Conserve momentum in a one-dimensional model
The idea
Choose a positive direction and calculate total initial momentum as the sum of mass × signed velocity.
Step by step
- Choose a positive direction and calculate total initial momentum as the sum of mass × signed velocity.
- When external impulse is negligible, total momentum is conserved.
- If objects stick together, divide total momentum by combined mass; kinetic energy need not be conserved.
Example
A 2 kg cart at +6 m/s sticks to a stationary 4 kg cart. External impulse is negligible. What is their shared final velocity?
Answer
2 m/s
Initial momentum = 2 × 6 = 12 kg·m/s; combined mass = 6 kg; v = 12 ÷ 6 = +2 m/s.
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Model two carts with signed arrows before and after they stick. Explain why the shared velocity uses total mass.
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