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

Solutions

169

1.67*. Let us suppose that at a certain instant, the

wheel is in one of the positions such that its cen-

tre of mass is above a rod, and its velocity is v.

At the moment of the impact against the next rod

(Fig. 171), the centre of mass of the wheel has a

Fig. 171

certain velocity v' perpendicular to the line con•

netting it to the previous rod. This velocity can be

obtained from the energy conservation law:

MV 2 mv/2^

2 = 2 •

Here h = r — i/r 2 --1 2 /4 P.', 12 /(8r). Therefore,

mgh+

v' = v 1/.1+

g1 2

4rv 2 •

By hypothesis (the motion is without jumps), the

impact of the whe el against the rod is perfectly

inelastic. This means that during the impact,

the projection of the momentum of the wheel on

the straight line connecting the centre of the

wheel to the rod vanishes. Thus, during each colli-

sion, the energy

QW __m (v' sin a) 22

2