Solutions
137whence the angle of rotation of the carriage about
the centre of the circle is cp = vt 3 /R ----- 6.28
2n rad, i.e. the carriage describes a complete
circumference.
On the last segment, the carriage brakes and
comes to a halt since the acceleration along the
carriage is equal to the initial acceleration and
acts during the same time interval. Therefore,
84 = sl = 60 m. The carriage stops at a distance
a = 28 1 + 8 2 = 210 m in front of the initial po-
sition (Fig. 146).
1.35. Let the hinge be displaced downwards by a
small distance Ax as a result of application of
the force F, and let the rods be elongated by Al
Fig. 147(Fig. 147). Then the rigidity k of the system of
rods can be determined from the equation k Ax =
2k 0 Al cos a', where 2a' is the angle between the
rods after the displacement. Since the displace-
ment is smalla' z a, Al 741 Ax cos a,,
and hence k x 2ko cosy a.
1.36. Let us first suppose that the air drag is ab-
sent. Then the balls will meet if the vertical com-
ponent of the initial velocity of the second ball is
equal to that of the first ball:
= v^2 sin a,