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

Solutions 187

Thus, the minimum force Fmk' for which the middle

rod retains its horizontal position is

Foil,. mg sin a = 2

mg

and directed at right angles to the rod BD.

1.88. By hypothesis, the coefficient of sliding fric-

tion between the pencil and the inclined plane

satisfies the condition Et ..>„ tan a. Indeed, the pen-

cil put at right angles to the generatrix is in equi-

librium, which means that mg sin a = Fir, where

mg is the force of gravity, and Fir is the force of

friction. But Fir < ping cos a. Consequently,

mg sin a < p.mg cos a, whence Ft tan a.

Thus, the pencil will not slide down the inclined

plane for any value of the angle cp.

The pencil may start rolling down at an angle

yo such that the vector of the force of gravity

Fig. 183

"leaves" the region of contact between the pencil and
the inclined plane (hatched region in Fig. 183).
In order to find this angle, we project the centre of
mass of the pencil (point A) on the inclined plane
and mark the point of intersection of the vertical
passing through the centre of mass and the in-
clined plane (point B). Obviously, points A and B
will be at rest for different orientations of the pen-
cil if its centre of mass remains stationary. In this