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 10 kg cart moving at 52 m/s collides with and couples to a stationary 3 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
10 kg (52 m/s) → [3 kg] → Coupled: (13 kg) v = ? · m₁u₁ = (m₁ + m₂)v
2. A 7 kg cart moving at 80 m/s collides with and couples to a stationary 3 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
7 kg (80 m/s) → [3 kg] → Coupled: (10 kg) v = ? · m₁u₁ = (m₁ + m₂)v
3. A 8 kg cart moving at 54 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 (54 m/s) → [10 kg] → Coupled: (18 kg) v = ? · m₁u₁ = (m₁ + m₂)v
4. A 4 kg cart moving at 54 m/s collides with and couples to a stationary 5 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
4 kg (54 m/s) → [5 kg] → Coupled: (9 kg) v = ? · m₁u₁ = (m₁ + m₂)v
5. A 5 kg cart moving at 63 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 (63 m/s) → [4 kg] → Coupled: (9 kg) v = ? · m₁u₁ = (m₁ + m₂)v
6. A 7 kg cart moving at 51 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 (51 m/s) → [10 kg] → Coupled: (17 kg) v = ? · m₁u₁ = (m₁ + m₂)v
7. A 8 kg cart moving at 16 m/s collides with and couples to a stationary 8 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
8 kg (16 m/s) → [8 kg] → Coupled: (16 kg) v = ? · m₁u₁ = (m₁ + m₂)v
8. A 7 kg cart moving at 91 m/s collides with and couples to a stationary 6 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
7 kg (91 m/s) → [6 kg] → Coupled: (13 kg) v = ? · m₁u₁ = (m₁ + m₂)v
9. A 7 kg cart moving at 14 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 (14 m/s) → [7 kg] → Coupled: (14 kg) v = ? · m₁u₁ = (m₁ + m₂)v
10. A 8 kg cart moving at 28 m/s collides with and couples to a stationary 6 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
8 kg (28 m/s) → [6 kg] → Coupled: (14 kg) v = ? · m₁u₁ = (m₁ + m₂)v
11. A 8 kg cart moving at 144 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 (144 m/s) → [10 kg] → Coupled: (18 kg) v = ? · m₁u₁ = (m₁ + m₂)v
12. A 4 kg cart moving at 49 m/s collides with and couples to a stationary 3 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
4 kg (49 m/s) → [3 kg] → Coupled: (7 kg) v = ? · m₁u₁ = (m₁ + m₂)v

