Bukhovtsev-et-al-Problems-in-Elementary-Physics

MECHANICS 49
the rod. Find the distance I from point 0 at which the bead
will be in equilibrium if the coefficient of friction between the
bead and the rod is k.
198. A weight with a mass m is attached to the end of
a string with a length I fastened to a vertical rod rotating
with an angular velocity ID. Another string of the same length
as the first and carrying on its end another weight with a mass
m is secured to the first weight.
Prove that during rotation the angle between the first string
and the vertical will be smaller than the angle between the
vertical and the second string. Disregard the weight of the
string.
199. A weightless rod carries two weights of mass m and JW.
The rod is hinge-jointed to vertical axis 00' (Fig. 81), which
rotates with an angular velocity ID. Determine the angle cp formed
by the rod and the vertical.
200. A horizontal straight bar rotates with a constant angular
velocity around a vertical axis. A body can move without friction
over the bar. Initially, the body is retained in equilibrium by
a spring (Fig. 82). What will happen to the body if an initial
velocity is imparted to it along the bar? The length of the spring
in an unstretehed state can be neglected. .
201. A metallic chain with a length of 1=62.8 em and whose
ends are joined together is fitted onto a wooden disk (Fig. 83).
The disk rotates with a speed of n = 60 rps. Find the tension
of the chain T if its mass is m = 40 g.
202. Water flows with a velocity v along a rubber tube having
the form of a ring (Fig. 84). The radius of the ring is Rand
the diameter of the tube d~R. What force is the rubber tube
stretched with?
203. A homogeneous rod with a length I and a mass m rotates
with an angular velocity (J) in a horizontal plane around an axis
passing through its end. Find the tension of the rod at a distance x
from its axis of rotation.
204. A ball with the mass m secured on a weightless rod rotates
with a constant velocity v in a horizontal plane (Fig. 85).
Its kinetic energy in a coordinate system that is stationary with
respect to the axis of rotation is constant and equal to mv'/2.
The kinetic energy changes with time from zero to 4mv"/2 with
respect to a reading system that moves rectilinearly in a horizontal
plane with a velocity v relative to the axis. What is the
reasIn for this change in the energy?
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