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 3 kg cart moving at 30 m/s collides with and couples to a stationary 7 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
3 kg (30 m/s) → [7 kg] → Coupled: (10 kg) v = ? · m₁u₁ = (m₁ + m₂)v
2. A 6 kg cart moving at 45 m/s collides with and couples to a stationary 9 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
6 kg (45 m/s) → [9 kg] → Coupled: (15 kg) v = ? · m₁u₁ = (m₁ + m₂)v
3. A 5 kg cart moving at 75 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 (75 m/s) → [10 kg] → Coupled: (15 kg) v = ? · m₁u₁ = (m₁ + m₂)v
4. A 10 kg cart moving at 12 m/s collides with and couples to a stationary 2 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
10 kg (12 m/s) → [2 kg] → Coupled: (12 kg) v = ? · m₁u₁ = (m₁ + m₂)v
5. A 8 kg cart moving at 44 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 (44 m/s) → [3 kg] → Coupled: (11 kg) v = ? · m₁u₁ = (m₁ + m₂)v
6. A 5 kg cart moving at 49 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 (49 m/s) → [2 kg] → Coupled: (7 kg) v = ? · m₁u₁ = (m₁ + m₂)v
7. A 5 kg cart moving at 39 m/s collides with and couples to a stationary 8 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
5 kg (39 m/s) → [8 kg] → Coupled: (13 kg) v = ? · m₁u₁ = (m₁ + m₂)v
8. 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
9. A 10 kg cart moving at 85 m/s collides with and couples to a stationary 7 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
10 kg (85 m/s) → [7 kg] → Coupled: (17 kg) v = ? · m₁u₁ = (m₁ + m₂)v
10. A 7 kg cart moving at 17 m/s collides with and couples to a stationary 10 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
7 kg (17 m/s) → [10 kg] → Coupled: (17 kg) v = ? · m₁u₁ = (m₁ + m₂)v
11. A 2 kg cart moving at 33 m/s collides with and couples to a stationary 9 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
2 kg (33 m/s) → [9 kg] → Coupled: (11 kg) v = ? · m₁u₁ = (m₁ + m₂)v
12. A 2 kg cart moving at 5 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 (5 m/s) → [3 kg] → Coupled: (5 kg) v = ? · m₁u₁ = (m₁ + m₂)v

12 questions · Seed 43 · 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 3 kg cart moving at 30 m/s collides with and couples to a stationary 7 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
9 m/s
Total momentum before collision p = 3 × 30 = 90 kg·m/s. Combined mass = 3 + 7 = 10 kg, so v = 90 ÷ 10 = 9 m/s.
2. A 6 kg cart moving at 45 m/s collides with and couples to a stationary 9 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
18 m/s
Total momentum before collision p = 6 × 45 = 270 kg·m/s. Combined mass = 6 + 9 = 15 kg, so v = 270 ÷ 15 = 18 m/s.
3. A 5 kg cart moving at 75 m/s collides with and couples to a stationary 10 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
25 m/s
Total momentum before collision p = 5 × 75 = 375 kg·m/s. Combined mass = 5 + 10 = 15 kg, so v = 375 ÷ 15 = 25 m/s.
4. A 10 kg cart moving at 12 m/s collides with and couples to a stationary 2 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
10 m/s
Total momentum before collision p = 10 × 12 = 120 kg·m/s. Combined mass = 10 + 2 = 12 kg, so v = 120 ÷ 12 = 10 m/s.
5. A 8 kg cart moving at 44 m/s collides with and couples to a stationary 3 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
32 m/s
Total momentum before collision p = 8 × 44 = 352 kg·m/s. Combined mass = 8 + 3 = 11 kg, so v = 352 ÷ 11 = 32 m/s.
6. A 5 kg cart moving at 49 m/s collides with and couples to a stationary 2 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
35 m/s
Total momentum before collision p = 5 × 49 = 245 kg·m/s. Combined mass = 5 + 2 = 7 kg, so v = 245 ÷ 7 = 35 m/s.
7. A 5 kg cart moving at 39 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 = 5 × 39 = 195 kg·m/s. Combined mass = 5 + 8 = 13 kg, so v = 195 ÷ 13 = 15 m/s.
8. 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.
9. A 10 kg cart moving at 85 m/s collides with and couples to a stationary 7 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
50 m/s
Total momentum before collision p = 10 × 85 = 850 kg·m/s. Combined mass = 10 + 7 = 17 kg, so v = 850 ÷ 17 = 50 m/s.
10. A 7 kg cart moving at 17 m/s collides with and couples to a stationary 10 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
7 m/s
Total momentum before collision p = 7 × 17 = 119 kg·m/s. Combined mass = 7 + 10 = 17 kg, so v = 119 ÷ 17 = 7 m/s.
11. A 2 kg cart moving at 33 m/s collides with and couples to a stationary 9 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
6 m/s
Total momentum before collision p = 2 × 33 = 66 kg·m/s. Combined mass = 2 + 9 = 11 kg, so v = 66 ÷ 11 = 6 m/s.
12. A 2 kg cart moving at 5 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 m/s
Total momentum before collision p = 2 × 5 = 10 kg·m/s. Combined mass = 2 + 3 = 5 kg, so v = 10 ÷ 5 = 2 m/s.

12 questions · Seed 43 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 13-15

Conservation of momentum in collisions

Take your time. Show your thinking.