12 questions · Seed 104737 · 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 10 kg cart moving at 52 m/s collides with and couples to a stationary 3 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
40 m/s
Total momentum before collision p = 10 × 52 = 520 kg·m/s. Combined mass = 10 + 3 = 13 kg, so v = 520 ÷ 13 = 40 m/s.
2. A 7 kg cart moving at 80 m/s collides with and couples to a stationary 3 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
56 m/s
Total momentum before collision p = 7 × 80 = 560 kg·m/s. Combined mass = 7 + 3 = 10 kg, so v = 560 ÷ 10 = 56 m/s.
3. A 8 kg cart moving at 54 m/s collides with and couples to a stationary 10 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
24 m/s
Total momentum before collision p = 8 × 54 = 432 kg·m/s. Combined mass = 8 + 10 = 18 kg, so v = 432 ÷ 18 = 24 m/s.
4. A 4 kg cart moving at 54 m/s collides with and couples to a stationary 5 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
24 m/s
Total momentum before collision p = 4 × 54 = 216 kg·m/s. Combined mass = 4 + 5 = 9 kg, so v = 216 ÷ 9 = 24 m/s.
5. A 5 kg cart moving at 63 m/s collides with and couples to a stationary 4 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
35 m/s
Total momentum before collision p = 5 × 63 = 315 kg·m/s. Combined mass = 5 + 4 = 9 kg, so v = 315 ÷ 9 = 35 m/s.
6. A 7 kg cart moving at 51 m/s collides with and couples to a stationary 10 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
21 m/s
Total momentum before collision p = 7 × 51 = 357 kg·m/s. Combined mass = 7 + 10 = 17 kg, so v = 357 ÷ 17 = 21 m/s.
7. A 8 kg cart moving at 16 m/s collides with and couples to a stationary 8 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
8 m/s
Total momentum before collision p = 8 × 16 = 128 kg·m/s. Combined mass = 8 + 8 = 16 kg, so v = 128 ÷ 16 = 8 m/s.
8. A 7 kg cart moving at 91 m/s collides with and couples to a stationary 6 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
49 m/s
Total momentum before collision p = 7 × 91 = 637 kg·m/s. Combined mass = 7 + 6 = 13 kg, so v = 637 ÷ 13 = 49 m/s.
9. A 7 kg cart moving at 14 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 m/s
Total momentum before collision p = 7 × 14 = 98 kg·m/s. Combined mass = 7 + 7 = 14 kg, so v = 98 ÷ 14 = 7 m/s.
10. A 8 kg cart moving at 28 m/s collides with and couples to a stationary 6 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
16 m/s
Total momentum before collision p = 8 × 28 = 224 kg·m/s. Combined mass = 8 + 6 = 14 kg, so v = 224 ÷ 14 = 16 m/s.
11. A 8 kg cart moving at 144 m/s collides with and couples to a stationary 10 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
64 m/s
Total momentum before collision p = 8 × 144 = 1152 kg·m/s. Combined mass = 8 + 10 = 18 kg, so v = 1152 ÷ 18 = 64 m/s.
12. A 4 kg cart moving at 49 m/s collides with and couples to a stationary 3 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
28 m/s
Total momentum before collision p = 4 × 49 = 196 kg·m/s. Combined mass = 4 + 3 = 7 kg, so v = 196 ÷ 7 = 28 m/s.

12 questions · Seed 104737 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 13-15

Conservation of momentum in collisions

Take your time. Show your thinking.

1. A 10 kg cart moving at 52 m/s collides with and couples to a stationary 3 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
10 kg (52 m/s) → [3 kg] → Coupled: (13 kg) v = ? · m₁u₁ = (m₁ + m₂)v
2. A 7 kg cart moving at 80 m/s collides with and couples to a stationary 3 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
7 kg (80 m/s) → [3 kg] → Coupled: (10 kg) v = ? · m₁u₁ = (m₁ + m₂)v
3. A 8 kg cart moving at 54 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 (54 m/s) → [10 kg] → Coupled: (18 kg) v = ? · m₁u₁ = (m₁ + m₂)v
4. A 4 kg cart moving at 54 m/s collides with and couples to a stationary 5 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
4 kg (54 m/s) → [5 kg] → Coupled: (9 kg) v = ? · m₁u₁ = (m₁ + m₂)v
5. A 5 kg cart moving at 63 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 (63 m/s) → [4 kg] → Coupled: (9 kg) v = ? · m₁u₁ = (m₁ + m₂)v
6. A 7 kg cart moving at 51 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 (51 m/s) → [10 kg] → Coupled: (17 kg) v = ? · m₁u₁ = (m₁ + m₂)v
7. A 8 kg cart moving at 16 m/s collides with and couples to a stationary 8 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
8 kg (16 m/s) → [8 kg] → Coupled: (16 kg) v = ? · m₁u₁ = (m₁ + m₂)v
8. A 7 kg cart moving at 91 m/s collides with and couples to a stationary 6 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
7 kg (91 m/s) → [6 kg] → Coupled: (13 kg) v = ? · m₁u₁ = (m₁ + m₂)v
9. A 7 kg cart moving at 14 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 (14 m/s) → [7 kg] → Coupled: (14 kg) v = ? · m₁u₁ = (m₁ + m₂)v
10. A 8 kg cart moving at 28 m/s collides with and couples to a stationary 6 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
8 kg (28 m/s) → [6 kg] → Coupled: (14 kg) v = ? · m₁u₁ = (m₁ + m₂)v
11. A 8 kg cart moving at 144 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 (144 m/s) → [10 kg] → Coupled: (18 kg) v = ? · m₁u₁ = (m₁ + m₂)v
12. A 4 kg cart moving at 49 m/s collides with and couples to a stationary 3 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
4 kg (49 m/s) → [3 kg] → Coupled: (7 kg) v = ? · m₁u₁ = (m₁ + m₂)v

12 questions · Seed 104737 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 13-15

Conservation of momentum in collisions

Answers and reasoning. Review before teaching.

