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 36 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 (36 m/s) → [4 kg] → Coupled: (9 kg) v = ? · m₁u₁ = (m₁ + m₂)v
2. A 8 kg cart moving at 66 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 kg (66 m/s) → [3 kg] → Coupled: (11 kg) v = ? · m₁u₁ = (m₁ + m₂)v
3. A 2 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.
2 kg (72 m/s) → [7 kg] → Coupled: (9 kg) v = ? · m₁u₁ = (m₁ + m₂)v
4. A 6 kg cart moving at 96 m/s collides with and couples to a stationary 6 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
6 kg (96 m/s) → [6 kg] → Coupled: (12 kg) v = ? · m₁u₁ = (m₁ + m₂)v
5. A 7 kg cart moving at 24 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 (24 m/s) → [5 kg] → Coupled: (12 kg) v = ? · m₁u₁ = (m₁ + m₂)v
6. A 2 kg cart moving at 32 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 (32 m/s) → [2 kg] → Coupled: (4 kg) v = ? · m₁u₁ = (m₁ + m₂)v
7. A 4 kg cart moving at 39 m/s collides with and couples to a stationary 9 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
4 kg (39 m/s) → [9 kg] → Coupled: (13 kg) v = ? · m₁u₁ = (m₁ + m₂)v
8. A 3 kg cart moving at 60 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 (60 m/s) → [9 kg] → Coupled: (12 kg) v = ? · m₁u₁ = (m₁ + m₂)v
9. A 4 kg cart moving at 77 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 (77 m/s) → [7 kg] → Coupled: (11 kg) v = ? · m₁u₁ = (m₁ + m₂)v
10. A 9 kg cart moving at 88 m/s collides with and couples to a stationary 2 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
9 kg (88 m/s) → [2 kg] → Coupled: (11 kg) v = ? · m₁u₁ = (m₁ + m₂)v
11. A 8 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.
8 kg (72 m/s) → [4 kg] → Coupled: (12 kg) v = ? · m₁u₁ = (m₁ + m₂)v
12. A 4 kg cart moving at 11 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 (11 m/s) → [7 kg] → Coupled: (11 kg) v = ? · m₁u₁ = (m₁ + m₂)v

12 questions · Seed 45 · 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 36 m/s collides with and couples to a stationary 4 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
20 m/s
Total momentum before collision p = 5 × 36 = 180 kg·m/s. Combined mass = 5 + 4 = 9 kg, so v = 180 ÷ 9 = 20 m/s.
2. A 8 kg cart moving at 66 m/s collides with and couples to a stationary 3 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
48 m/s
Total momentum before collision p = 8 × 66 = 528 kg·m/s. Combined mass = 8 + 3 = 11 kg, so v = 528 ÷ 11 = 48 m/s.
3. A 2 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.
16 m/s
Total momentum before collision p = 2 × 72 = 144 kg·m/s. Combined mass = 2 + 7 = 9 kg, so v = 144 ÷ 9 = 16 m/s.
4. A 6 kg cart moving at 96 m/s collides with and couples to a stationary 6 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
48 m/s
Total momentum before collision p = 6 × 96 = 576 kg·m/s. Combined mass = 6 + 6 = 12 kg, so v = 576 ÷ 12 = 48 m/s.
5. A 7 kg cart moving at 24 m/s collides with and couples to a stationary 5 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
14 m/s
Total momentum before collision p = 7 × 24 = 168 kg·m/s. Combined mass = 7 + 5 = 12 kg, so v = 168 ÷ 12 = 14 m/s.
6. A 2 kg cart moving at 32 m/s collides with and couples to a stationary 2 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
16 m/s
Total momentum before collision p = 2 × 32 = 64 kg·m/s. Combined mass = 2 + 2 = 4 kg, so v = 64 ÷ 4 = 16 m/s.
7. A 4 kg cart moving at 39 m/s collides with and couples to a stationary 9 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
12 m/s
Total momentum before collision p = 4 × 39 = 156 kg·m/s. Combined mass = 4 + 9 = 13 kg, so v = 156 ÷ 13 = 12 m/s.
8. A 3 kg cart moving at 60 m/s collides with and couples to a stationary 9 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
15 m/s
Total momentum before collision p = 3 × 60 = 180 kg·m/s. Combined mass = 3 + 9 = 12 kg, so v = 180 ÷ 12 = 15 m/s.
9. A 4 kg cart moving at 77 m/s collides with and couples to a stationary 7 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
28 m/s
Total momentum before collision p = 4 × 77 = 308 kg·m/s. Combined mass = 4 + 7 = 11 kg, so v = 308 ÷ 11 = 28 m/s.
10. A 9 kg cart moving at 88 m/s collides with and couples to a stationary 2 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
72 m/s
Total momentum before collision p = 9 × 88 = 792 kg·m/s. Combined mass = 9 + 2 = 11 kg, so v = 792 ÷ 11 = 72 m/s.
11. A 8 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.
48 m/s
Total momentum before collision p = 8 × 72 = 576 kg·m/s. Combined mass = 8 + 4 = 12 kg, so v = 576 ÷ 12 = 48 m/s.
12. A 4 kg cart moving at 11 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 m/s
Total momentum before collision p = 4 × 11 = 44 kg·m/s. Combined mass = 4 + 7 = 11 kg, so v = 44 ÷ 11 = 4 m/s.

