السلام عليكم .........
عندي سؤال في النسبية من كتاب (university physics) موجود جوابه في نهاية الكتاب . و لم يطابق هذا الجواب جوابي الذي حصلت عليه من حلي للمسئلة .
و السؤال هو :-
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 .
و كان جواب الكتاب هو 2494 MeV
اما حلي فهو :-
ان الطاقة الحركية للبروتون سوف تساوي طاقة الوضع للجسيمين الجديدين .
اي ان الطاقة الحركية للبروتون = 493.7 + 493.7 = 987.4MeV
فأي حل هو الصحيح و لماذا؟
و من فضلكم عندي سؤال اخر على النسبية ايضا و لا اعرف كيف يحل و هو كالتالي :-
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]
ارجوا ان يكون الحل مع الخطوات والتفاصيل الدقيقة .
و شكرا..........
