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

160 Aptitude Test Problems in Physics

of motion of the hoop is as follows: the centre of
the hoop moves to the right when the washer is on
segments BC and BE, and to the left when the
washer is on segments CD and DE (Fig. 163).

Fig. 163

The velocities v of the washer and u of the hoop

are connected through the energy conservation law:

q))

2

mgr (1+ cos q)

)mv , Mu2

(2)

2 2

The motion of the washer relative to a station-

ary observer can be represented at any instant as

the superposition of two motions: the motion rela-

tive to the centre of the hoop at a velocity vt di-

rected along the tangent to the hoop, and the mo-

tion together with the hoop at its velocity u having

the horizontal direction (Fig. 164). The figure shows

that

vx+ vy

Solving Eqs. (1)-(3) together, we determine the

velocity of the centre of the hoop at the instant

when the radius vector of the point of location of

the washer forms an angle q with the vertical

2gr (14-cos cp)

u=m cos 4. u ± (s1 m sin

vp

— tan cp. ( 3 )