1.139. A smooth rubber cord of length
1
whose coefficient of elas-
ticity is
k
is suspended by one end from the point
0
(Fig. L33).
The other end is fitted with a catch
B.
A small sleeve
A
of
mass m
starts falling from the point
0.
Neglecting the masses of the thread
and the catch, find the maximum elongation of the cord.
1.140.
A small bar
A
resting on a smooth horizontal plane is at-
tached by threads to a point
P
(Fig. 1.34) and, by means of a weightless
pulley, to a weight
B
possessing the same mass as the bar itself.
Fig. 1.34.
Fig. 1.35.
Besides, the bar is also attached to a point
0
by means of a light non-
deformed spring of length
1, =
50 cm and stiffness x = 5
mg/t
o
,
where m is the mass of the bar. The thread
PA
having been burned,
the bar starts moving. Find its velocity at the moment when it is
breaking off the plane.
1.141. A horizontal plane supports a plank with a bar of mass
m = 1.0 kg placed on it and attached by a light elastic non-de-
formed cord of length /
0
= 40 cm to a point
0
(Fig. 1.35). The coef-
ficient of friction between the bar and the plank equals
k =
0.20.
The plank is slowly shifted to the right until the bar starts sliding
over it. It occurs at the moment when the cord deviates from the
vertical by an angle 0 = 30°. Find the work that has been performed
by that moment by the friction force acting on the bar in the ref-
erence frame fixed to the plane.
1.142. A smooth light horizontal rod
AB
can rotate about a ver-
tical axis passing through its end
A.
The rod is fitted with a small
sleeve of mass m attached to the end A by a weightless spring of length
t
o
and stiffness x. What work must be performed to slowly get this
system going and reaching the angular velocity o?
1.143. A pulley fixed to the ceiling carries a thread with bodies of
masses m
1
and m
2
attached to its ends. The masses of the pulley and
the thread are negligible, friction is absent. Find the acceleration
we of the centre of inertia of this system.
1.144. Two interacting particles form a closed system whose centre
of inertia is at rest. Fig. 1.36 illustrates the positions of both par-
ticles at a certain moment and the trajectory of the particle of mass
Draw the trajectory of the particle of mass m
2
if m
2
= m
1
/2.
34
