(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known dataThis problem was given in the 2008 United States Physics Team qualifying test, called the F=ma Contest:

21. Consider a particle at rest which may decay into two (daughter) particles or into three (daughter) particles. Which of the following is true in the two-body case but false in the three-body case? (There are no external forces.)

A. The velocity vectors of the daughter particles must lie in a single plane.

B. Given the total kinetic energy of the system and the mass of each daughter particle, it is possible to determine the speed of each daughter particle.

C. Given the speed(s) of all but one daughter particle, it is possible to determine the speed of each daughter particle.

D. The total momentum of the daughter particles is zero.

E. None of the above.

2. Relevant equations[tex]\sum \vec{p}=0[/tex]

3. The attempt at a solutionIn the two-body case, A is definitely true because the velocities of the daughter particles must lie on the same line. In the three body case, the velocity of any of the three daughter particles can be written as a linear combination of the other two. Since the set of all linear combinations of a set of two vectors is a plane, the velocity vectors must all lie on the same plane. Since A holds for both cases, it is not the right answer.

Since D obviously holds for both cases, it is also not the right answer. That leaves B, C, and E. I am not sure where to proceed.

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# Homework Help: US Physics Test Problem

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