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

168 Aptitude Test Problems in Physics

to remain in contact with the surface of the pipe

the condition N = mv 2 ir — mg' cos 13 ,>.- 0 must

be fulfilled, whence

v 2 .>- g'r cos O. (2)

The relation between the velocity v at which

the body moves in a circle at a given instant and

Fig. 169 Fig. 170

the initial velocity vo can be obtained from the

energy conservation law: for any value of the

angle 8, the following relation must hold:

mv 2 m (vo sin 0 2

+ mg'r cos 8 — -Fmg'r,

(^2 2)
whence
v 2 = vl sin (^2) q -1- 2g'r — 2g'r cos 0. (^) ( (^3) )
Substituting Eq. (3) into Eq. (2), we obtain the
values of vo for which the body remains in contact
with the pipe:
3g'r cos 8 2g'r
U°

--- sin2 ip
sing q)
Since this condition must be satisfied for any value
of 13 E [0, 2n], we finally obtain
g'rgr cos a
v 2 > ---=
sin 2 q:, sing cp '