Aptitude Test Problems in Physics Science for Everyone by S Krotov ( PDFDrive.com )

(^164) Aptitude Test Problems in Physics
From Eqs. (1)-(3), we find the condition of motion
for the rope at the initial instant of time:
a=
1 •
1.61. It is clear that at the moment of impact, only
the extreme blocks come in contact with the wash-
er. The force acting on each such block is perpen-
dicular to the contact surface between the washer
and a block and passes through its centre (the
diameter of the washer is equal to the edge of the
block!).. Therefore, the middle block remains at
rest as a result of the impact. For the extreme
blocks and the washer, we can write the conserva-
tion law for the momentum in the direction of the
velocity v of the washer:
mu—
2mu
2
172
mv'.
Here m is the mass of each block and the washer,
v' is the velocity of the washer after the impact,
and u is the velocity of each extreme block. The
energy conservation law implies that
v 2 2u 2 v' 2.
As a result, we find that u = v 172 and v' = 0.
Consequently, the velocities of the extreme blocks
after the impact form the angles of 45° with the
velocity v, the washer stops, and the middle block
remains at rest.
1.62. In this case, the momentum conservation law
can be applied in a peculiar form. As a result of
explosion, the momentum component of the ball
along the pipe remains equal to zero since there is
no friction, and the reaction forces are directed at
right angles to the velocities of the fragments.
Inelastic collisions do not change the longitudinal
momentum component either. Consequently, the
final velocity of the body formed after all collisions
is zero.
1.63. For the liberated amount of heat to be maxi-
mum, the following conditions must be satisfied:
gh