An unstable particle with mass m = 3.71 10-27 kg is initially at rest. The parti

Question

An unstable particle with mass m = 3.71 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 = -0.887c. 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? isolated nonisolated (b) Based on your answer to part (a), what two analysis models are appropriate for this situation? Nonisolated system: conservation of energy Nonisolated system: conservation of momentum Isolated system: conservation of energy Isolated system: conservation of momentum (c) Find the values of ? for the two fragments after the decay. ?1 = ?2 = (d) Using one of the analysis models in part (b), find a relationship between the masses m1 and m2 of the fragments. (Do this on paper. Your instructor may ask you to turn in this work.) (e) Using the second analysis model in part (b), find a second relationship between the masses m1 and m2. (Do this on paper. Your instructor may ask you to turn in this work.) (f) Solve the relationships in parts (d) and (e) simultaneously for the masses m1 and m2. m1 = kg m2 = kg

Explanation / Answer

a) its non isolated system b) Nonisolated system: conservation of energy Nonisolated system: conservation of momentum c) d) momentum conservation m*0 = 0.987c*m1 - 0.887c*m2 or m2 = 1.11m1 but m1+m2 = m = 3.71 10-27 hence 2.11m1= 3.71 x 10-27 or m1 = 1.76 x 10-27 kg m2 = 1.11m1 = 1.95 x 10-27 e) energy difference = 1/2*m1*(0.987c)^2 + 1/2*m2*(-0.887c)^2 = 0.974m1 + 0.787m2 = 3.25 x 10-27 J

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