Chapter 38, Problem 40P

An unstable particle with mass m = 3.34 × 10⁻²⁷ kg is initially at rest. The particle decays into two fragments that fly off along the x axis with velocity components u₁ = 0.987c and u₂ = −0.868c. From this information, we wish to determine the masses of fragments 1 and 2. (a) Is the initial system of the unstable particle, which becomes the system of the two fragments, isolated or nonisolated? (b) Based on your answer to part (a), what two analysis models are appropriate for this situation? (c) Find the values of γ for the two fragments after the decay. (d) Using one of the analysis models in part (b), find a relationship between the masses m₁ and m₂ of the fragments. (e) Using the second analysis model in part (b). find a second relationship between the masses m₁ and m₂. (f) Solve the relationships in parts (d) and (c) simultaneously for the masses m₁ and m₂.