cart moving at 36 m/s collides with and couples to a stationary 7 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
8 m/s
Total momentum before collision p = 2 × 36 = 72 kg·m/s. Combined mass = 2 + 7 = 9 kg, so v = 72 ÷ 9 = 8 m/s.
6. A 3 kg cart moving at 14 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 m/s
Total momentum before collision p = 3 × 14 = 42 kg·m/s. Combined mass = 3 + 4 = 7 kg, so v = 42 ÷ 7 = 6 m/s.
7. A 5 kg cart moving at 27 m/s collides with and couples to a stationary 4 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
15 m/s
Total momentum before collision p = 5 × 27 = 135 kg·m/s. Combined mass = 5 + 4 = 9 kg, so v = 135 ÷ 9 = 15 m/s.
8. A 4 kg cart moving at 64 m/s collides with and couples to a stationary 4 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
32 m/s
Total momentum before collision p = 4 × 64 = 256 kg·m/s. Combined mass = 4 + 4 = 8 kg, so v = 256 ÷ 8 = 32 m/s.
9. A 7 kg cart moving at 16 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 m/s
Total momentum before collision p = 7 × 16 = 112 kg·m/s. Combined mass = 7 + 9 = 16 kg, so v = 112 ÷ 16 = 7 m/s.
10. A 10 kg cart moving at 90 m/s collides with and couples to a stationary 5 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
60 m/s
Total momentum before collision p = 10 × 90 = 900 kg·m/s. Combined mass = 10 + 5 = 15 kg, so v = 900 ÷ 15 = 60 m/s.
11. A 3 kg cart moving at 12 m/s collides with and couples to a stationary 9 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
3 m/s
Total momentum before collision p = 3 × 12 = 36 kg·m/s. Combined mass = 3 + 9 = 12 kg, so v = 36 ÷ 12 = 3 m/s.
12. A 4 kg cart moving at 88 m/s collides with and couples to a stationary 7 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
32 m/s
Total momentum before collision p = 4 × 88 = 352 kg·m/s. Combined mass = 4 + 7 = 11 kg, so v = 352 ÷ 11 = 32 m/s.

12 questions · Seed 48 · Age guidance, not curriculum certification