A pion of mass m moves with a speed u in the positive y direction in frame S with parametrs BETAu = u/c and GAMMAu = (1 - BETAu^2)^-1/2. The pion decays into two gammay rays. An observer S' moves in the positive x direction with speed v = (BETA)(c) [this is a different BETA and GAMMA than before] and detects the two photons.

A. Compute the sum of the x components of momentum in S' for the photons.
ANSWER: Px' = -(GAMMA)(GAMMAu)(BETA)mc
B. Compute the combined energy of the two photons in S'.
ANSWER: E' = (GAMMA)(GAMMAu)mc^2

Solution Preview

Since this decay of a pion into two photons conserves the 4-momentum, the sum of the 4-momenta of the photons (and therefore the sum of their energies as well as the sum of any component of their 3-momenta) are exactly the same as the 4-momentum of the original pion.

Therefore the answers to these questions are exactly the same as if they were asked for the original pion

In frame S, the 4-momentum of the original pion is

p1 = m1*gamma1*c*(1, 0, beta1, 0)

The 4-momentum of the observer (we give it a temporary mass m2 which will not enter the answer anyway) is
...

Solution Summary

The solution shows how to compute the sum of different momentums and combined energies in a system of four momentums.

... Isotopes of an element have the same number of _____ but different numbers of _____ ... 5. For an orbital angular momentum quantum number of 4, what is ...

... to Bob, the lights come on at different times, 45 ... he calls time 0. Then in his frame, we have ... problem can be solved by applying conservation of four-momentum. ...

... now assume that Kronecker delta in a different coordinate system ... particles having 4-momentum P µ = (E/c, P ) toward ... has the same value in all frames, given by. ...

...4. Fission the process that supplies energy in nuclear power plants occur when ... 6 different type of problems related to conservation of momentum and energy ...

... will stay constant due to conservation of momentum, the total ... 1/2 k (delta L)^2 = 1/4 M u^2 ... classical mechanics problem from first principles in different ways ...

... Comment on the different emphasis between your abstract ... Although the above four features mentioned are they ... key disadvantage of maintaining the momentum of the ...

... is mitigated by the general upward momentum of the ... how these hypotheses relate to two different situations: 1 ... be the average of two consecutive four-year rates ...

... and the change had occurred, what would be different? ... to create a shift or stop momentum, most times ... Rollnick organize this talk into four categories: problem ...

... Every point on the rim of the wheel has a different velocity. ... Ï/4. Ï/2. ... As no external force of torque is there, the angular momentum remains conserved. ...

... change managers are likely to experienceand Chapter 4 identifies key ... of coaching and encouraging others and building momentum is a different style of pro ...