Irodov – Problems in General Physics

1.145. A closed chain A of mass m = 0.36 kg is attached to a ver-

tical rotating shaft by means of a thread (Fig. 1.37), and rotates with

a constant angular velocity co = 35 rad/s. The thread forms an angle

0 = 45° with the vertical. Find the distance between the chain's

centre of gravity and the rotation axis, and the tension

of the thread.

1.146. A round cone A of mass m = 3.2 kg and half-

angle a = 10° rolls uniformly and without slipping

along a round conical surface B so that its apex 0 re-

mains stationary (Fig. 1.38). The centre of gravity of

the cone A is at the same level as the point 0 and at a

distance 1 = 17 cm from it. The cone's axis moves

with angular velocity w. Find:

(a) the static friction force acting on the cone A, Fig. 1.36.

if co = 1.0 rad/s;

(b) at what values of co the cone A will roll without

sliding, if the coefficient of friction between the surfaces is equal

to k = 0.25.

1.147. In the reference frame K two particles travel along the x

axis, one of mass m 1 with velocity v (^1) , and the other of mass m 2 with
velocity v 2. Find:
(a) the velocity V of the reference frame K' in which the cumulative
kinetic energy of these particles is minimum;
(b) the cumulative kinetic energy of these particles in the K'
frame.
1.148. The reference frame, in which the centre of inertia of a given
system of particles is at rest, translates with a velocity V relative

Bj

I

Fig. 1.37. Fig. 1.38.

to an inertial reference frame K. The mass of the system of particles

equals m, and the total energy of the system in the frame of the centre

of inertia is equal to E. Find the total energy E of this system of
particles in the reference frame K.
1.149. Two small discs of masses m 1 and m 2 interconnected by a
weightless spring rest on a smooth horizontal plane. The discs are
set in motion with initial velocities v 1 and v 2 whose directions are

3*