Physics · Grades 10–12
Objects stick together
For this isolated collision momentum is conserved; kinetic energy generally is not.
Rule and assumptions
For this isolated collision momentum is conserved; kinetic energy generally is not.
v = (m₁u₁ + m₂u₂)/(m₁ + m₂)
Worked examples
Carts 14 kg at 7 m/s and 9 kg at -3 m/s collide and stick. Velocities share one signed axis; external impulse is zero. Find their final velocity. Round to 3 decimal places if needed. Answer in m/s.
v = (m₁u₁ + m₂u₂)/(m₁ + m₂) (14 × 7 + 9 × (-3)) / (14 + 9) = 3.087
3.087 m/s
Carts 15 kg at 17 m/s and 3 kg at -4 m/s collide and stick. Velocities share one signed axis; external impulse is zero. Find their final velocity. Round to 3 decimal places if needed. Answer in m/s.
v = (m₁u₁ + m₂u₂)/(m₁ + m₂) (15 × 17 + 3 × (-4)) / (15 + 3) = 13.5
13.5 m/s
Try two questions
Carts 7 kg at 2 m/s and 8 kg at -2 m/s collide and stick. Velocities share one signed axis; external impulse is zero. Find their final velocity. Round to 3 decimal places if needed. Answer in m/s.
Carts 12 kg at 4 m/s and 7 kg at 1 m/s collide and stick. Velocities share one signed axis; external impulse is zero. Find their final velocity. Round to 3 decimal places if needed. Answer in m/s.
Answers and reasoning
Answers and marking notes
- -0.133 m/s
v = (m₁u₁ + m₂u₂)/(m₁ + m₂) (7 × 2 + 8 × (-2)) / (7 + 8) = -0.133
- 2.895 m/s
v = (m₁u₁ + m₂u₂)/(m₁ + m₂) (12 × 4 + 7 × (1)) / (12 + 7) = 2.895
Further reading and review references
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Learning preview · independent educational and translation review required. Suggested grades are not official curriculum alignment.