1. A 10 kg cart moving at 52 m/s collides with and couples to a stationary 3 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
40 m/s
Total momentum before collision p = 10 × 52 = 520 kg·m/s. Combined mass = 10 + 3 = 13 kg, so v = 520 ÷ 13 = 40 m/s.
2. A 7 kg cart moving at 80 m/s collides with and couples to a stationary 3 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
56 m/s
Total momentum before collision p = 7 × 80 = 560 kg·m/s. Combined mass = 7 + 3 = 10 kg, so v = 560 ÷ 10 = 56 m/s.
3. A 8 kg cart moving at 54 m/s collides with and couples to a stationary 10 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
24 m/s
Total momentum before collision p = 8 × 54 = 432 kg·m/s. Combined mass = 8 + 10 = 18 kg, so v = 432 ÷ 18 = 24 m/s.
4. A 4 kg cart moving at 54 m/s collides with and couples to a stationary 5 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
24 m/s
Total momentum before collision p = 4 × 54 = 216 kg·m/s. Combined mass = 4 + 5 = 9 kg, so v = 216 ÷ 9 = 24 m/s.
5. A 5 kg cart moving at 63 m/s collides with and couples to a stationary 4 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
35 m/s
Total momentum before collision p = 5 × 63 = 315 kg·m/s. Combined mass = 5 + 4 = 9 kg, so v = 315 ÷ 9 = 35 m/s.
6. A 7 kg cart moving at 51 m/s collides with and couples to a stationary 10 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
21 m/s
Total momentum before collision p = 7 × 51 = 357 kg·m/s. Combined mass = 7 + 10 = 17 kg, so v = 357 ÷ 17 = 21 m/s.
7. A 8 kg cart moving at 16 m/s collides with and couples to a stationary 8 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
8 m/s
Total momentum before collision p = 8 × 16 = 128 kg·m/s. Combined mass = 8 + 8 = 16 kg, so v = 128 ÷ 16 = 8 m/s.
8. A 7 kg cart moving at 91 m/s collides with and couples to a stationary 6 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
49 m/s
Total momentum before collision p = 7 × 91 = 637 kg·m/s. Combined mass = 7 + 6 = 13 kg, so v = 637 ÷ 13 = 49 m/s.
9. A 7 kg cart moving at 14 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 m/s
Total momentum before collision p = 7 × 14 = 98 kg·m/s. Combined mass = 7 + 7 = 14 kg, so v = 98 ÷ 14 = 7 m/s.
10. A 8 kg cart moving at 28 m/s collides with and couples to a stationary 6 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
16 m/s
Total momentum before collision p = 8 × 28 = 224 kg·m/s. Combined mass = 8 + 6 = 14 kg, so v = 224 ÷ 14 = 16 m/s.
11. A 8 kg cart moving at 144 m/s collides with and couples to a stationary 10 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
64 m/s
Total momentum before collision p = 8 × 144 = 1152 kg·m/s. Combined mass = 8 + 10 = 18 kg, so v = 1152 ÷ 18 = 64 m/s.
12. A 4 kg cart moving at 49 m/s collides with and couples to a stationary 3 kg cart on a frictionless track. Find their shared velocity immediately after the collision.
28 m/s
Total momentum before collision p = 4 × 49 = 196 kg·m/s. Combined mass = 4 + 3 = 7 kg, so v = 196 ÷ 7 = 28 m/s.

12 questions · Seed 104737 · Age guidance, not curriculum certification