Irodov – Problems in General Physics

(a) the combined kinetic energy T of both neutrons in the frame
of their centre of inertia and the momentum of 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 2 c 2 remaining con-
stant on transition from one inertial reference frame to another (E
is the total energy of the system, p is its composite momentum).
1.385. A particle of rest mass mo with kinetic energy T strikes a
stationary particle of the same rest mass. Find the rest mass and the
velocity of the compound particle formed as a result of the collision.
1.386. How high must be the kinetic energy of a proton striking
another, stationary, proton for their combined kinetic energy in the
frame of the centre of inertia to be equal to the total kinetic energy
of two protons moving toward each other with individual kinetic
energies T = 25.0 GeV?
1.387. A stationary particle of rest mass mo disintegrates into three
particles with rest masses m 1 , m 2 , and m 3. Find the maximum total
energy that, for example, the particle m 1 may possess.
1.388. A relativistic rocket emits a gas jet with non-relativistic
velocity u constant relative to the rocket. Find how the velocity v
of the rocket depends on its rest mass m if the initial rest mass of
the rocket equals mo.