6. A particle of mass m traveling at a relativistic speed...

Name: 6. A particle of mass m traveling at a relativistic speed makes a completely inelastic collision with an identical particle that is initially at rest. Find (a) the speed of the resulting single particle and (b) its mass. Express your answers in terms of the Lorentz factor ? of the incident particle.
Uploaded: 2022-04-17T17:47:08-08:00
Duration: 6 min 29 s
Channel: Sri K
Description: 6. A particle of mass m traveling at a relativistic speed makes a completely inelastic collision with an identical particle that is initially at rest. Find (a) the speed of the resulting single particle and (b) its mass. Express your answers in terms of the Lorentz factor ? of the incident particle.

6. A particle of mass m traveling at a relativistic speed makes a completely inelastic collision with an identical particle that is initially at rest. Find (a) the speed of the resulting single particle and (b) its mass. Express your answers in terms of the Lorentz factor ? of the incident particle.

Transcript

00:02 Hello, let us first consider the bit a of the question.

00:04 So in the beta of the question we have to find the speed of the resultant single particle.

00:09 The speed of a resultant single particle that is what we have to find a resultant single particle that is what we have to find over here.

00:21 Now let us consider the mass of the incident particle, the mass of incident particle over here, the incident particle let us consider it is equal to m the velocity of the incident particle the velocity of incident particle let us consider that is equal to v now the lawrence factor gamma gamma can be written as 1 by 1 minus of b square by c square root of it otherwise we can write gamma v that is this v over here the velocity of incident particle can be written as it is equal to c gamma square minus 1 hold to the power half let us consider this is equation 1 now the initial momentum of the particle let us consider the initial momentum of the system the initial momentum of the system or the two particle system here pi that equals gamma mv plus m multiplied 0 because the second particle is at rest so we can write it as m gamma v or that can be written as m multiplied c gamma square minus 1 hold to the power half using 1 that is equation 1 we can write this.

01:28 So this is the initial momentum of the two particles.

01:31 The initial energy let us consider of the two particles the initial energy.

01:35 Now let us consider initial energy is ei.

01:38 So we can write ei equals to mc square plus gamma mc square.

01:43 So we can write it as mc square 1 plus gamma.

01:47 So that is the initial energy of the two particle system...