- #1
m.medhat
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Hello,
I have a two question in relativity from the book”university physics” and the answers of these two questions was found in the end of this book , but the answer of the book do not correspond my answer .
The questions are :-
Kaon production . in high-energy physics , new particles can be created by collisions of fast-moving projectile particles with stationary particles . some of the kinetic energy of the incident particle is used to create the mass of the new particle . A proton – proton collision can result in the creation of a negative kaon (K-) and a positive kaon (K+) :-
Calculate the minimum kinetic energy of the incident proton that will allow this reaction to occur if the second (target) proton is initially at rest . the rest energy of each kaon is 493.7 MeV . the rest energy of each proton is 938.3 MeV . (Hint :- it is useful here to work in the frame in which the total momentum is zero . but note that here the lorentz transformation must be used to relate the velocities in the laboratory frame to those in the zero-total-momentum frame .
The answer of the book = 2494 MeV
While my solution was :-
The kinetic energy for proton equal to the rest energy for new two particles .
The kinetic energy for proton = 493.7+493.7 = 987.4 MeV
Which solution is correct ?why?
The next question is :-
Lorentz transformation for acceleration . find the lorentz transformation equation for velocity . let frame S’ have a constant x-component of velocity (u) relative to frame S . an object moves relative to frame S along the x-axis with instantaneous velocity (vx) and instantaneous acceleration (ax) . show that its instantaneous acceleration in frame S’ is
a’x = ax [(1-v2/c2)^3/2] [(1-uvx/c2)^-3]
(hint :- express the acceleration in S’ as a’x = dv’x / dt’ )
and show that the acceleration in frame S can be expressed as
ax = a’x [(1-v2/c2)^3/2] [(1+uv’x/c2)^-3]
please I want the solution be with steps and fine details .
I have a two question in relativity from the book”university physics” and the answers of these two questions was found in the end of this book , but the answer of the book do not correspond my answer .
The questions are :-
Kaon production . in high-energy physics , new particles can be created by collisions of fast-moving projectile particles with stationary particles . some of the kinetic energy of the incident particle is used to create the mass of the new particle . A proton – proton collision can result in the creation of a negative kaon (K-) and a positive kaon (K+) :-
Calculate the minimum kinetic energy of the incident proton that will allow this reaction to occur if the second (target) proton is initially at rest . the rest energy of each kaon is 493.7 MeV . the rest energy of each proton is 938.3 MeV . (Hint :- it is useful here to work in the frame in which the total momentum is zero . but note that here the lorentz transformation must be used to relate the velocities in the laboratory frame to those in the zero-total-momentum frame .
The answer of the book = 2494 MeV
While my solution was :-
The kinetic energy for proton equal to the rest energy for new two particles .
The kinetic energy for proton = 493.7+493.7 = 987.4 MeV
Which solution is correct ?why?
The next question is :-
Lorentz transformation for acceleration . find the lorentz transformation equation for velocity . let frame S’ have a constant x-component of velocity (u) relative to frame S . an object moves relative to frame S along the x-axis with instantaneous velocity (vx) and instantaneous acceleration (ax) . show that its instantaneous acceleration in frame S’ is
a’x = ax [(1-v2/c2)^3/2] [(1-uvx/c2)^-3]
(hint :- express the acceleration in S’ as a’x = dv’x / dt’ )
and show that the acceleration in frame S can be expressed as
ax = a’x [(1-v2/c2)^3/2] [(1+uv’x/c2)^-3]
please I want the solution be with steps and fine details .