ScienceAges 16-18

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 16-18

Conservation of momentum in collisions

Take your time. Show your thinking.

1. A 10 kg cart moving at 140 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 (140 m/s) → [10 kg] → Coupled: (20 kg) v = ? · m₁u₁ = (m₁ + m₂)v
2. A 6 kg cart moving at 22 m/s collides with and couples to a stationary 5 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
6 kg (22 m/s) → [5 kg] → Coupled: (11 kg) v = ? · m₁u₁ = (m₁ + m₂)v
3. A 5 kg cart moving at 90 m/s collides with and couples to a stationary 10 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
5 kg (90 m/s) → [10 kg] → Coupled: (15 kg) v = ? · m₁u₁ = (m₁ + m₂)v
4. A 9 kg cart moving at 77 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 (77 m/s) → [2 kg] → Coupled: (11 kg) v = ? · m₁u₁ = (m₁ + m₂)v
5. A 6 kg cart moving at 54 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 (54 m/s) → [3 kg] → Coupled: (9 kg) v = ? · m₁u₁ = (m₁ + m₂)v
6. A 8 kg cart moving at 18 m/s collides with and couples to a stationary 10 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
8 kg (18 m/s) → [10 kg] → Coupled: (18 kg) v = ? · m₁u₁ = (m₁ + m₂)v
7. A 2 kg cart moving at 16 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 (16 m/s) → [2 kg] → Coupled: (4 kg) v = ? · m₁u₁ = (m₁ + m₂)v
8. A 3 kg cart moving at 32 m/s collides with and couples to a stationary 5 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
3 kg (32 m/s) → [5 kg] → Coupled: (8 kg) v = ? · m₁u₁ = (m₁ + m₂)v
9. A 8 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.
8 kg (36 m/s) → [4 kg] → Coupled: (12 kg) v = ? · m₁u₁ = (m₁ + m₂)v
10. A 7 kg cart moving at 70 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 (70 m/s) → [7 kg] → Coupled: (14 kg) v = ? · m₁u₁ = (m₁ + m₂)v
11. A 6 kg cart moving at 48 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 (48 m/s) → [2 kg] → Coupled: (8 kg) v = ? · m₁u₁ = (m₁ + m₂)v
12. A 2 kg cart moving at 36 m/s collides with and couples to a stationary 10 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
2 kg (36 m/s) → [10 kg] → Coupled: (12 kg) v = ? · m₁u₁ = (m₁ + m₂)v

12 questions · Seed 49 · Age guidance, not curriculum certification

View the answer key

Worksheet StudioAnswer key · Ages 16-18

Conservation of momentum in collisions

Answers and reasoning. Review before teaching.

