Solutions (^159)
tween two successive collisions with the box (every
time the centre of the washer covers a distance
D — 2r at a velocity v).
Returning to the reference frame fixed to the
ground, we can plot the time dependence vwash (t)
of the velocity of the centre of the washer. Know-
ing the velocity graph vwash (t), we can easily
plot the time dependence of the displacement
wash (t) of the centre of the washer (Fig. 162).
L,,vash A
v E -2r D-2r ,
'wash A
t = - il -2r
1
z`i 2t 1 3t,^ 4ti^ 5t, t
Fig. 162
1.57. The forces acting on the hoop-washer system
are the force of gravity and the normal reaction of
the plane. These forces are directed along the ver-
tical. Consequently, the centre of mass of the
system does not move in the horizontal direction.
Since there is no friction between the hoop and
the plane, the motion of the hoop is translatory.
According to the momentum conservation law, at
any instant of time we have
Mu mvx = 0, (1)
where u and vx are the horizontal components of
the velocities of the centre of the hoop and the wash-
er. Since vx periodically changes its sign, u also
changes sign "synchronously". The general nature
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