186 Aptitude Test Problems in Physics
1/(2 tan a + cot a) is 1/(2172) = 172/4 and is at-
tained at z 2 = tan a = 1/2/2. Thus, the required
minimum coefficient of friction is
min — 174 • 21.87. Since the hinge C is in equilibrium, the sum
of the forces applied to it is zero. Writing the pro-
Fig. 182jections of the forces (Fig. 182) acting on the hinge
C on the axis perpendicular to AC, we obtainmhin) g sin a = T cos cc, (1)where mhin is the mass of the hinge. Similarly,
from the equilibrium condition for the hinge D
and from the condition that the middle rod is hori-
zontal, we obtain
T cos a = F cos 13 mhing sin a.^ (2)Solving Eqs. (1) and (2) together, we find thatT cos asin a mg sin a
F,— mg sin a.co..; (^) cos 0