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

(^170) Aptitude Test Problems in Physics
where sin a Pe, l/r, is lost (converted into heat).
For the velocity v to remain constant, the work
done by the tension T of the rope over the path^1
must compensate for this energy loss. Therefore,
mv 2 g/ 2 / 2
2 k 4rv 2 / r 2 '
whence
mv2l (
1+
gl 2 mv 21
T =
2r 2 4rv 2 2r 2 •
1.68. Since the wheels move without slipping, the
axle of the coupled wheels rotates about point 0
while passing through the boundary between the
Fig. 172
planes (Fig. 172). At the moment of separation,
the force of pressure of the coupled wheels on the
plane and the force of friction are equal to zero,
and hence the angle 13 at which the separation
takes place can be found from the condition
my,^2
mg cos 13=
r '
From the energy conservation law, we obtain
Ti —
mv (^2) mu
—mgr (1— cos t3).