Total momentum is conserved for a chosen system when external impulse is negligible over the interaction. In one dimension, add signed momenta before and after: m1u1+m2u2=m1v1+m2v2. Internal forces are equal and opposite, so their impulses cancel for the whole system. They can still change each object’s momentum.
If two objects stick together, use one shared final velocity and the combined mass. In an explosion or recoil from rest, final momenta sum to zero, not final speeds. An elastic collision conserves total kinetic energy as well as momentum; an inelastic collision does not conserve kinetic energy, although total energy remains conserved. State external-force assumptions before applying momentum conservation.
Example 1
A 2.0kg cart at+3.0m/s sticks to a stationary 1.0kg cart. Neglect external impulse. Find final velocity.
Initial momentum =2×3+1×0=6kgm/s. Combined mass =3kg. v=36=+2.0m/s.
Example 2
A system initially at rest separates into a 2.0kg part at+6.0m/s and a 3.0kg part. Neglect external impulse. Find the second velocity.
0=2×6+3v, so v=−4.0m/s. The parts have opposite equal momenta, not equal speeds.
Watch out: Momentum conservation requires negligible external impulse. Kinetic energy is additionally conserved only for an elastic collision.