Physics / Unit 6: Momentum and Collisions
6.4 Conservation of Momentum
Notes
Law of conservation of momentum: in a closed system with no outside net force, the total momentum before an event equals the total momentum after.
- $m_1v_{1i} + m_2v_{2i} = m_1v_{1f} + m_2v_{2f}$
- This works because of Newton's third law: the two objects push on each other with equal and opposite forces for the same time, so their momentum changes cancel.
- Remember signs: velocities in opposite directions have opposite signs.
- Example: a 2 kg cart at $3 \text{ m/s}$ hits a 1 kg cart at rest and they stick: $6 = 3v$, so $v = 2 \text{ m/s}$.
Practice
A 1,000 kg car moving at $20 \text{ m/s}$ hits a 3,000 kg truck at rest, and they lock together. What is their speed just after?
$1000 \times 20 = 4000v \Rightarrow v = 5 \text{ m/s}$.
Why is momentum conserved when two pool balls collide?
Newton's third law gives equal and opposite impulses.
Two 2 kg carts move toward each other, each at $3 \text{ m/s}$. They collide and stick. What is their final velocity?
Total momentum $= 2(3) + 2(-3) = 0$, so the stuck carts are at rest.
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