1.167. Find the increment of the kinetic energy of the closed system
comprising two spheres of masses m
l
and
m
2
due to their perfectly
inelastic collision, if the initial velocities of the spheres were equal
to v
1
and
v
2
.
1.168. A particle of mass m
1
experienced a perfectly elastic col-
lision with a stationary particle of mass m
2
. What fraction of the
kinetic energy does the striking particle lose, if
(a)
it recoils at right angles to its original motion direction;
(b)
the collision is a head-on one?
1.169. Particle 1 experiences a perfectly elastic collision with
a stationary particle
2.
Determine their mass ratio, if
(a)
after a head-on collision the particles fly apart in the opposite
directions with equal velocities;
(b)
the particles fly apart symmetrically relative to the initial
motion direction of particle
1
with the angle of divergence 0 = 60°.
1.170. A ball moving translationally collides elastically with
another, stationary, ball of the same mass. At the moment of impact
the angle between the straight line passing through the centres of
the balls and the direction of the initial motion of the striking ball
is equal to a = 45°. Assuming the balls to be smooth, find the frac-
tion ri of the kinetic energy of the striking ball that turned into poten-
tial energy at the moment of the maximum deformation.
1.171. A shell flying with velocity
v =
500 m/s bursts into three
identical fragments so that the kinetic energy of the system increases
= 1.5 times. What maximum velocity can one of the frag-
ments obtain?
1.172. Particle
1
moving with velocity v = 10 m/s experienced
a head-on collision with a stationary particle 2 of the same mass.
As a result of the collision, the kinetic energy of the system decreased
by = 1.0%. Find the magnitude and direction of the velocity
of particle
1
after the collision.
1.173. A particle of mass m having collided with a stationary
particle of mass
M
deviated by an angle n/2 whereas the particle
M
recoiled at an angle 0 = 30° to the direction of the initial motion
of the particle
tn.
How much (in per cent) and in what way has the
kinetic energy of this system changed after the collision, if
M/m
= 5.0?
1.174. A closed system consists of two particles of masses m
t
and m, which move at right angles to each other with velocities
v
1
and v
2
. Find:
(a)
the momentum of each particle and
(b)
the total kinetic energy of the two particles in the reference
frame fixed to their centre of inertia.
1.175. A particle of mass m
1
collides elastically with a stationary
particle of mass m
2
(m
i.
> m
2
). Find the maximum angle through
which the striking particle may deviate as a result of the collision.
1.176. Three identical discs
A, B,
and
C
(Fig. 1.45) rest on a smooth
horizontal plane. The disc A is set in motion with velocity
v
after
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