1. A 10 kg cart moving at 140 m/s collides with and couples to a stationary 10 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
70 m/s
Total momentum before collision p = 10 × 140 = 1400 kg·m/s. Combined mass = 10 + 10 = 20 kg, so v = 1400 ÷ 20 = 70 m/s.
2. A 6 kg cart moving at 22 m/s collides with and couples to a stationary 5 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
12 m/s
Total momentum before collision p = 6 × 22 = 132 kg·m/s. Combined mass = 6 + 5 = 11 kg, so v = 132 ÷ 11 = 12 m/s.
3. A 5 kg cart moving at 90 m/s collides with and couples to a stationary 10 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
30 m/s
Total momentum before collision p = 5 × 90 = 450 kg·m/s. Combined mass = 5 + 10 = 15 kg, so v = 450 ÷ 15 = 30 m/s.
4. A 9 kg cart moving at 77 m/s collides with and couples to a stationary 2 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
63 m/s
Total momentum before collision p = 9 × 77 = 693 kg·m/s. Combined mass = 9 + 2 = 11 kg, so v = 693 ÷ 11 = 63 m/s.
5. A 6 kg cart moving at 54 m/s collides with and couples to a stationary 3 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
36 m/s
Total momentum before collision p = 6 × 54 = 324 kg·m/s. Combined mass = 6 + 3 = 9 kg, so v = 324 ÷ 9 = 36 m/s.
6. A 8 kg cart moving at 18 m/s collides with and couples to a stationary 10 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
8 m/s
Total momentum before collision p = 8 × 18 = 144 kg·m/s. Combined mass = 8 + 10 = 18 kg, so v = 144 ÷ 18 = 8 m/s.
7. A 2 kg cart moving at 16 m/s collides with and couples to a stationary 2 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
8 m/s
Total momentum before collision p = 2 × 16 = 32 kg·m/s. Combined mass = 2 + 2 = 4 kg, so v = 32 ÷ 4 = 8 m/s.
8. A 3 kg cart moving at 32 m/s collides with and couples to a stationary 5 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
12 m/s
Total momentum before collision p = 3 × 32 = 96 kg·m/s. Combined mass = 3 + 5 = 8 kg, so v = 96 ÷ 8 = 12 m/s.
9. A 8 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.
24 m/s
Total momentum before collision p = 8 × 36 = 288 kg·m/s. Combined mass = 8 + 4 = 12 kg, so v = 288 ÷ 12 = 24 m/s.
10. A 7 kg cart moving at 70 m/s collides with and couples to a stationary 7 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
35 m/s
Total momentum before collision p = 7 × 70 = 490 kg·m/s. Combined mass = 7 + 7 = 14 kg, so v = 490 ÷ 14 = 35 m/s.
11. A 6 kg cart moving at 48 m/s collides with and couples to a stationary 2 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
36 m/s
Total momentum before collision p = 6 × 48 = 288 kg·m/s. Combined mass = 6 + 2 = 8 kg, so v = 288 ÷ 8 = 36 m/s.
12. A 2 kg cart moving at 36 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 m/s
Total momentum before collision p = 2 × 36 = 72 kg·m/s. Combined mass = 2 + 10 = 12 kg, so v = 72 ÷ 12 = 6 m/s.

12 questions · Seed 49 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 16-18

Conservation of momentum in collisions

Take your time. Show your thinking.

1. A 10 kg cart moving at 140 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 (140 m/s) → [10 kg] → Coupled: (20 kg) v = ? · m₁u₁ = (m₁ + m₂)v
2. A 6 kg cart moving at 22 m/s collides with and couples to a stationary 5 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
6 kg (22 m/s) → [5 kg] → Coupled: (11 kg) v = ? · m₁u₁ = (m₁ + m₂)v
3. A 5 kg cart moving at 90 m/s collides with and couples to a stationary 10 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
5 kg (90 m/s) → [10 kg] → Coupled: (15 kg) v = ? · m₁u₁ = (m₁ + m₂)v
4. A 9 kg cart moving at 77 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 (77 m/s) → [2 kg] → Coupled: (11 kg) v = ? · m₁u₁ = (m₁ + m₂)v
5. A 6 kg cart moving at 54 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 (54 m/s) → [3 kg] → Coupled: (9 kg) v = ? · m₁u₁ = (m₁ + m₂)v
6. A 8 kg cart moving at 18 m/s collides with and couples to a stationary 10 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
8 kg (18 m/s) → [10 kg] → Coupled: (18 kg) v = ? · m₁u₁ = (m₁ + m₂)v
7. A 2 kg cart moving at 16 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 (16 m/s) → [2 kg] → Coupled: (4 kg) v = ? · m₁u₁ = (m₁ + m₂)v
8. A 3 kg cart moving at 32 m/s collides with and couples to a stationary 5 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
3 kg (32 m/s) → [5 kg] → Coupled: (8 kg) v = ? · m₁u₁ = (m₁ + m₂)v
9. A 8 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.
8 kg (36 m/s) → [4 kg] → Coupled: (12 kg) v = ? · m₁u₁ = (m₁ + m₂)v
10. A 7 kg cart moving at 70 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 (70 m/s) → [7 kg] → Coupled: (14 kg) v = ? · m₁u₁ = (m₁ + m₂)v
11. A 6 kg cart moving at 48 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 (48 m/s) → [2 kg] → Coupled: (8 kg) v = ? · m₁u₁ = (m₁ + m₂)v
12. A 2 kg cart moving at 36 m/s collides with and couples to a stationary 10 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
2 kg (36 m/s) → [10 kg] → Coupled: (12 kg) v = ? · m₁u₁ = (m₁ + m₂)v

