1.375. Find how the momentum of a particle of rest mass m 0 de-
pends on its kinetic energy. Calculate the momentum of a proton
whose kinetic energy equals 5C0 MeV.
1.376. A beam of relativistic particles with kinetic energy T strikes
against an absorbing target. The beam current equals I, the charge
and rest mass of each particle are equal to e and mo respectively. Find
the pressure developed by the beam on the target surface, and the
power liberated there.
1.377. A sphere moves with a relativistic velocity v through a gas
whose unit volume contains n slowly moving particles, each of mass
m. Find the pressure p exerted by the gas on a spherical surface ele-
ment perpendicular to the velocity of the sphere, provided that the
particles scatter elastically. Show that the pressure is the same both
in the reference frame fixed to the sphere and in the reference frame
fixed to the gas.
1.378. A particle of rest mass mo starts moving at a moment t =
due to a constant force F. Find the time dependence of the particle's
velocity and of the distance covered.
1.379. A particle of rest mass mo moves along the x axis of theframe K in accordance with the law x = y a^2 c2t2, where a is
a constant, c is the velocity of light, and t is time. Find the force
acting on the particle in this reference frame.
1.380. Proceeding from the fundamental equation of relativistic
dynamics, find:
(a) under what circumstances the acceleration of a particle coin-
cides in direction with the force F acting on it;
(b) the proportionality factors relating the force F and the accele-
ration w in the cases when F.1 v and F II v, where v is the velocity
of the particle.
1.381. A relativistic particle with momentum p and total energy
E moves along the x axis of the frame K. Demonstrate that in the
frame K' moving with a constant velocity V relative to the frame K
in the positive direction of its axis x the momentum and the total
energy of the given particle are defined by the formulas:
, px—Ev/c 2 E- p,V
Px^ ,^ —^ 1/1-132^
where [3 = V/c.
1.382. The photon energy in the frame K is equal to a. Making use
of the transformation formulas cited in the foregoing problem, find
the energy a' of this photon in the frame K' moving with a velocity
V relative to the frame K in the photon's motion direction. At what
value of V is the energy of the photon equal to a' = 6/2?
1.383. Demonstrate that the quantity E 2 — p 2 c 2 for a particle is
an invariant, i.e. it has the same magnitude in all inertial reference
frames. What is the magnitude of this invariant?
1.384. A neutron with kinetic energy T = 2m 0 c 2 , where mo is its
rest mass, strikes another, stationary, neutron. Determine: