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

132 Aptitude Test Problems in Physics

where

2cooi/TV2g)

In the second case (after the jerk), the motion
can be regarded as if the sledge stuck in the sand
had a velocity v 1 > vo and having traversed the
distance xo were decelerated to the velocity vo
(starting from this moment, the second case is
observed). The motion of the sledge after the jerk
can be represented as a part of the total vibratory
motion according to the law

x (t) = x 1 sin coot, v (t) = v 1 cos coot

starting from the instant t 2 when the velocity of

the sledge becomes equal to vo. As before, x 1 =

v 1 /coo. Besides,

mg 2 MV? MV:

2/ Px° 2 2

whence

The

jerk is

v1 = xocoo^ l/2.

distance covered by the sledge after the

x1—xo =

coo coo coo

Consequently, the ratio of the braking lengths is

Xi — Xo =

y2-1.

xo

In order to determine the time of motion of the

sledge after the jerk, we must find the time of mo-

tion of the sledge from point xo to point x 1 by

xo , 17-- m rt.

V0 k^ g

coo

It can easily be seen that the time before the sledge
comes to rest is equal to quarter the "period of vi-
brations". Therefore,

31/2

V1

vo

1

(v1— v0) = X0 (17-2 -.