(^172) F
Fig. 1.41.
mutually perpendicular and lie in a horizontal plane. Find the total
energy of this system in the frame of the centre of inertia.
1.150. A system consists of two small spheres of masses ml and m 2
interconnected by a weightless spring. At the moment t = 0 the
spheres are set in motion with the initial velocities v 1 and v 2 after
which the system starts moving in the Earth's uniform gravitational
field. Neglecting the air drag, find the time dependence of the total
momentum of this system in the process of motion and of the radius
vector of its centre of inertia relative to the initial position of the
centre.
1.151. Two bars of masses ml and m 2 connected by a weightless
spring of stiffness x (Fig. 1.39) rest on a smooth horizontal plane.
Fig. 1.39.^ Fig. 1.40.
Bar 2 is shifted a small distance x to the left and then released. Find
the velocity of the centre of inertia of the system after bar 1 breaks
off the wall.
1.152. Two bars connected by a weightless spring of stiffness x
and length (in the non-deformed state) / 0 rest on a horizontal plane.
A constant horizontal force F starts acting on one of the bars as shown
in Fig. 1.40. Find the maximum and minimum distances between the
bars during the subsequent motion of the system, if the masses of
the bars are:
(a) equal;
(b) equal to ml and m^2 , and the force F is applied to the bar of
mass m 2.
1.153. A system consists of two identical cubes, each of mass 7n,
linked together by the compressed weightless spring of stiffness x
(Fig. 1.41). The cubes are also connected by a thread
which is burned through at a certain moment. Find:
(a) at what values of Al, the initial compression
of the spring, the lower cube will bounce up after
the thread has been burned through:
(b) to what height h the centre of gravity of this
system will rise if the initial compression of the spring
Al = 7 mg/x.
1.154. Two identical buggies 1 and 2 with one man
in each move without friction due to inertia along
the parallel rails toward each other. When the buggies get opposite
each other, the men exchange their places by jumping in the direc-
tion perpendicular to the motion direction. As a consequence, buggy
joyce
(Joyce)
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