Fig. 1.27.Find the distance traversed by the body during the first t seconds after
the force action began.
1.104. A body of mass m is thrown straight up with velocity vo.
Find the velocity v' with which the body comes down if the air drag
equals kv 2 , where k is a constant and v is the velocity of the body.
1.105. A particle of mass m moves
in a certain plane P due to a force
F whose magnitude is constant and
whose vector rotates in that plane with
a constant angular velocity co. Assum-
ing the particle to be stationary at
the moment t = 0, find:
(a) its velocity as a function of
time;
(b) the distance covered by the
particle between two successive stops,
and the mean velocity over this time.
1.106. A small disc A is placed on an inclined plane forming an
angle a with the horizontal (Fig. 1.27) and is imparted an initial
velocity v 0. Find how the velocity of the disc depends on the angle y
if the friction coefficient k = tan a and at the initial moment yo =
= nI2.
1.107. A chain of length 1 is placed on a smooth spherical surface
of radius R with one of its ends fixed at the top of the sphere. What
will be the acceleration w of each element of the chain when its upper
end is released? It is assumed that the length of the chain 1<-- 1 2. nR.
1.108. A small body is placed on the top of a smooth sphere of
radius R. Then the sphere is imparted a constant acceleration wo^
in the horizontal direction and the body begins sliding down. Find:
(a) the velocity of the body relative to the sphere at the moment of
break-off;
(b) the angle 0 0 between the vertical and the radius vector drawn
from the centre of the sphere to the break-off point; calculate 0 0
for w 0 = g.
1.109. A particle moves in a plane under the action of a force
which is always perpendicular to the particle's velocity and depends
on a distance to a certain point on the plane as 1/rn, where n is a
constant. At what value of n will the motion of the particle along
the circle be steady?
1.110. A sleeve A can slide freely along a smooth rod bent in the
shape of a half-circle of radius R (Fig. 1.28). The system is set in rota-
tion with a constant angular velocity co about a vertical axis 00'.
Find the angle 0 corresponding to the steady position of the sleeve.
1.111. A rifle was aimed at the vertical line on the target located
precisely in the northern direction, and then fired. Assuming the air
drag to be negligible, find how much off the line, and in what direc-
tion, will the bullet hit the target. The shot was fired in the horizontal