Conservation of momentum

In all isolated systems, total momentum is conserved:

`vec p_"tot" = vec p'_"tot"`.


Car A (2.5 kg) begins at 1.5 m/s [fwd], while Car B (1.5 kg) beings at rest. Car A collides into Car B, and they stick together. What is the velocity of AB after the collision?

We begin with the conservation of momentum,

`vec p_"tot" = vec p'_"tot"`,

into which we substitute the individual momenta:

`vec p_"A" + vec p_"B" = vec p'_"AB"`.

Now we can substitute the masses and velocities with

`m_"A"vec v_"A" + m_"B"vec v_"B" = m_"AB"vec v'_"AB"`,

and solve for the final velocity:

`vec v'_"AB" = (m_"A"vec v_"A" + m_"B"vec v_"B")/m_"AB"`.

Substituting the known values where [fwd] is positive, we have

`vec v'_"AB" = ((2.5\ "kg")(1.5\ "m/s") - 0)/(2.5\ "kg" + 1.5\ "kg") = 0.9375\ "m/s"`,

therefore the final velocity is 0.94 m/s [fwd].

This was a simple one-dimensional case. You will also need to solve two-dimensional conservation of momentum problems using vector charts.