Measuring Mass

Consider the inelastic collision shown above. Conservation of momentum demands that

Divide through by m₁ to get

where a₂ � m₂/m₁ and a₃ � m₃/m₁ are mass ratios. Taking the dot product of Eq. (2) with u₁ yields

 Taking the dot product of Eq. (2) with u₂ yields

Letting   Eqs. (3) and (4) become

Solving Eq. (5a) for the a‘s gives

Substituting Eq. (6b) into Eq. (6a) gives

  Substituting Eq. (7) into Eq. (6b)