Which equation expresses momentum conservation for a two-body collision in one dimension?

Which equation expresses momentum conservation for a two-body collision in one dimension?

• A. m1 v1 + m2 v2 = m1 v3 + m2 v4
• B. m1 v1 = m1 v3
• C. m1 v1 + m2 v2 = m1 v3 + m2 v4
• D. m1 v1 - m2 v2 = m1 v3 - m2 v4

Answer: (C)

Momentum in a closed system stays the same, so the total momentum before a collision must equal the total momentum after. In one dimension this means summing the momenta of both objects along that axis: m1 v1 + m2 v2 before equals m1 v3 + m2 v4 after. This expression directly encodes conservation of momentum for a two-body collision. Other forms drop one term or use a different combination of signs, which does not represent the total momentum being conserved for the whole system.

Momentum in a closed system stays the same, so the total momentum before a collision must equal the total momentum after. In one dimension this means summing the momenta of both objects along that axis: m1 v1 + m2 v2 before equals m1 v3 + m2 v4 after. This expression directly encodes conservation of momentum for a two-body collision. Other forms drop one term or use a different combination of signs, which does not represent the total momentum being conserved for the whole system.