1. A 3 kg cart moving at 30 m/s collides with and couples to a stationary 7 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
3 kg (30 m/s) → [7 kg] → Coupled: (10 kg) v = ? · m₁u₁ = (m₁ + m₂)v
2. A 6 kg cart moving at 45 m/s collides with and couples to a stationary 9 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
6 kg (45 m/s) → [9 kg] → Coupled: (15 kg) v = ? · m₁u₁ = (m₁ + m₂)v
3. A 5 kg cart moving at 75 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 (75 m/s) → [10 kg] → Coupled: (15 kg) v = ? · m₁u₁ = (m₁ + m₂)v
4. A 10 kg cart moving at 12 m/s collides with and couples to a stationary 2 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
10 kg (12 m/s) → [2 kg] → Coupled: (12 kg) v = ? · m₁u₁ = (m₁ + m₂)v
5. A 8 kg cart moving at 44 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 (44 m/s) → [3 kg] → Coupled: (11 kg) v = ? · m₁u₁ = (m₁ + m₂)v
6. A 5 kg cart moving at 49 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 (49 m/s) → [2 kg] → Coupled: (7 kg) v = ? · m₁u₁ = (m₁ + m₂)v
7. A 5 kg cart moving at 39 m/s collides with and couples to a stationary 8 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
5 kg (39 m/s) → [8 kg] → Coupled: (13 kg) v = ? · m₁u₁ = (m₁ + m₂)v
8. 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
9. A 10 kg cart moving at 85 m/s collides with and couples to a stationary 7 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
10 kg (85 m/s) → [7 kg] → Coupled: (17 kg) v = ? · m₁u₁ = (m₁ + m₂)v
10. A 7 kg cart moving at 17 m/s collides with and couples to a stationary 10 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
7 kg (17 m/s) → [10 kg] → Coupled: (17 kg) v = ? · m₁u₁ = (m₁ + m₂)v
11. A 2 kg cart moving at 33 m/s collides with and couples to a stationary 9 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
2 kg (33 m/s) → [9 kg] → Coupled: (11 kg) v = ? · m₁u₁ = (m₁ + m₂)v
12. A 2 kg cart moving at 5 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 (5 m/s) → [3 kg] → Coupled: (5 kg) v = ? · m₁u₁ = (m₁ + m₂)v

12 questions · Seed 43 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 13-15

Conservation of momentum in collisions

Answers and reasoning. Review before teaching.

1. A 3 kg cart moving at 30 m/s collides with and couples to a stationary 7 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
9 m/s
Total momentum before collision p = 3 × 30 = 90 kg·m/s. Combined mass = 3 + 7 = 10 kg, so v = 90 ÷ 10 = 9 m/s.
2. A 6 kg cart moving at 45 m/s collides with and couples to a stationary 9 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
18 m/s
Total momentum before collision p = 6 × 45 = 270 kg·m/s. Combined mass = 6 + 9 = 15 kg, so v = 270 ÷ 15 = 18 m/s.
3. A 5 kg cart moving at 75 m/s collides with and couples to a stationary 10 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
25 m/s
Total momentum before collision p = 5 × 75 = 375 kg·m/s. Combined mass = 5 + 10 = 15 kg, so v = 375 ÷ 15 = 25 m/s.
4. A 10 kg cart moving at 12 m/s collides with and couples to a stationary 2 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
10 m/s
Total momentum before collision p = 10 × 12 = 120 kg·m/s. Combined mass = 10 + 2 = 12 kg, so v = 120 ÷ 12 = 10 m/s.
5. A 8 kg cart moving at 44 m/s collides with and couples to a stationary 3 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
32 m/s
Total momentum before collision p = 8 × 44 = 352 kg·m/s. Combined mass = 8 + 3 = 11 kg, so v = 352 ÷ 11 = 32 m/s.
6. A 5 kg cart moving at 49 m/s collides with and couples to a stationary 2 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
35 m/s
Total momentum before collision p = 5 × 49 = 245 kg·m/s. Combined mass = 5 + 2 = 7 kg, so v = 245 ÷ 7 = 35 m/s.
7. A 5 kg cart moving at 39 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 = 5 × 39 = 195 kg·m/s. Combined mass = 5 + 8 = 13 kg, so v = 195 ÷ 13 = 15 m/s.
8. 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.
9. A 10 kg cart moving at 85 m/s collides with and couples to a stationary 7 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
50 m/s
Total momentum before collision p = 10 × 85 = 850 kg·m/s. Combined mass = 10 + 7 = 17 kg, so v = 850 ÷ 17 = 50 m/s.
10. A 7 kg cart moving at 17 m/s collides with and couples to a stationary 10 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
7 m/s
Total momentum before collision p = 7 × 17 = 119 kg·m/s. Combined mass = 7 + 10 = 17 kg, so v = 119 ÷ 17 = 7 m/s.
11. A 2 kg cart moving at 33 m/s collides with and couples to a stationary 9 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
6 m/s
Total momentum before collision p = 2 × 33 = 66 kg·m/s. Combined mass = 2 + 9 = 11 kg, so v = 66 ÷ 11 = 6 m/s.
12. A 2 kg cart moving at 5 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 m/s
Total momentum before collision p = 2 × 5 = 10 kg·m/s. Combined mass = 2 + 3 = 5 kg, so v = 10 ÷ 5 = 2 m/s.

12 questions · Seed 43 · Age guidance, not curriculum certification