Two carts collide on a track. Before the crash, cart A carries 8.0 kg·m/s and cart B carries 2.0 kg·m/s, both rightward. The crash is violent: the carts bang and change speeds. After it, A carries 4.0 kg·m/s and B carries 6.0 kg·m/s. Something about the pair did not change.
Totals are the thing to track. Total the pair before; total the pair after.
Take rightward as positive, so every momentum here is positive.
Before the crash, the total is 8.0 + 2.0 = 10 kg·m/s.
After the crash, the total is 4.0 + 6.0 = 10 kg·m/s. The total is the same number.
Each cart's own momentum changed. Cart A lost 4.0 kg·m/s, and cart B gained 4.0 kg·m/s. The trade moved momentum between the carts and left the total alone.
When the total of a quantity for a system stays the same over time, we say the quantity is conserved.
Conserved is a claim about the system's total, never about one object. Cart A's momentum changed; the system's total momentum was conserved.
Take rightward as positive. A two-glider system has total momentum +12 kg·m/s before the gliders collide and +12 kg·m/s after. Was the system's momentum conserved?
A total that changes is not conserved. If the after-total had come out at 9 kg·m/s, the crash would not have conserved momentum.
Take rightward as positive. A two-cart system has total momentum +9.5 kg·m/s before a collision and +7.5 kg·m/s after. Was the system's momentum conserved?
A system's total momentum measures +15 kg·m/s before an interaction, +15 kg·m/s during it, and +15 kg·m/s after it. Was the system's momentum conserved?
The total stayed at +15 kg·m/s at every measured time.
A quantity whose total for the system stays the same over time is conserved.
Yes. The system's momentum was conserved.
In the same interaction, one object's momentum fell from +9.0 kg·m/s to +5.0 kg·m/s. Does that mean momentum was not conserved?
Conserved is a claim about the system's total, never about one object.
The system's total stayed at +15 kg·m/s even while this object's momentum fell.
No. One object's change says nothing about the total. The total stayed the same, so momentum was conserved.
Lando says: in a collision each cart's momentum changed, but the total for the two-cart system stayed the same, so the system's momentum was conserved. Is he correct?
Take rightward as positive. During a collision, cart A's momentum drops from +14 kg·m/s to +10 kg·m/s. A student concludes that the two-cart system's momentum was not conserved. Which statement is correct?
Take rightward as positive. A box slides into a second box on a rough floor. The two-box system's total momentum is +6.5 kg·m/s before the collision and +5.0 kg·m/s after it. Which statement is correct?
When the total of a quantity for a system stays the same over time, what do we say about that quantity?