Solutions (^165)
(1) the potential energy of the bodies must be
maximum at the initial moment;
(2) the bodies must collide simultaneously at the
lowest point of the cup;
(3) the velocity of the bodies must be zero
immediately after the collision.
If these conditions are satisfied, the whole of the
initial potential energy of the bodies will be
transformed into heat. Consequently, at the ini-
tial instant the bodies must be arranged on the
brim of the cup at a height r above the lowest
point. The arrangement of the bodies must be such
that their total momentum before the collision is
zero (in this case, the body formed as a result of
collision from the bodies stuck together will re-
main at rest at the bottom of the cup). Since the
values of the momenta of the bodies at any instant
are to one another as 3:4:5, the arrangement of the
Fig. 167
bodies at the initial instant must be as in Fig. 167
(top view). After the bodies are left to themselves,
the amount of heat Q liberated in the system is
maximum and equal to 4mgr.
1.64. Let the proton be initially at rest relative to
a stationary reference frame, and let the a-particle
have a velocity uo. The process of their elastic
collision is described by the momentum conserva-
tion law
4mvo =-- 4mv2
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