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LoginA neutron with kinetic energy T=2m_0c^2, where m_0 is its rest mass, strikes another, stationary, neutron. Determine:
(a) the combined kinetic energy overset~T of both neutrons in the frame of their centre of inertia and the momentum overset~p of each neutron in that frame,
(b) the velocity of the centre of inertia of this system of particles.
Instruction. Make use of the invariant E^2-p^2c^2 remaining constant on transition from one inertial reference frame to another (E is the total energy of the system, p is its composite momentum).
Class 12 Physics in Class 12 3 years ago
`V/c=(cp_(1x))/(E_1+E_2)=(sqrt(T(T+2m_0c^2)))/(T+2m_0c^2)=sqrt((T)/(T+2m_0c^2))`
where we have used the result of problem
Then
`(1)/(sqrt(1-V^2//c^2))=(1)/(sqrt(1-(T)/(T+2m_0c^2)))=sqrt((T+2m_0c^2)/(2m_0c^2))`
Total ENERGY in the CM frame is
`(2m_0c^2)/(sqrt(1-V^2//c^2))=2m_0c^2sqrt((T+2m_0c^2)/(2m_0c^2))=sqrt(2m_0c^2(T+2m_0c^2))=overset~T+2m_0c^2`
So `overset~T=2m_0c^2(sqrt(1+(T)/(2m_0c^2))-1)`
Also `2sqrt(c^2overset~p^2+m_0^2c^4)=sqrt(2m_0c^2(T+2m_0c^2)), 4c^2overset~p^2=2m_0c^2T`, or `overset~p=sqrt(1/2m_0T)`
Posted on 11 Dec 2021, this text provides information on Class 12 related to Physics in Class 12. Please note that while accuracy is prioritized, the data presented might not be entirely correct or up-to-date. This information is offered for general knowledge and informational purposes only, and should not be considered as a substitute for professional advice.
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