12 questions · Seed 45 · 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 36 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 (36 m/s) → [4 kg] → Coupled: (9 kg) v = ? · m₁u₁ = (m₁ + m₂)v
2. A 8 kg cart moving at 66 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 kg (66 m/s) → [3 kg] → Coupled: (11 kg) v = ? · m₁u₁ = (m₁ + m₂)v
3. A 2 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.
2 kg (72 m/s) → [7 kg] → Coupled: (9 kg) v = ? · m₁u₁ = (m₁ + m₂)v
4. A 6 kg cart moving at 96 m/s collides with and couples to a stationary 6 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
6 kg (96 m/s) → [6 kg] → Coupled: (12 kg) v = ? · m₁u₁ = (m₁ + m₂)v
5. A 7 kg cart moving at 24 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 (24 m/s) → [5 kg] → Coupled: (12 kg) v = ? · m₁u₁ = (m₁ + m₂)v
6. A 2 kg cart moving at 32 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 (32 m/s) → [2 kg] → Coupled: (4 kg) v = ? · m₁u₁ = (m₁ + m₂)v
7. A 4 kg cart moving at 39 m/s collides with and couples to a stationary 9 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
4 kg (39 m/s) → [9 kg] → Coupled: (13 kg) v = ? · m₁u₁ = (m₁ + m₂)v
8. A 3 kg cart moving at 60 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 (60 m/s) → [9 kg] → Coupled: (12 kg) v = ? · m₁u₁ = (m₁ + m₂)v
9. A 4 kg cart moving at 77 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 (77 m/s) → [7 kg] → Coupled: (11 kg) v = ? · m₁u₁ = (m₁ + m₂)v
10. A 9 kg cart moving at 88 m/s collides with and couples to a stationary 2 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
9 kg (88 m/s) → [2 kg] → Coupled: (11 kg) v = ? · m₁u₁ = (m₁ + m₂)v
11. A 8 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.
8 kg (72 m/s) → [4 kg] → Coupled: (12 kg) v = ? · m₁u₁ = (m₁ + m₂)v
12. A 4 kg cart moving at 11 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 (11 m/s) → [7 kg] → Coupled: (11 kg) v = ? · m₁u₁ = (m₁ + m₂)v

12 questions · Seed 45 · 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 36 m/s collides with and couples to a stationary 4 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
20 m/s
Total momentum before collision p = 5 × 36 = 180 kg·m/s. Combined mass = 5 + 4 = 9 kg, so v = 180 ÷ 9 = 20 m/s.
2. A 8 kg cart moving at 66 m/s collides with and couples to a stationary 3 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
48 m/s
Total momentum before collision p = 8 × 66 = 528 kg·m/s. Combined mass = 8 + 3 = 11 kg, so v = 528 ÷ 11 = 48 m/s.
3. A 2 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.
16 m/s
Total momentum before collision p = 2 × 72 = 144 kg·m/s. Combined mass = 2 + 7 = 9 kg, so v = 144 ÷ 9 = 16 m/s.
4. A 6 kg cart moving at 96 m/s collides with and couples to a stationary 6 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
48 m/s
Total momentum before collision p = 6 × 96 = 576 kg·m/s. Combined mass = 6 + 6 = 12 kg, so v = 576 ÷ 12 = 48 m/s.
5. A 7 kg cart moving at 24 m/s collides with and couples to a stationary 5 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
14 m/s
Total momentum before collision p = 7 × 24 = 168 kg·m/s. Combined mass = 7 + 5 = 12 kg, so v = 168 ÷ 12 = 14 m/s.
6. A 2 kg cart moving at 32 m/s collides with and couples to a stationary 2 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
16 m/s
Total momentum before collision p = 2 × 32 = 64 kg·m/s. Combined mass = 2 + 2 = 4 kg, so v = 64 ÷ 4 = 16 m/s.
7. A 4 kg cart moving at 39 m/s collides with and couples to a stationary 9 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
12 m/s
Total momentum before collision p = 4 × 39 = 156 kg·m/s. Combined mass = 4 + 9 = 13 kg, so v = 156 ÷ 13 = 12 m/s.
8. A 3 kg cart moving at 60 m/s collides with and couples to a stationary 9 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
15 m/s
Total momentum before collision p = 3 × 60 = 180 kg·m/s. Combined mass = 3 + 9 = 12 kg, so v = 180 ÷ 12 = 15 m/s.
9. A 4 kg cart moving at 77 m/s collides with and couples to a stationary 7 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
28 m/s
Total momentum before collision p = 4 × 77 = 308 kg·m/s. Combined mass = 4 + 7 = 11 kg, so v = 308 ÷ 11 = 28 m/s.
10. A 9 kg cart moving at 88 m/s collides with and couples to a stationary 2 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
72 m/s
Total momentum before collision p = 9 × 88 = 792 kg·m/s. Combined mass = 9 + 2 = 11 kg, so v = 792 ÷ 11 = 72 m/s.
11. A 8 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.
48 m/s
Total momentum before collision p = 8 × 72 = 576 kg·m/s. Combined mass = 8 + 4 = 12 kg, so v = 576 ÷ 12 = 48 m/s.
12. A 4 kg cart moving at 11 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 m/s
Total momentum before collision p = 4 × 11 = 44 kg·m/s. Combined mass = 4 + 7 = 11 kg, so v = 44 ÷ 11 = 4 m/s.

12 questions · Seed 45 · Age guidance, not curriculum certification