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.

An object of mass 2 kg travelling in a straight line with a velocity of 20m/sec collides with, and strikes to, a stationary object of mass 3 kg. They both move off together in the same straight line with a velocity of v m/sec. If no external forces are acting calculate
a. the total momentum just before the impact
b. the tot

Question: A 50 kg cart is moving across a friction-less floor at 2 m/s. A 70 kg boy, riding the cart, jumps off so that he hits the floor with zero velocity.
1. What impulse did the boy give to the cart?
2. What was the velocity of the cart after the boy jumped?

1. There are three main frames - top, middle, and bottom as indicated above with the three rows. The top frame has a table with three columns. The middle frame is divided into two frames. The bottom frame is the hot links frame. You may replace the frames with tables i.e. instead of frames, use tables throughout.
** You may u

In an inelastic collision, is the final total momentum more than the initial momentum, less than the initial momentum or is it the same as the initial momentum?

If two objects collide and one is initially at rest, answer the following (ignore any frictional effects):
a) Is it possible for both of them to be at rest after the collision?
b) Is it possible for one of them to be at rest after the collision?
c) Under what condition is their total energy conserved?

A group of stations share a 16 kbps slotted Aloha channel. Each station outputs a 80 Bytes frame and buffers any outgoing frames until they can be sent. Collectively (recall that this means original frames plus resending of frames that suffered a collision previously) the stations attempt to send 30 frames/sec. What is the throu

Please help in understanding how to create frames using Dreamweaver. It was noticed for instance when creating a web page called index.html with frames in it, every time when trying to open the index.html for editing it does not open up but presents the frames instead. Therefore, how do you go back to the original index page and

The expected value of the momentum operator in quantum mechanics can be calculated using the spatial wave function. Using that the momentum wave function is the Fourier transform of the spatial wave function we obtain an expression for this expected value in term of the momentum wave function, that is, we prove the Equation 15.6

Angular Momentum. See attached file for full problem description.
A 1.5 kg particle moves in the xy plane with velocity = (4.2i - 3.6j)m/s. What is the angular momentum of the particle when its position vector is r = 1.5i + 2.2j m