Aptitude Test Problems in Physics Science for Everyone by S Krotov ( PDFDrive.com )

166 Aptitude Test Problems in Physics

and by the energy conservation law

4mvt,my! 2 -4_^ 4mq,

2 ' 2 '

where v 1 and v 2 are the velocities of the proton and
the a-particle in the stationary reference frame
after the collision, and in and 4m are the masses
of the proton and the a-particle respectively.
Let us consider the collision of these particles
in the centre-of-mass system, i.e. in an inertial
reference frame moving relative to the stationary
reference frame at a velocity

4mvo 4

+

v' vo
4m 5
(the numerator of the first fraction contains the
total momentum of the system, and the denomina-
tor contains its total mass). Figure 168 shows the

oo

O

'2

2/

Al-- —

U~Svo

Fig. 168

velocity vo and the velocities of the a-particle

(vector OB) and the proton (vector OA) in the cen-

tre-of-mass system before the collision: OB

(1/5)vo and OA = (4/5)vo. According to the mo-

mentum conservation law, after the collision, the

velocity vectors OB and OA of the a-particle and

the proton must lie on the same straight line, and

the relation OB':OA' = 1:4 (see Fig. 168) must

be satisfied. According to the energy conservation

law, OB' = OB and OA' OA (prove this!).