Conservation of momentum with direction
Momentum is a vector — pick a positive direction and keep the signs.
The common mistake
Adding momenta as positive numbers when the objects move in opposite directions.
Instead: Choose one direction as positive before you start. Anything moving the other way gets a negative velocity. Total momentum before equals total momentum after, signs included.
Worked example with Guide me
A 2 kg cart at 3 m/s right hits a 1 kg cart at 4 m/s left. They stick. Final velocity?
- Sugar · Take right as positive. What's each momentum?Student · 2 × 3 = 6, and 1 × −4 = −4.
- Sugar · What's the total momentum?Student · 6 − 4 = 2 kg·m/s.
- Sugar · They move together as 3 kg. What's v?Student · 2 ÷ 3 ≈ 0.67 m/s.
Answer: About 0.67 m/s to the right.
Try 3 practice questions
1. A 3 kg ball at 2 m/s right and a 3 kg ball at 2 m/s left collide and stick. Final velocity?
2. What is the momentum of a 5 kg object at −4 m/s?
3. A 4 kg cart at 5 m/s hits a stationary 1 kg cart and they stick. Final speed?
Quick answers
- What is the most common mistake with conservation of momentum with direction?
- Adding momenta as positive numbers when the objects move in opposite directions.
- How do I get conservation of momentum with direction right?
- Choose one direction as positive before you start. Anything moving the other way gets a negative velocity. Total momentum before equals total momentum after, signs included.
- Can you show a worked example?
- A 2 kg cart at 3 m/s right hits a 1 kg cart at 4 m/s left. They stick. Final velocity? About 0.67 m/s to the right.
Related concepts
Save this as a miss — practice it before your test
Sugar brings it back for review until it sticks. Free, no card.
Save this as a miss — practice it before your test