12 questions · Seed 49 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 16-18

Conservation of momentum in collisions

Answers and reasoning. Review before teaching.

1. A 10 kg cart moving at 140 m/s collides with and couples to a stationary 10 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
70 m/s
Total momentum before collision p = 10 × 140 = 1400 kg·m/s. Combined mass = 10 + 10 = 20 kg, so v = 1400 ÷ 20 = 70 m/s.
2. A 6 kg cart moving at 22 m/s collides with and couples to a stationary 5 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
12 m/s
Total momentum before collision p = 6 × 22 = 132 kg·m/s. Combined mass = 6 + 5 = 11 kg, so v = 132 ÷ 11 = 12 m/s.
3. A 5 kg cart moving at 90 m/s collides with and couples to a stationary 10 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
30 m/s
Total momentum before collision p = 5 × 90 = 450 kg·m/s. Combined mass = 5 + 10 = 15 kg, so v = 450 ÷ 15 = 30 m/s.
4. A 9 kg cart moving at 77 m/s collides with and couples to a stationary 2 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
63 m/s
Total momentum before collision p = 9 × 77 = 693 kg·m/s. Combined mass = 9 + 2 = 11 kg, so v = 693 ÷ 11 = 63 m/s.
5. A 6 kg cart moving at 54 m/s collides with and couples to a stationary 3 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
36 m/s
Total momentum before collision p = 6 × 54 = 324 kg·m/s. Combined mass = 6 + 3 = 9 kg, so v = 324 ÷ 9 = 36 m/s.
6. A 8 kg cart moving at 18 m/s collides with and couples to a stationary 10 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
8 m/s
Total momentum before collision p = 8 × 18 = 144 kg·m/s. Combined mass = 8 + 10 = 18 kg, so v = 144 ÷ 18 = 8 m/s.
7. A 2 kg cart moving at 16 m/s collides with and couples to a stationary 2 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
8 m/s
Total momentum before collision p = 2 × 16 = 32 kg·m/s. Combined mass = 2 + 2 = 4 kg, so v = 32 ÷ 4 = 8 m/s.
8. A 3 kg cart moving at 32 m/s collides with and couples to a stationary 5 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
12 m/s
Total momentum before collision p = 3 × 32 = 96 kg·m/s. Combined mass = 3 + 5 = 8 kg, so v = 96 ÷ 8 = 12 m/s.
9. A 8 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.
24 m/s
Total momentum before collision p = 8 × 36 = 288 kg·m/s. Combined mass = 8 + 4 = 12 kg, so v = 288 ÷ 12 = 24 m/s.
10. A 7 kg cart moving at 70 m/s collides with and couples to a stationary 7 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
35 m/s
Total momentum before collision p = 7 × 70 = 490 kg·m/s. Combined mass = 7 + 7 = 14 kg, so v = 490 ÷ 14 = 35 m/s.
11. A 6 kg cart moving at 48 m/s collides with and couples to a stationary 2 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
36 m/s
Total momentum before collision p = 6 × 48 = 288 kg·m/s. Combined mass = 6 + 2 = 8 kg, so v = 288 ÷ 8 = 36 m/s.
12. A 2 kg cart moving at 36 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 m/s
Total momentum before collision p = 2 × 36 = 72 kg·m/s. Combined mass = 2 + 10 = 12 kg, so v = 72 ÷ 12 = 6 m/s.

12 questions · Seed 49 · Age guidance, not curriculum certification